Source: https://www.usitc.gov/publications/332/working_papers/ecwp-2017-07-a-07-13-17_revision3_0.htm
Timestamp: 2019-07-17 10:17:43
Document Index: 601983209

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﻿ The Effects of Tariffs on Employment in Global Value Chains
THE EFFECTS OF TARIFFS ON EMPLOYMENT
Working Paper 2017-07-A
The authors are grateful to Dan Kim and James Stamps for helpful comments and suggestions.
The Effects of Tariffs on Employment in Global Value Chains
Office of Economics Working Paper 2017-07-A
We develop a two-country model of international trade and domestic employment in an industry with firm heterogeneity and global value chains. The model can be used to simulate the changes in trade and employment that would result from a tariff or other barrier to trade that increases the price of imports. We also identify the data that is needed to apply the model to a specific industry. As an example application, we use the model to simulate the effects of a hypothetical import barrier that raises the price of imports by 10 percent. We find that the import barrier would have a positive effect on domestic employment in the part of the industry that sells final products in the domestic market because it limits import competition. On the other hand, the import barrier would have a negative effect on employment in the part of the domestic industry that exports intermediate products for further manufacture before returning to the domestic market. The net effect on domestic employment – MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaqefeKCPfgBaG qbaKqzGfaeaaaaaaaaa8qacaWFtacaaa@39A6@ whether it increases or decreases – MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaqefeKCPfgBaG qbaKqzGfaeaaaaaaaaa8qacaWFtacaaa@39A6@ depends on many economic attributes of the industry, including its pattern of global value chains.
Keywords: global value, chains, global supply chains, offshoring, employment, international trade
JEL Codes: F16, F12, F23
Several manufacturing industries are well-known for their global value chains, including the motor vehicles, textiles and apparel, and electronics industries. In these industries, it is possible to split the production process into different stages and locate these production stages in different countries. Generally, the more technically advanced and capital-intensive production processes are located in advanced countries, while the more labor-intensive production processes and assembly are located in lower wage, developing countries. This pattern of linked, multinational production is often called offshoring.
In this paper, we analyze how tariffs or other barriers to the imports of an advanced country like the United States can interrupt these back-and-forth trade flows and thus affect employment within the global value chains. First and foremost, a tariff on the imports of the advanced country will have a positive effect on domestic employment in the import-competing part of the industry that sells the final product, because the tariff limits import competition. This positive effect on domestic employment provides the traditional motivation for protecting domestic industries by restricting imports. On the other hand, the tariff will also have a negative effect on domestic employment in the part of the industry that exports intermediate products. Since the demand for the advanced country’s exports of intermediate products is linked to the country’s demand for imports of further processed versions of these products, a barrier to one link in the supply chain can have a ripple effect throughout the chain. However, is this second effect large enough to offset the traditional positive employment effects of protecting a domestic industry?
To address this question, we developed a theoretical model of trade in intermediate and final products with firm heterogeneity and global value chains. We show how the model can be used to estimate the change in industry employment that would result from a barrier to imports of the final product into the market of the advanced country.[1]
Then we identify the data that are needed to apply the model to a specific industry. The goal of our analysis is to highlight the attributes of the industry’s global value chain that are determinants of the magnitude, and even the direction, of the changes in industry employment in the advanced country. These data inputs include the share of domestic shipments that are competing with imports, the share of exports that return to the advanced country rather than serving foreign markets, and the substitutability between domestic and foreign products in the domestic market.
Our paper contributes to the economics literature that models the effects of global value chains and trade in intermediate goods (sometimes called offshoring) on labor markets. Our paper incorporates recent theoretical innovations in this area. Grossman and Rossi-Hansberg (2008) develop a theoretical model of international trade in tasks. Firms are able to split their production process into a continuum of distinct tasks and then decide where to locate each task, based on costs of trade and costs of multinational production. Grossman and Rossi-Hansberg use their model to predict how changes in trade costs affect the feasibility of offshoring and the wages of workers at different skill levels in different countries. They find that increased offshoring can lead to productivity benefits and higher labor demand in the Home country, especially less skilled workers.[2] Feenstra (2008, 2016) provides excellent summaries of this theoretical literature.[3] In addition, the analysis of multinational production in Helpman, Melitz, and Yeaple (2004) provides modeling structure that we are able to incorporate in our paper, though Helpman, Melitz, and Yeaple focus on foreign affiliates placed for proximity to the foreign market (horizontal FDI), while our model focuses on global value chains (vertical FDI).
The rest of our paper is organized into four parts. Section 2 presents the structure and assumptions of our modeling framework. Section 3 estimates the net employment effects for a wide range of potential data inputs. Section 4 discusses the data needed to apply the model to a specific industry. Section 5 offers concluding remarks.
We have developed a modeling framework for estimating the changes in domestic employment if a tariff or other barrier were imposed on imports. The framework is based on the models of trade with firm heterogeneity in Melitz (2003) and Helpman, Melitz, and Yeaple (2004) and the model of offshoring in Grossman and Rossi-Hansberg (2008). In this section, we describe the assumptions of our model and the equations that characterize the market equilibrium. Then we derive how trade flows and industry employment would change in response to an increase in barriers to imports.
2.1 General Setup of the Model
The model focuses on a vertically integrated manufacturing industry. Firms in the industry produce differentiated final products. Labor is the only factor of production in the model, and producers vary in their unit labor requirements. The model includes two regions, Home and Foreign, indicated by subscripts H MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr 0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaabaaaaaaaaape Gaamisaaaa@36D9@ and F MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr 0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaabaaaaaaaaape GaamOraaaa@36D7@ . These two regions are distinct consumer markets and also potential production sites. There are two stages of production in the model, manufacturing of intermediate products and then manufacturing of the final products. The final products are then consumed by households in each region. Each firm chooses the location of each stage of its production process and the location of its final market based on relative production and trade costs.[4]
In the model, the two potential regions for intermediate production, final production, and consumption define eight possible supply chains. We refer to each supply chain by a three-letter label, with the first letter indicating the location of intermediate production, the second the location of final production, and the third the location of consumption. However, some of these supply chains may not exist in particular industries. For example, we assume that FHH and FHF are not profitable alternatives in the industry. This would be the case, for example, if it were not cost effective to locate final production in Home unless the entire vertically integrated production process and the consumer are in Home. In this case, imports to Home are all final products and most exports from Home to Foreign are intermediate products. Based on this assumption, we omit the FHH and FHF supply chains from our model, leaving the six relevant supply chains in Figure 1.
Figure 1: Six Different Supply Chains
A new barrier to Home imports would impede the last link in the FFH and HFH supply chains. The reduction in HFH imports would reduce the demand for intermediate exports from Home. The reductions in FFH and HFH imports would increase the demand for domestic shipments (the HHH supply chain).[5]
We assume that there are n H MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr 0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaabaaaaaaaaape GaamOBa8aadaWgaaWcbaWdbiaadIeaa8aabeaaaaa@3826@ potential Home producers and n F MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr 0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaabaaaaaaaaape GaamOBa8aadaWgaaWcbaWdbiaadAeaa8aabeaaaaa@3824@ potential Foreign producers in the industry. Each firm produces a single variety of the good.[6] We assume that consumers have CES preferences between the varieties within the industry, and a unit elastic demand for the products of the industry in aggregate. The parameter σ MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr 0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaabaaaaaaaaape Gaeq4Wdmhaaa@37CF@ is the elasticity of substitution between the different varieties. The firms that produce the differentiated varieties engage in monopolistic competition.
The costs of supplying each national market depend on the location of production. The unit labor requirement of each producer, a MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr 0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaabaaaaaaaaape Gaamyyaaaa@36F2@ , is drawn from a Pareto distribution with cumulative distribution function G( a ) MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr 0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaabaaaaaaaaape Gaam4ramaabmaapaqaa8qacaWGHbaacaGLOaGaayzkaaaaaa@3966@ , following Helpman, Melitz, and Yeaple (2004). In addition to the variable costs of production, there are variable costs of importing into Home and Foreign, represented by the gross trade cost factors τ H MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr 0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaabaaaaaaaaape GaeqiXdq3damaaBaaaleaapeGaamisaaWdaeqaaaaa@38F8@ and τ F MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr 0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaabaaaaaaaaape GaeqiXdq3damaaBaaaleaapeGaamOraaWdaeqaaaaa@38F6@ .[7] The trade cost factors could include tariffs and non-tariff measures as well as international transport costs. There are also fixed costs of establishing production in each region and fixed costs of trading intermediate and final products. The total fixed costs for each of the supply chains, summing all of the fixed cost components, are represented by C HHH MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr 0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaabaaaaaaaaape Gaam4qa8aadaWgaaWcbaWdbiaadIeacaWGibGaamisaaWdaeqaaaaa @3995@ , C FFH MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr 0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaabaaaaaaaaape Gaam4qa8aadaWgaaWcbaWdbiaadAeacaWGgbGaamisaaWdaeqaaaaa @3991@ , C HFH MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr 0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaabaaaaaaaaape Gaam4qa8aadaWgaaWcbaWdbiaadIeacaWGgbGaamisaaWdaeqaaaaa @3993@ , C FFF MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr 0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaabaaaaaaaaape Gaam4qa8aadaWgaaWcbaWdbiaadAeacaWGgbGaamOraaWdaeqaaaaa @398F@ , C HFF MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr 0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaabaaaaaaaaape Gaam4qa8aadaWgaaWcbaWdbiaadIeacaWGgbGaamOraaWdaeqaaaaa @3991@ , and C HHF MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr 0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaabaaaaaaaaape Gaam4qa8aadaWgaaWcbaWdbiaadIeacaWGibGaamOraaWdaeqaaaaa @3993@ . For example, C HFH MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr 0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaabaaaaaaaaape Gaam4qa8aadaWgaaWcbaWdbiaadIeacaWGgbGaamisaaWdaeqaaaaa @3993@ includes the fixed costs of producing the intermediate products in Home, the fixed costs of exporting the intermediate products to Foreign, the fixed costs of final production in Foreign, and finally the fixed costs of exporting the final products to Home. We assume that the fixed costs and the variable trade costs use a combination of materials and labor from outside of the industry and non-production workers within the industry, but do not employ production workers within the industry.[8]
Production requires labor inputs in multiple stages. We simplify the model by only including two stages of production that are combined in fixed proportions.[9] Equation (1) represents the marginal cost of locating intermediate production in region i MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr 0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaabaaaaaaaaape GaamyAaaaa@36FA@ and final production in region j MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr 0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaabaaaaaaaaape GaamOAaaaa@36FB@ for a firm with unit labor requirement a MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr 0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaabaaaaaaaaape Gaamyyaaaa@36F2@ in the first stage of production and unit labor requirement λa MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr 0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaabaaaaaaaaape Gaeq4UdWMaamyyaaaa@38A6@ in the second stage, and then delivering the final product to region k MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr 0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaabaaaaaaaaape Gaam4Aaaaa@36FC@ .
m c ijk ( a )=( w i τ j +λ w j ) τ k a MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr 0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaabaaaaaaaaape GaamyBaiaadogapaWaaSbaaSqaa8qacaWGPbGaamOAaiaadUgaa8aa beaak8qadaqadaWdaeaapeGaamyyaaGaayjkaiaawMcaaiabg2da9m aabmaapaqaa8qacaWG3bWdamaaBaaaleaapeGaamyAaaWdaeqaaOWd biaacckacqaHepaDpaWaaSbaaSqaa8qacaWGQbaapaqabaGcpeGaey 4kaSIaeq4UdWMaaiiOaiaadEhapaWaaSbaaSqaa8qacaWGQbaapaqa baaak8qacaGLOaGaayzkaaGaaiiOaiabes8a09aadaWgaaWcbaWdbi aadUgaa8aabeaak8qacaGGGcGaamyyaaaa@537D@ (1)
The variables w i MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr 0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaabaaaaaaaaape Gaam4Da8aadaWgaaWcbaWdbiaadMgaa8aabeaaaaa@3850@ and w j MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr 0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaabaaaaaaaaape Gaam4Da8aadaWgaaWcbaWdbiaadQgaa8aabeaaaaa@3851@ are the wage rates in the two regions. Equation (2) represents the demand for this MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr 0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaabaaaaaaaaape GaaiiOaaaa@3730@ product in region k MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr 0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaabaaaaaaaaape Gaam4Aaaaa@36FC@ .
q ijk ( a )=ϕ E k P k ( p ijk ( a ) P k ) −σ MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr 0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaabaaaaaaaaape GaamyCa8aadaWgaaWcbaWdbiaadMgacaWGQbGaam4AaaWdaeqaaOWd bmaabmaapaqaa8qacaWGHbaacaGLOaGaayzkaaGaeyypa0Jaeqy1dy MaaiiOamaalaaapaqaa8qacaWGfbWdamaaBaaaleaapeGaam4AaaWd aeqaaaGcbaWdbiaadcfapaWaaSbaaSqaa8qacaWGRbaapaqabaaaaO WdbiaacckadaqadaWdaeaapeWaaSaaa8aabaWdbiaadchapaWaaSba aSqaa8qacaWGPbGaamOAaiaadUgaa8aabeaak8qadaqadaWdaeaape GaamyyaaGaayjkaiaawMcaaaWdaeaapeGaamiua8aadaWgaaWcbaWd biaadUgaa8aabeaaaaaak8qacaGLOaGaayzkaaWdamaaCaaaleqaba WdbiabgkHiTiabeo8aZbaaaaa@546C@ (2)
The variable E H MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr 0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaabaaaaaaaaape Gaamyra8aadaWgaaWcbaWdbiaadIeaa8aabeaaaaa@37FD@ represents the aggregate expenditure level in Home, P H MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr 0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaabaaaaaaaaape Gaamiua8aadaWgaaWcbaWdbiaadIeaa8aabeaaaaa@3808@ is the CES price index for the industry in Home, and ϕ MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr 0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaabaaaaaaaaape Gaeqy1dygaaa@37D4@ is the expenditure share on the products of the industry. The model assumes that the industry or sector receives a constant share of aggregate expenditures, corresponding to Cobb-Douglas preferences across the products of the different sectors of the economy. This is a common assumption in multi-sector models of international trade. It implies that the price elasticity of the composite product of the industry is equal to minus one.
The firms in the industry set prices to maximize profits, taking the industry price index as given. The CES demand and monopolistic competition imply the constant mark-up pricing in equation (3).
p ijk ( a )= σ σ−1 m c ijk ( a ) MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr 0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaabaaaaaaaaape GaamiCa8aadaWgaaWcbaWdbiaadMgacaWGQbGaam4AaaWdaeqaaOWd bmaabmaapaqaa8qacaWGHbaacaGLOaGaayzkaaGaeyypa0ZaaSaaa8 aabaWdbiabeo8aZbWdaeaapeGaeq4WdmNaeyOeI0IaaGymaaaacaGG GcGaamyBaiaadogapaWaaSbaaSqaa8qacaWGPbGaamOAaiaadUgaa8 aabeaak8qadaqadaWdaeaapeGaamyyaaGaayjkaiaawMcaaaaa@4C1F@ (3)
2.3 Firm Revenue and Profits
Similar to costs, firms have different revenues and profits depending on which supply chain they use. Equation (4) represents the revenue in the Home market of a domestic firm with unit labor requirement a MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr 0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaabaaaaaaaaape Gaamyyaaaa@36F2@ and completely domestic production (an HHH supply chain), and equation (5) represents the firm’s profits from this revenue stream.
R HHH ( a )=ϕ E H P H σ−1 ( σ σ−1 w H ( 1+λ ) a ) 1−σ MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr 0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaabaaaaaaaaape GaamOua8aadaWgaaWcbaWdbiaadIeacaWGibGaamisaaWdaeqaaOWd bmaabmaapaqaa8qacaWGHbaacaGLOaGaayzkaaGaeyypa0Jaeqy1dy MaaiiOaiaadweapaWaaSbaaSqaa8qacaWGibaapaqabaGcpeGaaiiO aiaadcfapaWaaSbaaSqaa8qacaWGibaapaqabaGcdaahaaWcbeqaa8 qacqaHdpWCcqGHsislcaaIXaaaaOWaaeWaa8aabaWdbmaalaaapaqa a8qacqaHdpWCa8aabaWdbiabeo8aZjabgkHiTiaaigdaaaGaam4Da8 aadaWgaaWcbaWdbiaadIeaa8aabeaak8qacaGGGcWaaeWaa8aabaWd biaaigdacqGHRaWkcqaH7oaBaiaawIcacaGLPaaacaGGGcGaamyyaa GaayjkaiaawMcaa8aadaahaaWcbeqaa8qacaaIXaGaeyOeI0Iaeq4W dmhaaaaa@5E64@ (4)
π HHH ( a )= 1 σ ϕ E H P H σ−1 ( σ σ−1 w H ( 1+λ ) a ) 1−σ − C HHH MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr 0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaabaaaaaaaaape GaeqiWda3damaaBaaaleaapeGaamisaiaadIeacaWGibaapaqabaGc peWaaeWaa8aabaWdbiaadggaaiaawIcacaGLPaaacqGH9aqpdaWcaa WdaeaapeGaaGymaaWdaeaapeGaeq4Wdmhaaiabew9aMjaacckacaWG fbWdamaaBaaaleaapeGaamisaaWdaeqaaOWdbiaacckacaWGqbWdam aaBaaaleaapeGaamisaaWdaeqaaOWaaWbaaSqabeaapeGaeq4WdmNa eyOeI0IaaGymaaaakmaabmaapaqaa8qadaWcaaWdaeaapeGaeq4Wdm hapaqaa8qacqaHdpWCcqGHsislcaaIXaaaaiaadEhapaWaaSbaaSqa a8qacaWGibaapaqabaGcpeGaaiiOamaabmaapaqaa8qacaaIXaGaey 4kaSIaeq4UdWgacaGLOaGaayzkaaGaaiiOaiaadggaaiaawIcacaGL PaaapaWaaWbaaSqabeaapeGaaGymaiabgkHiTiabeo8aZbaakiabgk HiTiaadoeapaWaaSbaaSqaa8qacaWGibGaamisaiaadIeaa8aabeaa aaa@6696@ (5)
Equations (6) through (10) are the profits associated with the other five supply chains in Figure 1.
π HFH ( a )= 1 σ ϕ E H P H σ−1 ( σ σ−1 ( w H τ F τ H +λ w F τ H ) a ) 1−σ − C HFH MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr 0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaabaaaaaaaaape GaeqiWda3damaaBaaaleaapeGaamisaiaadAeacaWGibaapaqabaGc peWaaeWaa8aabaWdbiaadggaaiaawIcacaGLPaaacqGH9aqpdaWcaa WdaeaapeGaaGymaaWdaeaapeGaeq4Wdmhaaiabew9aMjaacckacaWG fbWdamaaBaaaleaapeGaamisaaWdaeqaaOWdbiaacckacaWGqbWdam aaBaaaleaapeGaamisaaWdaeqaaOWaaWbaaSqabeaapeGaeq4WdmNa eyOeI0IaaGymaaaakmaabmaapaqaa8qadaWcaaWdaeaapeGaeq4Wdm hapaqaa8qacqaHdpWCcqGHsislcaaIXaaaaiaacckadaqadaWdaeaa peGaam4Da8aadaWgaaWcbaWdbiaadIeaa8aabeaak8qacaGGGcGaeq iXdq3damaaBaaaleaapeGaamOraaWdaeqaaOWdbiaacckacqaHepaD paWaaSbaaSqaa8qacaWGibaapaqabaGcpeGaey4kaSIaeq4UdWMaai iOaiaadEhapaWaaSbaaSqaa8qacaWGgbaapaqabaGcpeGaaiiOaiab es8a09aadaWgaaWcbaWdbiaadIeaa8aabeaaaOWdbiaawIcacaGLPa aacaGGGcGaaiiOaiaadggaaiaawIcacaGLPaaapaWaaWbaaSqabeaa peGaaGymaiabgkHiTiabeo8aZbaakiabgkHiTiaadoeapaWaaSbaaS qaa8qacaWGibGaamOraiaadIeaa8aabeaaaaa@76D6@ (6)
π FFH ( a )= 1 σ ϕ E H P H σ−1 ( σ σ−1 w F ( 1+λ ) τ H a ) 1−σ − C FFH MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr 0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaabaaaaaaaaape GaeqiWda3damaaBaaaleaapeGaamOraiaadAeacaWGibaapaqabaGc peWaaeWaa8aabaWdbiaadggaaiaawIcacaGLPaaacqGH9aqpdaWcaa WdaeaapeGaaGymaaWdaeaapeGaeq4Wdmhaaiabew9aMjaacckacaWG fbWdamaaBaaaleaapeGaamisaaWdaeqaaOWdbiaacckacaWGqbWdam aaBaaaleaapeGaamisaaWdaeqaaOWaaWbaaSqabeaapeGaeq4WdmNa eyOeI0IaaGymaaaakmaabmaapaqaa8qadaWcaaWdaeaapeGaeq4Wdm hapaqaa8qacqaHdpWCcqGHsislcaaIXaaaaiaacckacaWG3bWdamaa BaaaleaapeGaamOraaWdaeqaaOWdbmaabmaapaqaa8qacaaIXaGaey 4kaSIaeq4UdWMaaiiOaaGaayjkaiaawMcaaiaacckacqaHepaDpaWa aSbaaSqaa8qacaWGibaapaqabaGcpeGaaiiOaiaadggaaiaawIcaca GLPaaapaWaaWbaaSqabeaapeGaaGymaiabgkHiTiabeo8aZbaakiab gkHiTiaadoeapaWaaSbaaSqaa8qacaWGgbGaamOraiaadIeaa8aabe aaaaa@6BDA@ (7)
π FFF ( a )= 1 σ ϕ E F P F σ−1 ( σ σ−1 w F ( 1+λ ) a ) 1−σ − C FFF MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr 0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaabaaaaaaaaape GaeqiWda3damaaBaaaleaapeGaamOraiaadAeacaWGgbaapaqabaGc peWaaeWaa8aabaWdbiaadggaaiaawIcacaGLPaaacqGH9aqpdaWcaa WdaeaapeGaaGymaaWdaeaapeGaeq4Wdmhaaiabew9aMjaacckacaWG fbWdamaaBaaaleaapeGaamOraaWdaeqaaOWdbiaacckacaWGqbWdam aaBaaaleaapeGaamOraaWdaeqaaOWaaWbaaSqabeaapeGaeq4WdmNa eyOeI0IaaGymaaaakmaabmaapaqaa8qadaWcaaWdaeaapeGaeq4Wdm hapaqaa8qacqaHdpWCcqGHsislcaaIXaaaaiaacckacaWG3bWdamaa BaaaleaapeGaamOraaWdaeqaaOWdbmaabmaapaqaa8qacaaIXaGaey 4kaSIaeq4UdWgacaGLOaGaayzkaaGaaiiOaiaadggaaiaawIcacaGL PaaapaWaaWbaaSqabeaapeGaaGymaiabgkHiTiabeo8aZbaakiabgk HiTiaadoeapaWaaSbaaSqaa8qacaWGgbGaamOraiaadAeaa8aabeaa aaa@6684@ . (8)
π HFF ( a )= 1 σ ϕ E F P F σ−1 ( σ σ−1 ( w H τ F +λ w F ) a ) 1−σ − C HFF MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr 0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaabaaaaaaaaape GaeqiWda3damaaBaaaleaapeGaamisaiaadAeacaWGgbaapaqabaGc peWaaeWaa8aabaWdbiaadggaaiaawIcacaGLPaaacqGH9aqpdaWcaa WdaeaapeGaaGymaaWdaeaapeGaeq4Wdmhaaiabew9aMjaacckacaWG fbWdamaaBaaaleaapeGaamOraaWdaeqaaOWdbiaacckacaWGqbWdam aaBaaaleaapeGaamOraaWdaeqaaOWaaWbaaSqabeaapeGaeq4WdmNa eyOeI0IaaGymaaaakmaabmaapaqaa8qadaWcaaWdaeaapeGaeq4Wdm hapaqaa8qacqaHdpWCcqGHsislcaaIXaaaaiaacckadaqadaWdaeaa peGaam4Da8aadaWgaaWcbaWdbiaadIeaa8aabeaak8qacaGGGcGaeq iXdq3damaaBaaaleaapeGaamOraaWdaeqaaOWdbiabgUcaRiabeU7a SjaacckacaWG3bWdamaaBaaaleaapeGaamOraaWdaeqaaaGcpeGaay jkaiaawMcaaiaacckacaGGGcGaamyyaaGaayjkaiaawMcaa8aadaah aaWcbeqaa8qacaaIXaGaeyOeI0Iaeq4WdmhaaOGaeyOeI0Iaam4qa8 aadaWgaaWcbaWdbiaadIeacaWGgbGaamOraaWdaeqaaaaa@6E7A@ (9)
π HHF ( a )= 1 σ ϕ E F P F σ−1 ( σ σ−1 w H ( 1+λ ) τ F a ) 1−σ − C HHF MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr 0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaabaaaaaaaaape GaeqiWda3damaaBaaaleaapeGaamisaiaadIeacaWGgbaapaqabaGc peWaaeWaa8aabaWdbiaadggaaiaawIcacaGLPaaacqGH9aqpdaWcaa WdaeaapeGaaGymaaWdaeaapeGaeq4Wdmhaaiabew9aMjaacckacaWG fbWdamaaBaaaleaapeGaamOraaWdaeqaaOWdbiaacckacaWGqbWdam aaBaaaleaapeGaamOraaWdaeqaaOWaaWbaaSqabeaapeGaeq4WdmNa eyOeI0IaaGymaaaakmaabmaapaqaa8qadaWcaaWdaeaapeGaeq4Wdm hapaqaa8qacqaHdpWCcqGHsislcaaIXaaaaiaacckacaWG3bWdamaa BaaaleaapeGaamisaaWdaeqaaOWdbiaacckadaqadaWdaeaapeGaaG ymaiabgUcaRiabeU7aSbGaayjkaiaawMcaaiaacckacqaHepaDpaWa aSbaaSqaa8qacaWGgbaapaqabaGcpeGaaiiOaiaadggaaiaawIcaca GLPaaapaWaaWbaaSqabeaapeGaaGymaiabgkHiTiabeo8aZbaakiab gkHiTiaadoeapaWaaSbaaSqaa8qacaWGibGaamisaiaadAeaa8aabe aaaaa@6BDA@ (10)
2.4 Productivity Cutoffs
Different firms will serve different supply chains, depending on whether their productivity is above or below certain productivity cutoffs. All firms in Home with unit labor requirements below a HHH MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr 0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaabaaaaaaaaape Gaamyya8aadaWgaaWcbaWdbiaadIeacaWGibGaamisaaWdaeqaaaaa @39B3@ supply the Home market, either through completely domestic production (an HHH supply chain) or by offshoring the final stage of production (an HFH supply chain). The cutoff unit labor requirement for a firm to supply the Home market is implicitly defined in equation (11).
π HHH ( a HHH )=0 MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr 0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaabaaaaaaaaape GaeqiWda3damaaBaaaleaapeGaamisaiaadIeacaWGibaapaqabaGc peWaaeWaa8aabaWdbiaadggapaWaaSbaaSqaa8qacaWGibGaamisai aadIeaa8aabeaaaOWdbiaawIcacaGLPaaacqGH9aqpcaaIWaaaaa@41CD@ (11)
Equations (5) and (11) imply the equilibrium cutoff level a HHH MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr 0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaabaaaaaaaaape Gaamyya8aadaWgaaWcbaWdbiaadIeacaWGibGaamisaaWdaeqaaaaa @39B3@ in equation (12).
a HHH = ( σ C HHH ϕ E H ) 1 1−σ P H w H ( 1+λ ) ( σ−1 σ ) MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr 0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaabaaaaaaaaape Gaamyya8aadaWgaaWcbaWdbiaadIeacaWGibGaamisaaWdaeqaaOWd biabg2da9maabmaapaqaa8qadaWcaaWdaeaapeGaeq4WdmNaaiiOai aadoeapaWaaSbaaSqaa8qacaWGibGaamisaiaadIeaa8aabeaak8qa caGGGcaapaqaa8qacqaHvpGzcaGGGcGaamyra8aadaWgaaWcbaWdbi aadIeaa8aabeaaaaaak8qacaGLOaGaayzkaaWdamaaCaaaleqabaWd bmaalaaapaqaa8qacaaIXaaapaqaa8qacaaIXaGaeyOeI0Iaeq4Wdm haaaaakmaalaaapaqaa8qacaWGqbWdamaaBaaaleaapeGaamisaaWd aeqaaaGcbaWdbiaadEhapaWaaSbaaSqaa8qacaWGibaapaqabaGcpe GaaiiOamaabmaapaqaa8qacaaIXaGaey4kaSIaeq4UdWgacaGLOaGa ayzkaaaaamaabmaapaqaa8qadaWcaaWdaeaapeGaeq4WdmNaeyOeI0 IaaGymaaWdaeaapeGaeq4WdmhaaaGaayjkaiaawMcaaaaa@5FFB@ (12)
Firms with unit labor requirements below a second cutoff a HFH MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr 0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaabaaaaaaaaape Gaamyya8aadaWgaaWcbaWdbiaadIeacaWGgbGaamisaaWdaeqaaaaa @39B1@ , defined in equations (13) and (14), supply Home by offshoring the final stage of production.
π HFH ( a HFH )− π HHH ( a HFH )=0 MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr 0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaabaaaaaaaaape GaeqiWda3damaaBaaaleaapeGaamisaiaadAeacaWGibaapaqabaGc peWaaeWaa8aabaWdbiaadggapaWaaSbaaSqaa8qacaWGibGaamOrai aadIeaa8aabeaaaOWdbiaawIcacaGLPaaacqGHsislcqaHapaCpaWa aSbaaSqaa8qacaWGibGaamisaiaadIeaa8aabeaak8qadaqadaWdae aapeGaamyya8aadaWgaaWcbaWdbiaadIeacaWGgbGaamisaaWdaeqa aaGcpeGaayjkaiaawMcaaiabg2da9iaaicdaaaa@4CB5@ (13)
a HFH = ( σ ( C HHH − C HFH ) ϕ E H ) 1 1−σ P H ( ( w H ( 1+λ ) ) 1−σ − ( ( w H τ F τ H +λ w F τ H ) ) 1−σ ) 1 σ−1 ( σ−1 σ ) MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr 0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaabaaaaaaaaape Gaamyya8aadaWgaaWcbaWdbiaadIeacaWGgbGaamisaaWdaeqaaOWd biabg2da9maabmaapaqaa8qadaWcaaWdaeaapeGaeq4WdmNaaiiOam aabmaapaqaa8qacaWGdbWdamaaBaaaleaapeGaamisaiaadIeacaWG ibaapaqabaGcpeGaeyOeI0Iaam4qa8aadaWgaaWcbaWdbiaadIeaca WGgbGaamisaaWdaeqaaaGcpeGaayjkaiaawMcaaiaacckaa8aabaWd biabew9aMjaacckacaWGfbWdamaaBaaaleaapeGaamisaaWdaeqaaa aaaOWdbiaawIcacaGLPaaapaWaaWbaaSqabeaapeWaaSaaa8aabaWd biaaigdaa8aabaWdbiaaigdacqGHsislcqaHdpWCaaaaaOGaamiua8 aadaWgaaWcbaWdbiaadIeaa8aabeaak8qadaqadaWdaeaapeWaaeWa a8aabaWdbiaadEhapaWaaSbaaSqaa8qacaWGibaapaqabaGcpeGaai iOamaabmaapaqaa8qacaaIXaGaey4kaSIaeq4UdWgacaGLOaGaayzk aaaacaGLOaGaayzkaaWdamaaCaaaleqabaWdbiaaigdacqGHsislcq aHdpWCaaGccqGHsisldaqadaWdaeaapeWaaeWaa8aabaWdbiaadEha paWaaSbaaSqaa8qacaWGibaapaqabaGcpeGaaiiOaiabes8a09aada WgaaWcbaWdbiaadAeaa8aabeaak8qacaGGGcGaeqiXdq3damaaBaaa leaapeGaamisaaWdaeqaaOWdbiabgUcaRiabeU7aSjaacckacaWG3b WdamaaBaaaleaapeGaamOraaWdaeqaaOWdbiaacckacqaHepaDpaWa aSbaaSqaa8qacaWGibaapaqabaaak8qacaGLOaGaayzkaaGaaiiOaa GaayjkaiaawMcaa8aadaahaaWcbeqaa8qacaaIXaGaeyOeI0Iaeq4W dmhaaaGccaGLOaGaayzkaaWdamaaCaaaleqabaWdbmaalaaapaqaa8 qacaaIXaaapaqaa8qacqaHdpWCcqGHsislcaaIXaaaaaaakmaabmaa paqaa8qadaWcaaWdaeaapeGaeq4WdmNaeyOeI0IaaGymaaWdaeaape Gaeq4WdmhaaaGaayjkaiaawMcaaaaa@8FAB@ (14)
We assume that C HHH MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr 0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaabaaaaaaaaape Gaam4qa8aadaWgaaWcbaWdbiaadIeacaWGibGaamisaaWdaeqaaaaa @3995@ is less than C HFH MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr 0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaabaaaaaaaaape Gaam4qa8aadaWgaaWcbaWdbiaadIeacaWGgbGaamisaaWdaeqaaaaa @3993@ , since offshoring incurs additional fixed costs, and therefore a HFH MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr 0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaabaaaaaaaaape Gaamyya8aadaWgaaWcbaWdbiaadIeacaWGgbGaamisaaWdaeqaaaaa @39B1@ is less than a HHH MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr 0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaabaaaaaaaaape Gaamyya8aadaWgaaWcbaWdbiaadIeacaWGibGaamisaaWdaeqaaaaa @39B3@ . The most productive firms offshore their final production stage.
Equations (15) and (16) define the cutoff unit labor requirements for Foreign firms to export to Home.
π FFH ( a FFH )=0 MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr 0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaabaaaaaaaaape GaeqiWda3damaaBaaaleaapeGaamOraiaadAeacaWGibaapaqabaGc peWaaeWaa8aabaWdbiaadggapaWaaSbaaSqaa8qacaWGgbGaamOrai aadIeaa8aabeaaaOWdbiaawIcacaGLPaaacqGH9aqpcaaIWaaaaa@41C5@ (15)
a FFH = ( σ C FFH ϕ E H ) 1 1−σ P H w F ( 1+λ ) τ H ( σ−1 σ ) MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr 0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaabaaaaaaaaape Gaamyya8aadaWgaaWcbaWdbiaadAeacaWGgbGaamisaaWdaeqaaOWd biabg2da9maabmaapaqaa8qadaWcaaWdaeaapeGaeq4WdmNaaiiOai aadoeapaWaaSbaaSqaa8qacaWGgbGaamOraiaadIeaa8aabeaak8qa caGGGcaapaqaa8qacqaHvpGzcaGGGcGaamyra8aadaWgaaWcbaWdbi aadIeaa8aabeaaaaaak8qacaGLOaGaayzkaaWdamaaCaaaleqabaWd bmaalaaapaqaa8qacaaIXaaapaqaa8qacaaIXaGaeyOeI0Iaeq4Wdm haaaaakmaalaaapaqaa8qacaWGqbWdamaaBaaaleaapeGaamisaaWd aeqaaaGcbaWdbiaadEhapaWaaSbaaSqaa8qacaWGgbaapaqabaGcpe GaaiiOamaabmaapaqaa8qacaaIXaGaey4kaSIaeq4UdWgacaGLOaGa ayzkaaGaaiiOaiabes8a09aadaWgaaWcbaWdbiaadIeaa8aabeaaaa GcpeWaaeWaa8aabaWdbmaalaaapaqaa8qacqaHdpWCcqGHsislcaaI Xaaapaqaa8qacqaHdpWCaaaacaGLOaGaayzkaaaaaa@641B@ (16)
Likewise, equations (17) through (22) define the cutoff unit labor requirements for supplying Foreign through each of the alternative supply chains.
π FFF ( a FFF )=0 MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr 0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaabaaaaaaaaape GaeqiWda3damaaBaaaleaapeGaamOraiaadAeacaWGgbaapaqabaGc peWaaeWaa8aabaWdbiaadggapaWaaSbaaSqaa8qacaWGgbGaamOrai aadAeaa8aabeaaaOWdbiaawIcacaGLPaaacqGH9aqpcaaIWaaaaa@41C1@ (17)
a FFF = ( σ C FFF ϕ E F ) 1 1−σ P F w F ( 1+λ ) ( σ−1 σ ) MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr 0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaabaaaaaaaaape Gaamyya8aadaWgaaWcbaWdbiaadAeacaWGgbGaamOraaWdaeqaaOWd biabg2da9maabmaapaqaa8qadaWcaaWdaeaapeGaeq4WdmNaaeiOai aadoeapaWaaSbaaSqaa8qacaWGgbGaamOraiaadAeaa8aabeaak8qa caqGGcaapaqaa8qacqaHvpGzcaqGGcGaamyra8aadaWgaaWcbaWdbi aadAeaa8aabeaaaaaak8qacaGLOaGaayzkaaWdamaaCaaaleqabaWd bmaalaaapaqaa8qacaaIXaaapaqaa8qacaaIXaGaeyOeI0Iaeq4Wdm haaaaakmaalaaapaqaa8qacaWGqbWdamaaBaaaleaapeGaamOraaWd aeqaaaGcbaWdbiaadEhapaWaaSbaaSqaa8qacaWGgbaapaqabaGcpe GaaeiOamaabmaapaqaa8qacaaIXaGaey4kaSIaeq4UdWgacaGLOaGa ayzkaaaaamaabmaapaqaa8qadaWcaaWdaeaapeGaeq4WdmNaeyOeI0 IaaGymaaWdaeaapeGaeq4WdmhaaaGaayjkaiaawMcaaaaa@5FE5@ (18)
π HFF ( a HFF )− π HHF ( a HFF )=0 MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr 0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaabaaaaaaaaape GaeqiWda3damaaBaaaleaapeGaamisaiaadAeacaWGgbaapaqabaGc peWaaeWaa8aabaWdbiaadggapaWaaSbaaSqaa8qacaWGibGaamOrai aadAeaa8aabeaaaOWdbiaawIcacaGLPaaacqGHsislcqaHapaCpaWa aSbaaSqaa8qacaWGibGaamisaiaadAeaa8aabeaak8qadaqadaWdae aapeGaamyya8aadaWgaaWcbaWdbiaadIeacaWGgbGaamOraaWdaeqa aaGcpeGaayjkaiaawMcaaiabg2da9iaaicdaaaa@4CAD@ (19)
a HFF = ( σ ( C HFF − C HHF ) ϕ E F ) 1 1−σ P F ( σ−1 σ ) ( ( w H ( 1+λ ) τ F ) 1−σ − ( w H τ F +λ w F ) 1−σ ) 1 σ−1 MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr 0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaabaaaaaaaaape Gaamyya8aadaWgaaWcbaWdbiaadIeacaWGgbGaamOraaWdaeqaaOWd biabg2da9maabmaapaqaa8qadaWcaaWdaeaapeGaeq4WdmNaaeiOam aabmaapaqaa8qacaWGdbWdamaaBaaaleaapeGaamisaiaadAeacaWG gbaapaqabaGcpeGaeyOeI0Iaam4qa8aadaWgaaWcbaWdbiaadIeaca WGibGaamOraaWdaeqaaaGcpeGaayjkaiaawMcaaiaabckaa8aabaWd biabew9aMjaabckacaWGfbWdamaaBaaaleaapeGaamOraaWdaeqaaa aaaOWdbiaawIcacaGLPaaapaWaaWbaaSqabeaapeWaaSaaa8aabaWd biaaigdaa8aabaWdbiaaigdacqGHsislcqaHdpWCaaaaaOGaamiua8 aadaWgaaWcbaWdbiaadAeaa8aabeaak8qadaqadaWdaeaapeWaaSaa a8aabaWdbiabeo8aZjabgkHiTiaaigdaa8aabaWdbiabeo8aZbaaai aawIcacaGLPaaadaqadaWdaeaapeWaaeWaa8aabaWdbiaadEhapaWa aSbaaSqaa8qacaWGibaapaqabaGcpeWaaeWaa8aabaWdbiaaigdacq GHRaWkcqaH7oaBaiaawIcacaGLPaaacaqGGcGaeqiXdq3damaaBaaa leaapeGaamOraaWdaeqaaaGcpeGaayjkaiaawMcaa8aadaahaaWcbe qaa8qacaaIXaGaeyOeI0Iaeq4WdmhaaOGaeyOeI0YaaeWaa8aabaWd biaadEhapaWaaSbaaSqaa8qacaWGibaapaqabaGcpeGaaeiOaiabes 8a09aadaWgaaWcbaWdbiaadAeaa8aabeaak8qacqGHRaWkcqaH7oaB caWG3bWdamaaBaaaleaapeGaamOraaWdaeqaaaGcpeGaayjkaiaawM caa8aadaahaaWcbeqaa8qacaaIXaGaeyOeI0Iaeq4WdmhaaaGccaGL OaGaayzkaaWdamaaCaaaleqabaWdbmaalaaapaqaa8qacaaIXaaapa qaa8qacqaHdpWCcqGHsislcaaIXaaaaaaaaaa@8652@ (20)
π HHF ( a HHF )=0 MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr 0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaabaaaaaaaaape GaeqiWda3damaaBaaaleaapeGaamisaiaadIeacaWGgbaapaqabaGc peWaaeWaa8aabaWdbiaadggapaWaaSbaaSqaa8qacaWGibGaamisai aadAeaa8aabeaaaOWdbiaawIcacaGLPaaacqGH9aqpcaaIWaaaaa@41C9@ (21)
a HHF = ( σ C HHF ϕ E F ) 1 1−σ P F w H ( 1+λ ) τ F ( σ−1 σ ) MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr 0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaabaaaaaaaaape Gaamyya8aadaWgaaWcbaWdbiaadIeacaWGibGaamOraaWdaeqaaOWd biabg2da9maabmaapaqaa8qadaWcaaWdaeaapeGaeq4WdmNaaeiOai aadoeapaWaaSbaaSqaa8qacaWGibGaamisaiaadAeaa8aabeaak8qa caqGGcaapaqaa8qacqaHvpGzcaqGGcGaamyra8aadaWgaaWcbaWdbi aadAeaa8aabeaaaaaak8qacaGLOaGaayzkaaWdamaaCaaaleqabaWd bmaalaaapaqaa8qacaaIXaaapaqaa8qacaaIXaGaeyOeI0Iaeq4Wdm haaaaakmaalaaapaqaa8qacaWGqbWdamaaBaaaleaapeGaamOraaWd aeqaaaGcbaWdbiaadEhapaWaaSbaaSqaa8qacaWGibaapaqabaGcpe GaaeiOamaabmaapaqaa8qacaaIXaGaey4kaSIaeq4UdWgacaGLOaGa ayzkaaGaaeiOaiabes8a09aadaWgaaWcbaWdbiaadAeaa8aabeaaaa GcpeWaaeWaa8aabaWdbmaalaaapaqaa8qacqaHdpWCcqGHsislcaaI Xaaapaqaa8qacqaHdpWCaaaacaGLOaGaayzkaaaaaa@6416@ (22)
We assume that C HHF MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr 0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaabaaaaaaaaape Gaam4qa8aadaWgaaWcbaWdbiaadIeacaWGibGaamOraaWdaeqaaaaa @3993@ is less than C HFF MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr 0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaabaaaaaaaaape Gaam4qa8aadaWgaaWcbaWdbiaadIeacaWGgbGaamOraaWdaeqaaaaa @3991@ , since offshoring incurs additional fixed costs, and therefore a HFF MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr 0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaabaaaaaaaaape Gaamyya8aadaWgaaWcbaWdbiaadIeacaWGgbGaamOraaWdaeqaaaaa @39AF@ is less than a HHF MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr 0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaabaaaaaaaaape Gaamyya8aadaWgaaWcbaWdbiaadIeacaWGibGaamOraaWdaeqaaaaa @39B1@ . Again, the most productive firms offshore their final production stage.
2.5 Sales and Prices
The equilibrium value of sales (trade flows) for each supply chain and the overall price indices can be expressed in 3 different ways, depending on which variables you prefer it to be a function of.
2.5.1 Sales and Prices as a Function of Unit Labor Requirements and the Distribution of Productivities
Equations (23) through (25) represent the equilibrium values of sales in Home for each of the supply chains that serve that market, as a function of the cutoff unit labor requirements above and the distribution of unit labor requirements G( a ) MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr 0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaabaaaaaaaaape Gaam4ramaabmaapaqaa8qacaWGHbaacaGLOaGaayzkaaaaaa@3966@ .
V HHH = n H ϕ E H P H σ−1 ( σ σ−1 w H ( 1+λ ) ) 1−σ ∫ a HFH a HHH a 1−σ dG( a ) MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr 0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaabaaaaaaaaape GaamOva8aadaWgaaWcbaWdbiaadIeacaWGibGaamisaaWdaeqaaOWd biabg2da9iaad6gapaWaaSbaaSqaa8qacaWGibaapaqabaGcpeGaai iOaiabew9aMjaacckacaWGfbWdamaaBaaaleaapeGaamisaaWdaeqa aOWdbiaadcfapaWaaSbaaSqaa8qacaWGibaapaqabaGcdaahaaWcbe qaa8qacqaHdpWCcqGHsislcaaIXaaaaOWaaeWaa8aabaWdbmaalaaa paqaa8qacqaHdpWCa8aabaWdbiabeo8aZjabgkHiTiaaigdaaaGaam 4Da8aadaWgaaWcbaWdbiaadIeaa8aabeaak8qacaGGGcWaaeWaa8aa baWdbiaaigdacqGHRaWkcqaH7oaBaiaawIcacaGLPaaaaiaawIcaca GLPaaapaWaaWbaaSqabeaapeGaaGymaiabgkHiTiabeo8aZbaakmaa wahabeWcpaqaa8qacaWGHbWdamaaBaaameaapeGaamisaiaadAeaca WGibaapaqabaaaleaapeGaamyya8aadaWgaaadbaWdbiaadIeacaWG ibGaamisaaWdaeqaaaqdbaWdbiabgUIiYdaakiaadggapaWaaWbaaS qabeaapeGaaGymaiabgkHiTiabeo8aZbaakiaacckacaWGKbGaam4r amaabmaapaqaa8qacaWGHbaacaGLOaGaayzkaaaaaa@702F@ (23)
V HFH = n H ϕ E H P H σ−1 ( σ σ−1 ( w H τ F τ H +λ w F τ H ) ) 1−σ ∫ 0 a HFH a 1−σ dG( a ) MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr 0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaabaaaaaaaaape GaamOva8aadaWgaaWcbaWdbiaadIeacaWGgbGaamisaaWdaeqaaOWd biabg2da9iaad6gapaWaaSbaaSqaa8qacaWGibaapaqabaGcpeGaai iOaiabew9aMjaacckacaWGfbWdamaaBaaaleaapeGaamisaaWdaeqa aOWdbiaadcfapaWaaSbaaSqaa8qacaWGibaapaqabaGcdaahaaWcbe qaa8qacqaHdpWCcqGHsislcaaIXaaaaOWaaeWaa8aabaWdbmaalaaa paqaa8qacqaHdpWCa8aabaWdbiabeo8aZjabgkHiTiaaigdaaaGaai iOamaabmaapaqaa8qacaWG3bWdamaaBaaaleaapeGaamisaaWdaeqa aOWdbiaacckacqaHepaDpaWaaSbaaSqaa8qacaWGgbaapaqabaGcpe GaaiiOaiabes8a09aadaWgaaWcbaWdbiaadIeaa8aabeaak8qacqGH RaWkcqaH7oaBcaWG3bWdamaaBaaaleaapeGaamOraaWdaeqaaOWdbi aacckacqaHepaDpaWaaSbaaSqaa8qacaWGibaapaqabaaak8qacaGL OaGaayzkaaGaaiiOaaGaayjkaiaawMcaa8aadaahaaWcbeqaa8qaca aIXaGaeyOeI0Iaeq4WdmhaaOWaaybCaeqal8aabaWdbiaaicdaa8aa baWdbiaadggapaWaaSbaaWqaa8qacaWGibGaamOraiaadIeaa8aabe aaa0qaa8qacqGHRiI8aaGccaWGHbWdamaaCaaaleqabaWdbiaaigda cqGHsislcqaHdpWCaaGccaGGGcGaamizaiaadEeadaqadaWdaeaape GaamyyaaGaayjkaiaawMcaaaaa@7C63@ (24)
V FFH = n F ϕ E H P H σ−1 ( σ σ−1 w F ( 1+λ ) τ H ) 1−σ ∫ 0 a FFH a 1−σ dG( a ) MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr 0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaabaaaaaaaaape GaamOva8aadaWgaaWcbaWdbiaadAeacaWGgbGaamisaaWdaeqaaOWd biabg2da9iaad6gapaWaaSbaaSqaa8qacaWGgbaapaqabaGcpeGaai iOaiabew9aMjaacckacaWGfbWdamaaBaaaleaapeGaamisaaWdaeqa aOWdbiaadcfapaWaaSbaaSqaa8qacaWGibaapaqabaGcdaahaaWcbe qaa8qacqaHdpWCcqGHsislcaaIXaaaaOWaaeWaa8aabaWdbmaalaaa paqaa8qacqaHdpWCa8aabaWdbiabeo8aZjabgkHiTiaaigdaaaGaam 4Da8aadaWgaaWcbaWdbiaadAeaa8aabeaak8qacaGGGcWaaeWaa8aa baWdbiaaigdacqGHRaWkcqaH7oaBaiaawIcacaGLPaaacaGGGcGaeq iXdq3damaaBaaaleaapeGaamisaaWdaeqaaaGcpeGaayjkaiaawMca a8aadaahaaWcbeqaa8qacaaIXaGaeyOeI0Iaeq4WdmhaaOWaaybCae qal8aabaWdbiaaicdaa8aabaWdbiaadggapaWaaSbaaWqaa8qacaWG gbGaamOraiaadIeaa8aabeaaa0qaa8qacqGHRiI8aaGccaWGHbWdam aaCaaaleqabaWdbiaaigdacqGHsislcqaHdpWCaaGccaGGGcGaamiz aiaadEeadaqadaWdaeaapeGaamyyaaGaayjkaiaawMcaaaaa@7165@ (25)
Equation (26) represents the corresponding CES price index in Home.
P H =( σ σ−1 ) ( n H ( w H ( 1+λ ) ) 1−σ ∫ a HFH a HHH a 1−σ dG( a )+ n H ( ( w H τ F τ H +λ w F τ H ) ) 1−σ ∫ 0 a HFH a 1−σ dG( a )+ n F ( w F ( 1+λ ) τ H ) 1−σ ∫ 0 a FFH a 1−σ dG( a ) ) 1 1−σ MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr 0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaabaaaaaaaaape Gaamiua8aadaWgaaWcbaWdbiaadIeaa8aabeaak8qacqGH9aqpdaqa daWdaeaapeWaaSaaa8aabaWdbiabeo8aZbWdaeaapeGaeq4WdmNaey OeI0IaaGymaaaaaiaawIcacaGLPaaadaqadaWdaeaapeGaamOBa8aa daWgaaWcbaWdbiaadIeaa8aabeaak8qacaGGGcWaaeWaa8aabaWdbi aadEhapaWaaSbaaSqaa8qacaWGibaapaqabaGcpeGaaiiOamaabmaa paqaa8qacaaIXaGaey4kaSIaeq4UdWgacaGLOaGaayzkaaaacaGLOa GaayzkaaWdamaaCaaaleqabaWdbiaaigdacqGHsislcqaHdpWCaaGc daGfWbqabSWdaeaapeGaamyya8aadaWgaaadbaWdbiaadIeacaWGgb GaamisaaWdaeqaaaWcbaWdbiaadggapaWaaSbaaWqaa8qacaWGibGa amisaiaadIeaa8aabeaaa0qaa8qacqGHRiI8aaGccaWGHbWdamaaCa aaleqabaWdbiaaigdacqGHsislcqaHdpWCaaGccaGGGcGaamizaiaa dEeadaqadaWdaeaapeGaamyyaaGaayjkaiaawMcaaiabgUcaRiaad6 gapaWaaSbaaSqaa8qacaWGibaapaqabaGcpeGaaiiOamaabmaapaqa a8qadaqadaWdaeaapeGaam4Da8aadaWgaaWcbaWdbiaadIeaa8aabe aak8qacaGGGcGaeqiXdq3damaaBaaaleaapeGaamOraaWdaeqaaOWd biaacckacqaHepaDpaWaaSbaaSqaa8qacaWGibaapaqabaGcpeGaey 4kaSIaeq4UdWMaam4Da8aadaWgaaWcbaWdbiaadAeaa8aabeaak8qa caGGGcGaeqiXdq3damaaBaaaleaapeGaamisaaWdaeqaaaGcpeGaay jkaiaawMcaaaGaayjkaiaawMcaa8aadaahaaWcbeqaa8qacaaIXaGa eyOeI0Iaeq4WdmhaaOWaaybCaeqal8aabaWdbiaaicdaa8aabaWdbi aadggapaWaaSbaaWqaa8qacaWGibGaamOraiaadIeaa8aabeaaa0qa a8qacqGHRiI8aaGccaWGHbWdamaaCaaaleqabaWdbiaaigdacqGHsi slcqaHdpWCaaGccaGGGcGaamizaiaadEeadaqadaWdaeaapeGaamyy aaGaayjkaiaawMcaaiabgUcaRiaad6gapaWaaSbaaSqaa8qacaWGgb aapaqabaGcpeGaaiiOamaabmaapaqaa8qacaWG3bWdamaaBaaaleaa peGaamOraaWdaeqaaOWdbiaacckadaqadaWdaeaapeGaaGymaiabgU caRiabeU7aSbGaayjkaiaawMcaaiaacckacqaHepaDpaWaaSbaaSqa a8qacaWGibaapaqabaaak8qacaGLOaGaayzkaaWdamaaCaaaleqaba WdbiaaigdacqGHsislcqaHdpWCaaGcdaGfWbqabSWdaeaapeGaaGim aaWdaeaapeGaamyya8aadaWgaaadbaWdbiaadAeacaWGgbGaamisaa WdaeqaaaqdbaWdbiabgUIiYdaakiaadggapaWaaWbaaSqabeaapeGa aGymaiabgkHiTiabeo8aZbaakiaacckacaWGKbGaam4ramaabmaapa qaa8qacaWGHbaacaGLOaGaayzkaaGaaeiOaaGaayjkaiaawMcaa8aa daahaaWcbeqaa8qadaWcaaWdaeaapeGaaGymaaWdaeaapeGaaGymai abgkHiTiabeo8aZbaaaaaaaa@C477@ (26)
Equations (27) through (29) represent the equilibrium values of sales in Foreign for each of the alternative supply chains that serve that market.
V FFF = n F ϕ E F P F σ−1 ( σ σ−1 w F ( 1+λ ) ) 1−σ ∫ 0 a FFF a 1−σ dG( a ) MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr 0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaabaaaaaaaaape GaamOva8aadaWgaaWcbaWdbiaadAeacaWGgbGaamOraaWdaeqaaOWd biabg2da9iaad6gapaWaaSbaaSqaa8qacaWGgbaapaqabaGcpeGaai iOaiabew9aMjaacckacaWGfbWdamaaBaaaleaapeGaamOraaWdaeqa aOWdbiaadcfapaWaaSbaaSqaa8qacaWGgbaapaqabaGcdaahaaWcbe qaa8qacqaHdpWCcqGHsislcaaIXaaaaOWaaeWaa8aabaWdbmaalaaa paqaa8qacqaHdpWCa8aabaWdbiabeo8aZjabgkHiTiaaigdaaaGaam 4Da8aadaWgaaWcbaWdbiaadAeaa8aabeaak8qacaGGGcWaaeWaa8aa baWdbiaaigdacqGHRaWkcqaH7oaBaiaawIcacaGLPaaaaiaawIcaca GLPaaapaWaaWbaaSqabeaapeGaaGymaiabgkHiTiabeo8aZbaakmaa wahabeWcpaqaa8qacaaIWaaapaqaa8qacaWGHbWdamaaBaaameaape GaamOraiaadAeacaWGgbaapaqabaaaneaapeGaey4kIipaaOGaamyy a8aadaahaaWcbeqaa8qacaaIXaGaeyOeI0Iaeq4WdmhaaOGaaiiOai aadsgacaWGhbWaaeWaa8aabaWdbiaadggaaiaawIcacaGLPaaaaaa@6D33@ (27)
V HFF = n H ϕ E F P F σ−1 ( σ σ−1 ( τ F w H +λ w F ) ) 1−σ ∫ 0 a HFF a 1−σ dG( a ) MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr 0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaabaaaaaaaaape GaamOva8aadaWgaaWcbaWdbiaadIeacaWGgbGaamOraaWdaeqaaOWd biabg2da9iaad6gapaWaaSbaaSqaa8qacaWGibaapaqabaGcpeGaai iOaiabew9aMjaacckacaWGfbWdamaaBaaaleaapeGaamOraaWdaeqa aOWdbiaadcfapaWaaSbaaSqaa8qacaWGgbaapaqabaGcdaahaaWcbe qaa8qacqaHdpWCcqGHsislcaaIXaaaaOWaaeWaa8aabaWdbmaalaaa paqaa8qacqaHdpWCa8aabaWdbiabeo8aZjabgkHiTiaaigdaaaGaai iOamaabmaapaqaa8qacqaHepaDpaWaaSbaaSqaa8qacaWGgbaapaqa baGcpeGaaiiOaiaadEhapaWaaSbaaSqaa8qacaWGibaapaqabaGcpe Gaey4kaSIaeq4UdWMaam4Da8aadaWgaaWcbaWdbiaadAeaa8aabeaa aOWdbiaawIcacaGLPaaaaiaawIcacaGLPaaapaWaaWbaaSqabeaape GaaGymaiabgkHiTiabeo8aZbaakmaawahabeWcpaqaa8qacaaIWaaa paqaa8qacaWGHbWdamaaBaaameaapeGaamisaiaadAeacaWGgbaapa qabaaaneaapeGaey4kIipaaOGaamyya8aadaahaaWcbeqaa8qacaaI XaGaeyOeI0Iaeq4WdmhaaOGaaiiOaiaadsgacaWGhbWaaeWaa8aaba WdbiaadggaaiaawIcacaGLPaaaaaa@72E3@ (28)
V HHF = n H ϕ E F P F σ−1 ( σ σ−1 w H ( 1+λ ) τ F ) 1−σ ∫ a HFF a HHF a 1−σ dG( a ) MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr 0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaabaaaaaaaaape GaamOva8aadaWgaaWcbaWdbiaadIeacaWGibGaamOraaWdaeqaaOWd biabg2da9iaad6gapaWaaSbaaSqaa8qacaWGibaapaqabaGcpeGaai iOaiabew9aMjaacckacaWGfbWdamaaBaaaleaapeGaamOraaWdaeqa aOWdbiaadcfapaWaaSbaaSqaa8qacaWGgbaapaqabaGcdaahaaWcbe qaa8qacqaHdpWCcqGHsislcaaIXaaaaOWaaeWaa8aabaWdbmaalaaa paqaa8qacqaHdpWCa8aabaWdbiabeo8aZjabgkHiTiaaigdaaaGaam 4Da8aadaWgaaWcbaWdbiaadIeaa8aabeaak8qacaGGGcWaaeWaa8aa baWdbiaaigdacqGHRaWkcqaH7oaBaiaawIcacaGLPaaacaGGGcGaeq iXdq3damaaBaaaleaapeGaamOraaWdaeqaaaGcpeGaayjkaiaawMca a8aadaahaaWcbeqaa8qacaaIXaGaeyOeI0Iaeq4WdmhaaOWaaybCae qal8aabaWdbiaadggapaWaaSbaaWqaa8qacaWGibGaamOraiaadAea a8aabeaaaSqaa8qacaWGHbWdamaaBaaameaapeGaamisaiaadIeaca WGgbaapaqabaaaneaapeGaey4kIipaaOGaamyya8aadaahaaWcbeqa a8qacaaIXaGaeyOeI0Iaeq4WdmhaaOGaaiiOaiaadsgacaWGhbWaae Waa8aabaWdbiaadggaaiaawIcacaGLPaaaaaa@744D@ (29)
Equation (30) represents the CES price index in Foreign.
P F =( σ σ−1 ) ( n F ( w F ( 1+λ ) ) 1−σ ∫ 0 a FFF a 1−σ dG( a )+ n H ( τ F w H +λ w F ) 1−σ ∫ 0 a HFF a 1−σ dG( a )+ n H ( w H ( 1+λ ) τ F ) 1−σ ∫ a HFF a HHF a 1−σ dG( a ) ) 1 1−σ MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr 0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaabaaaaaaaaape Gaamiua8aadaWgaaWcbaWdbiaadAeaa8aabeaak8qacqGH9aqpdaqa daWdaeaapeWaaSaaa8aabaWdbiabeo8aZbWdaeaapeGaeq4WdmNaey OeI0IaaGymaaaaaiaawIcacaGLPaaadaqadaWdaeaapeGaamOBa8aa daWgaaWcbaWdbiaadAeaa8aabeaak8qacaGGGcWaaeWaa8aabaWdbi aadEhapaWaaSbaaSqaa8qacaWGgbaapaqabaGcpeGaaiiOamaabmaa paqaa8qacaaIXaGaey4kaSIaeq4UdWgacaGLOaGaayzkaaaacaGLOa GaayzkaaWdamaaCaaaleqabaWdbiaaigdacqGHsislcqaHdpWCaaGc daGfWbqabSWdaeaapeGaaGimaaWdaeaapeGaamyya8aadaWgaaadba WdbiaadAeacaWGgbGaamOraaWdaeqaaaqdbaWdbiabgUIiYdaakiaa dggapaWaaWbaaSqabeaapeGaaGymaiabgkHiTiabeo8aZbaakiaacc kacaWGKbGaam4ramaabmaapaqaa8qacaWGHbaacaGLOaGaayzkaaGa ey4kaSIaamOBa8aadaWgaaWcbaWdbiaadIeaa8aabeaak8qacaGGGc WaaeWaa8aabaWdbiabes8a09aadaWgaaWcbaWdbiaadAeaa8aabeaa k8qacaGGGcGaam4Da8aadaWgaaWcbaWdbiaadIeaa8aabeaak8qacq GHRaWkcqaH7oaBcaWG3bWdamaaBaaaleaapeGaamOraaWdaeqaaaGc peGaayjkaiaawMcaa8aadaahaaWcbeqaa8qacaaIXaGaeyOeI0Iaeq 4WdmhaaOWaaybCaeqal8aabaWdbiaaicdaa8aabaWdbiaadggapaWa aSbaaWqaa8qacaWGibGaamOraiaadAeaa8aabeaaa0qaa8qacqGHRi I8aaGccaWGHbWdamaaCaaaleqabaWdbiaaigdacqGHsislcqaHdpWC aaGccaGGGcGaamizaiaadEeadaqadaWdaeaapeGaamyyaaGaayjkai aawMcaaiabgUcaRiaad6gapaWaaSbaaSqaa8qacaWGibaapaqabaGc peGaaiiOamaabmaapaqaa8qacaWG3bWdamaaBaaaleaapeGaamisaa WdaeqaaOWdbiaacckadaqadaWdaeaapeGaaGymaiabgUcaRiabeU7a SbGaayjkaiaawMcaaiaacckacqaHepaDpaWaaSbaaSqaa8qacaWGgb aapaqabaaak8qacaGLOaGaayzkaaWdamaaCaaaleqabaWdbiaaigda cqGHsislcqaHdpWCaaGcdaGfWbqabSWdaeaapeGaamyya8aadaWgaa adbaWdbiaadIeacaWGgbGaamOraaWdaeqaaaWcbaWdbiaadggapaWa aSbaaWqaa8qacaWGibGaamisaiaadAeaa8aabeaaa0qaa8qacqGHRi I8aaGccaWGHbWdamaaCaaaleqabaWdbiaaigdacqGHsislcqaHdpWC aaGccaGGGcGaamizaiaadEeadaqadaWdaeaapeGaamyyaaGaayjkai aawMcaaiaabckaaiaawIcacaGLPaaapaWaaWbaaSqabeaapeWaaSaa a8aabaWdbiaaigdaa8aabaWdbiaaigdacqGHsislcqaHdpWCaaaaaa aa@BA6F@ (30)
2.5.2 Sales and Prices as a Function of Unit Labor Requirements and the Distribution of Productivities’ Shape Parameter
Assuming that the unit labor requirements for individual varieties have a Pareto distribution with shape parameter k>σ−1>0 MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr 0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaabaaaaaaaaape Gaam4Aaiabg6da+iabeo8aZjabgkHiTiaaigdacqGH+aGpcaaIWaaa aa@3D31@ , we can rewrite equations (23) through (30) as follows:
V HHH = n H ϕ E H P H σ−1 ( σ σ−1 w H ( 1+λ ) ) 1−σ [ ( a HHH ) k−( σ−1 ) − ( a HFH ) k−( σ−1 ) ]( k k−( σ−1 ) ) MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr 0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaabaaaaaaaaape GaamOva8aadaWgaaWcbaWdbiaadIeacaWGibGaamisaaWdaeqaaOWd biabg2da9iaad6gapaWaaSbaaSqaa8qacaWGibaapaqabaGcpeGaai iOaiabew9aMjaacckacaWGfbWdamaaBaaaleaapeGaamisaaWdaeqa aOWdbiaadcfapaWaaSbaaSqaa8qacaWGibaapaqabaGcdaahaaWcbe qaa8qacqaHdpWCcqGHsislcaaIXaaaaOWaaeWaa8aabaWdbmaalaaa paqaa8qacqaHdpWCa8aabaWdbiabeo8aZjabgkHiTiaaigdaaaGaam 4Da8aadaWgaaWcbaWdbiaadIeaa8aabeaak8qacaGGGcWaaeWaa8aa baWdbiaaigdacqGHRaWkcqaH7oaBaiaawIcacaGLPaaaaiaawIcaca GLPaaapaWaaWbaaSqabeaapeGaaGymaiabgkHiTiabeo8aZbaakmaa dmaapaqaa8qadaqadaWdaeaapeGaamyya8aadaWgaaWcbaWdbiaadI eacaWGibGaamisaaWdaeqaaaGcpeGaayjkaiaawMcaa8aadaahaaWc beqaa8qacaWGRbGaeyOeI0YaaeWaa8aabaWdbiabeo8aZjabgkHiTi aaigdaaiaawIcacaGLPaaaaaGccqGHsisldaqadaWdaeaapeGaamyy a8aadaWgaaWcbaWdbiaadIeacaWGgbGaamisaaWdaeqaaaGcpeGaay jkaiaawMcaa8aadaahaaWcbeqaa8qacaWGRbGaeyOeI0YaaeWaa8aa baWdbiabeo8aZjabgkHiTiaaigdaaiaawIcacaGLPaaaaaaakiaawU facaGLDbaadaqadaWdaeaapeWaaSaaa8aabaWdbiaadUgaa8aabaWd biaadUgacqGHsisldaqadaWdaeaapeGaeq4WdmNaeyOeI0IaaGymaa GaayjkaiaawMcaaaaaaiaawIcacaGLPaaaaaa@823E@ (31)
V HFH = n H ϕ E H P H σ−1 ( σ σ−1 ( w H τ F τ H +λ w F τ H ) ) 1−σ ( a HFH ) k−( σ−1 ) ( k k−( σ−1 ) ) MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr 0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaabaaaaaaaaape GaamOva8aadaWgaaWcbaWdbiaadIeacaWGgbGaamisaaWdaeqaaOWd biabg2da9iaad6gapaWaaSbaaSqaa8qacaWGibaapaqabaGcpeGaai iOaiabew9aMjaacckacaWGfbWdamaaBaaaleaapeGaamisaaWdaeqa aOWdbiaadcfapaWaaSbaaSqaa8qacaWGibaapaqabaGcdaahaaWcbe qaa8qacqaHdpWCcqGHsislcaaIXaaaaOWaaeWaa8aabaWdbmaalaaa paqaa8qacqaHdpWCa8aabaWdbiabeo8aZjabgkHiTiaaigdaaaGaai iOamaabmaapaqaa8qacaWG3bWdamaaBaaaleaapeGaamisaaWdaeqa aOWdbiaacckacqaHepaDpaWaaSbaaSqaa8qacaWGgbaapaqabaGcpe GaaiiOaiabes8a09aadaWgaaWcbaWdbiaadIeaa8aabeaak8qacqGH RaWkcqaH7oaBcaWG3bWdamaaBaaaleaapeGaamOraaWdaeqaaOWdbi aacckacqaHepaDpaWaaSbaaSqaa8qacaWGibaapaqabaaak8qacaGL OaGaayzkaaaacaGLOaGaayzkaaWdamaaCaaaleqabaWdbiaaigdacq GHsislcqaHdpWCaaGcdaqadaWdaeaapeGaamyya8aadaWgaaWcbaWd biaadIeacaWGgbGaamisaaWdaeqaaaGcpeGaayjkaiaawMcaa8aada ahaaWcbeqaa8qacaWGRbGaeyOeI0YaaeWaa8aabaWdbiabeo8aZjab gkHiTiaaigdaaiaawIcacaGLPaaaaaGcdaqadaWdaeaapeWaaSaaa8 aabaWdbiaadUgaa8aabaWdbiaadUgacqGHsisldaqadaWdaeaapeGa eq4WdmNaeyOeI0IaaGymaaGaayjkaiaawMcaaaaaaiaawIcacaGLPa aaaaa@808B@ (32)
V FFH = n F ϕ E H P H σ−1 ( σ σ−1 w F ( 1+λ ) τ H ) 1−σ ( a FFH ) k−( σ−1 ) ( k k−( σ−1 ) ) MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr 0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaabaaaaaaaaape GaamOva8aadaWgaaWcbaWdbiaadAeacaWGgbGaamisaaWdaeqaaOWd biabg2da9iaad6gapaWaaSbaaSqaa8qacaWGgbaapaqabaGcpeGaai iOaiabew9aMjaacckacaWGfbWdamaaBaaaleaapeGaamisaaWdaeqa aOWdbiaadcfapaWaaSbaaSqaa8qacaWGibaapaqabaGcdaahaaWcbe qaa8qacqaHdpWCcqGHsislcaaIXaaaaOWaaeWaa8aabaWdbmaalaaa paqaa8qacqaHdpWCa8aabaWdbiabeo8aZjabgkHiTiaaigdaaaGaam 4Da8aadaWgaaWcbaWdbiaadAeaa8aabeaak8qacaGGGcWaaeWaa8aa baWdbiaaigdacqGHRaWkcqaH7oaBaiaawIcacaGLPaaacaGGGcGaeq iXdq3damaaBaaaleaapeGaamisaaWdaeqaaaGcpeGaayjkaiaawMca a8aadaahaaWcbeqaa8qacaaIXaGaeyOeI0Iaeq4WdmhaaOWaaeWaa8 aabaWdbiaadggapaWaaSbaaSqaa8qacaWGgbGaamOraiaadIeaa8aa beaaaOWdbiaawIcacaGLPaaapaWaaWbaaSqabeaapeGaam4Aaiabgk HiTmaabmaapaqaa8qacqaHdpWCcqGHsislcaaIXaaacaGLOaGaayzk aaaaaOWaaeWaa8aabaWdbmaalaaapaqaa8qacaWGRbaapaqaa8qaca WGRbGaeyOeI0YaaeWaa8aabaWdbiabeo8aZjabgkHiTiaaigdaaiaa wIcacaGLPaaaaaaacaGLOaGaayzkaaaaaa@76B1@ (33)
P H =( σ σ−1 ) ( k k−( σ−1 ) ) 1 1−σ ( n H ( w H ( 1+λ ) ) 1−σ [ ( a HHH ) k−( σ−1 ) − ( a HFH ) k−( σ−1 ) ]+ n H ( w H τ F τ H +λ w F τ H ) 1−σ ( a HFH ) k−( σ−1 ) + n F ( w F ( 1+λ ) τ H ) 1−σ ( a FFH ) k−( σ−1 ) ) 1 1−σ MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr 0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaabaaaaaaaaape Gaamiua8aadaWgaaWcbaWdbiaadIeaa8aabeaak8qacqGH9aqpdaqa daWdaeaapeWaaSaaa8aabaWdbiabeo8aZbWdaeaapeGaeq4WdmNaey OeI0IaaGymaaaaaiaawIcacaGLPaaadaqadaWdaeaapeWaaSaaa8aa baWdbiaadUgaa8aabaWdbiaadUgacqGHsisldaqadaWdaeaapeGaeq 4WdmNaeyOeI0IaaGymaaGaayjkaiaawMcaaaaaaiaawIcacaGLPaaa paWaaWbaaSqabeaapeWaaSaaa8aabaWdbiaaigdaa8aabaWdbiaaig dacqGHsislcqaHdpWCaaaaaOWaaeWaa8aabaWdbiaad6gapaWaaSba aSqaa8qacaWGibaapaqabaGcpeGaaiiOamaabmaapaqaa8qacaWG3b WdamaaBaaaleaapeGaamisaaWdaeqaaOWdbiaacckadaqadaWdaeaa peGaaGymaiabgUcaRiabeU7aSbGaayjkaiaawMcaaaGaayjkaiaawM caa8aadaahaaWcbeqaa8qacaaIXaGaeyOeI0Iaeq4WdmhaaOWaamWa a8aabaWdbmaabmaapaqaa8qacaWGHbWdamaaBaaaleaapeGaamisai aadIeacaWGibaapaqabaaak8qacaGLOaGaayzkaaWdamaaCaaaleqa baWdbiaadUgacqGHsisldaqadaWdaeaapeGaeq4WdmNaeyOeI0IaaG ymaaGaayjkaiaawMcaaaaakiabgkHiTmaabmaapaqaa8qacaWGHbWd amaaBaaaleaapeGaamisaiaadAeacaWGibaapaqabaaak8qacaGLOa GaayzkaaWdamaaCaaaleqabaWdbiaadUgacqGHsisldaqadaWdaeaa peGaeq4WdmNaeyOeI0IaaGymaaGaayjkaiaawMcaaaaaaOGaay5wai aaw2faaiabgUcaRiaad6gapaWaaSbaaSqaa8qacaWGibaapaqabaGc peGaaiiOamaabmaapaqaa8qacaWG3bWdamaaBaaaleaapeGaamisaa WdaeqaaOWdbiaacckacqaHepaDpaWaaSbaaSqaa8qacaWGgbaapaqa baGcpeGaaiiOaiabes8a09aadaWgaaWcbaWdbiaadIeaa8aabeaak8 qacqGHRaWkcqaH7oaBcaWG3bWdamaaBaaaleaapeGaamOraaWdaeqa aOWdbiaacckacqaHepaDpaWaaSbaaSqaa8qacaWGibaapaqabaaak8 qacaGLOaGaayzkaaWdamaaCaaaleqabaWdbiaaigdacqGHsislcqaH dpWCaaGcdaqadaWdaeaapeGaamyya8aadaWgaaWcbaWdbiaadIeaca WGgbGaamisaaWdaeqaaaGcpeGaayjkaiaawMcaa8aadaahaaWcbeqa a8qacaWGRbGaeyOeI0YaaeWaa8aabaWdbiabeo8aZjabgkHiTiaaig daaiaawIcacaGLPaaaaaGccqGHRaWkcaWGUbWdamaaBaaaleaapeGa amOraaWdaeqaaOWdbiaacckadaqadaWdaeaapeGaam4Da8aadaWgaa WcbaWdbiaadAeaa8aabeaak8qacaGGGcWaaeWaa8aabaWdbiaaigda cqGHRaWkcqaH7oaBaiaawIcacaGLPaaacaGGGcGaeqiXdq3damaaBa aaleaapeGaamisaaWdaeqaaaGcpeGaayjkaiaawMcaa8aadaahaaWc beqaa8qacaaIXaGaeyOeI0Iaeq4WdmhaaOWaaeWaa8aabaWdbiaadg gapaWaaSbaaSqaa8qacaWGgbGaamOraiaadIeaa8aabeaaaOWdbiaa wIcacaGLPaaapaWaaWbaaSqabeaapeGaam4AaiabgkHiTmaabmaapa qaa8qacqaHdpWCcqGHsislcaaIXaaacaGLOaGaayzkaaaaaOGaaeiO aaGaayjkaiaawMcaa8aadaahaaWcbeqaa8qadaWcaaWdaeaapeGaaG ymaaWdaeaapeGaaGymaiabgkHiTiabeo8aZbaaaaaaaa@D094@ (34)
V FFF = n F ϕ E F P F σ−1 ( σ σ−1 w F ( 1+λ ) ) 1−σ ( a FFF ) k−( σ−1 ) ( k k−( σ−1 ) ) MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr 0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaabaaaaaaaaape GaamOva8aadaWgaaWcbaWdbiaadAeacaWGgbGaamOraaWdaeqaaOWd biabg2da9iaad6gapaWaaSbaaSqaa8qacaWGgbaapaqabaGcpeGaai iOaiabew9aMjaacckacaWGfbWdamaaBaaaleaapeGaamOraaWdaeqa aOWdbiaadcfapaWaaSbaaSqaa8qacaWGgbaapaqabaGcdaahaaWcbe qaa8qacqaHdpWCcqGHsislcaaIXaaaaOWaaeWaa8aabaWdbmaalaaa paqaa8qacqaHdpWCa8aabaWdbiabeo8aZjabgkHiTiaaigdaaaGaam 4Da8aadaWgaaWcbaWdbiaadAeaa8aabeaak8qacaGGGcWaaeWaa8aa baWdbiaaigdacqGHRaWkcqaH7oaBaiaawIcacaGLPaaaaiaawIcaca GLPaaapaWaaWbaaSqabeaapeGaaGymaiabgkHiTiabeo8aZbaakmaa bmaapaqaa8qacaWGHbWdamaaBaaaleaapeGaamOraiaadAeacaWGgb aapaqabaaak8qacaGLOaGaayzkaaWdamaaCaaaleqabaWdbiaadUga cqGHsisldaqadaWdaeaapeGaeq4WdmNaeyOeI0IaaGymaaGaayjkai aawMcaaaaakmaabmaapaqaa8qadaWcaaWdaeaapeGaam4AaaWdaeaa peGaam4AaiabgkHiTmaabmaapaqaa8qacqaHdpWCcqGHsislcaaIXa aacaGLOaGaayzkaaaaaaGaayjkaiaawMcaaaaa@727F@ (35)
V HFF = n H ϕ E F P F σ−1 ( σ σ−1 ( w H τ F +λ w F ) ) 1−σ ( a HFF ) k−( σ−1 ) ( k k−( σ−1 ) ) MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr 0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaabaaaaaaaaape GaamOva8aadaWgaaWcbaWdbiaadIeacaWGgbGaamOraaWdaeqaaOWd biabg2da9iaad6gapaWaaSbaaSqaa8qacaWGibaapaqabaGcpeGaai iOaiabew9aMjaacckacaWGfbWdamaaBaaaleaapeGaamOraaWdaeqa aOWdbiaadcfapaWaaSbaaSqaa8qacaWGgbaapaqabaGcdaahaaWcbe qaa8qacqaHdpWCcqGHsislcaaIXaaaaOWaaeWaa8aabaWdbmaalaaa paqaa8qacqaHdpWCa8aabaWdbiabeo8aZjabgkHiTiaaigdaaaGaai iOamaabmaapaqaa8qacaWG3bWdamaaBaaaleaapeGaamisaaWdaeqa aOWdbiaacckacqaHepaDpaWaaSbaaSqaa8qacaWGgbaapaqabaGcpe Gaey4kaSIaeq4UdWMaam4Da8aadaWgaaWcbaWdbiaadAeaa8aabeaa aOWdbiaawIcacaGLPaaaaiaawIcacaGLPaaapaWaaWbaaSqabeaape GaaGymaiabgkHiTiabeo8aZbaakmaabmaapaqaa8qacaWGHbWdamaa BaaaleaapeGaamisaiaadAeacaWGgbaapaqabaaak8qacaGLOaGaay zkaaWdamaaCaaaleqabaWdbiaadUgacqGHsisldaqadaWdaeaapeGa eq4WdmNaeyOeI0IaaGymaaGaayjkaiaawMcaaaaakmaabmaapaqaa8 qadaWcaaWdaeaapeGaam4AaaWdaeaapeGaam4AaiabgkHiTmaabmaa paqaa8qacqaHdpWCcqGHsislcaaIXaaacaGLOaGaayzkaaaaaaGaay jkaiaawMcaaaaa@782F@ (36)
V HHF = n H ϕ E F P F σ−1 ( σ σ−1 w H ( 1+λ ) τ F ) 1−σ [ ( a HHF ) k−( σ−1 ) − ( a HFF ) k−( σ−1 ) ]( k k−( σ−1 ) ) MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr 0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaabaaaaaaaaape GaamOva8aadaWgaaWcbaWdbiaadIeacaWGibGaamOraaWdaeqaaOWd biabg2da9iaad6gapaWaaSbaaSqaa8qacaWGibaapaqabaGcpeGaai iOaiabew9aMjaacckacaWGfbWdamaaBaaaleaapeGaamOraaWdaeqa aOWdbiaadcfapaWaaSbaaSqaa8qacaWGgbaapaqabaGcdaahaaWcbe qaa8qacqaHdpWCcqGHsislcaaIXaaaaOWaaeWaa8aabaWdbmaalaaa paqaa8qacqaHdpWCa8aabaWdbiabeo8aZjabgkHiTiaaigdaaaGaam 4Da8aadaWgaaWcbaWdbiaadIeaa8aabeaak8qacaGGGcWaaeWaa8aa baWdbiaaigdacqGHRaWkcqaH7oaBaiaawIcacaGLPaaacaGGGcGaeq iXdq3damaaBaaaleaapeGaamOraaWdaeqaaaGcpeGaayjkaiaawMca a8aadaahaaWcbeqaa8qacaaIXaGaeyOeI0Iaeq4WdmhaaOWaamWaa8 aabaWdbmaabmaapaqaa8qacaWGHbWdamaaBaaaleaapeGaamisaiaa dIeacaWGgbaapaqabaaak8qacaGLOaGaayzkaaWdamaaCaaaleqaba WdbiaadUgacqGHsisldaqadaWdaeaapeGaeq4WdmNaeyOeI0IaaGym aaGaayjkaiaawMcaaaaakiabgkHiTmaabmaapaqaa8qacaWGHbWdam aaBaaaleaapeGaamisaiaadAeacaWGgbaapaqabaaak8qacaGLOaGa ayzkaaWdamaaCaaaleqabaWdbiaadUgacqGHsisldaqadaWdaeaape Gaeq4WdmNaeyOeI0IaaGymaaGaayjkaiaawMcaaaaaaOGaay5waiaa w2faamaabmaapaqaa8qadaWcaaWdaeaapeGaam4AaaWdaeaapeGaam 4AaiabgkHiTmaabmaapaqaa8qacqaHdpWCcqGHsislcaaIXaaacaGL OaGaayzkaaaaaaGaayjkaiaawMcaaaaa@865C@ (37)
P F =( σ σ−1 ) ( k k−( σ−1 ) ) 1 1−σ ( n F ( w F ( 1+λ ) ) 1−σ ( a FFF ) k−( σ−1 ) + n H ( w H τ F +λ w F ) 1−σ ( a HFF ) k−( σ−1 ) + n H ( w H ( 1+λ ) τ F ) 1−σ [ ( a HHF ) k−( σ−1 ) − ( a HFF ) k−( σ−1 ) ] ) 1 1−σ MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr 0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaabaaaaaaaaape Gaamiua8aadaWgaaWcbaWdbiaadAeaa8aabeaak8qacqGH9aqpdaqa daWdaeaapeWaaSaaa8aabaWdbiabeo8aZbWdaeaapeGaeq4WdmNaey OeI0IaaGymaaaaaiaawIcacaGLPaaadaqadaWdaeaapeWaaSaaa8aa baWdbiaadUgaa8aabaWdbiaadUgacqGHsisldaqadaWdaeaapeGaeq 4WdmNaeyOeI0IaaGymaaGaayjkaiaawMcaaaaaaiaawIcacaGLPaaa paWaaWbaaSqabeaapeWaaSaaa8aabaWdbiaaigdaa8aabaWdbiaaig dacqGHsislcqaHdpWCaaaaaOWaaeWaa8aabaWdbiaad6gapaWaaSba aSqaa8qacaWGgbaapaqabaGcpeGaaiiOamaabmaapaqaa8qacaWG3b WdamaaBaaaleaapeGaamOraaWdaeqaaOWdbiaacckadaqadaWdaeaa peGaaGymaiabgUcaRiabeU7aSbGaayjkaiaawMcaaaGaayjkaiaawM caa8aadaahaaWcbeqaa8qacaaIXaGaeyOeI0Iaeq4WdmhaaOWaaeWa a8aabaWdbiaadggapaWaaSbaaSqaa8qacaWGgbGaamOraiaadAeaa8 aabeaaaOWdbiaawIcacaGLPaaapaWaaWbaaSqabeaapeGaam4Aaiab gkHiTmaabmaapaqaa8qacqaHdpWCcqGHsislcaaIXaaacaGLOaGaay zkaaaaaOGaey4kaSIaamOBa8aadaWgaaWcbaWdbiaadIeaa8aabeaa k8qacaGGGcWaaeWaa8aabaWdbiaadEhapaWaaSbaaSqaa8qacaWGib aapaqabaGcpeGaaiiOaiabes8a09aadaWgaaWcbaWdbiaadAeaa8aa beaak8qacqGHRaWkcqaH7oaBcaWG3bWdamaaBaaaleaapeGaamOraa WdaeqaaaGcpeGaayjkaiaawMcaa8aadaahaaWcbeqaa8qacaaIXaGa eyOeI0Iaeq4WdmhaaOWaaeWaa8aabaWdbiaadggapaWaaSbaaSqaa8 qacaWGibGaamOraiaadAeaa8aabeaaaOWdbiaawIcacaGLPaaapaWa aWbaaSqabeaapeGaam4AaiabgkHiTmaabmaapaqaa8qacqaHdpWCcq GHsislcaaIXaaacaGLOaGaayzkaaaaaOGaey4kaSIaamOBa8aadaWg aaWcbaWdbiaadIeaa8aabeaak8qacaGGGcWaaeWaa8aabaWdbiaadE hapaWaaSbaaSqaa8qacaWGibaapaqabaGcpeGaaiiOamaabmaapaqa a8qacaaIXaGaey4kaSIaeq4UdWgacaGLOaGaayzkaaGaaiiOaiabes 8a09aadaWgaaWcbaWdbiaadAeaa8aabeaaaOWdbiaawIcacaGLPaaa paWaaWbaaSqabeaapeGaaGymaiabgkHiTiabeo8aZbaakmaadmaapa qaa8qadaqadaWdaeaapeGaamyya8aadaWgaaWcbaWdbiaadIeacaWG ibGaamOraaWdaeqaaaGcpeGaayjkaiaawMcaa8aadaahaaWcbeqaa8 qacaWGRbGaeyOeI0YaaeWaa8aabaWdbiabeo8aZjabgkHiTiaaigda aiaawIcacaGLPaaaaaGccqGHsisldaqadaWdaeaapeGaamyya8aada WgaaWcbaWdbiaadIeacaWGgbGaamOraaWdaeqaaaGcpeGaayjkaiaa wMcaa8aadaahaaWcbeqaa8qacaWGRbGaeyOeI0YaaeWaa8aabaWdbi abeo8aZjabgkHiTiaaigdaaiaawIcacaGLPaaaaaaakiaawUfacaGL DbaacaqGGcaacaGLOaGaayzkaaWdamaaCaaaleqabaWdbmaalaaapa qaa8qacaaIXaaapaqaa8qacaaIXaGaeyOeI0Iaeq4Wdmhaaaaaaaa@C834@ (38)
2.5.3 Sales and Prices as a Function of Unit Labor Requirements, the Distribution of Productivities’ Shape Parameter, and Z
Next, we can rewrite equations (31) through (38) in terms of the ratio of the cutoff unit labor requirements for the different supply chains and relative wages, using common terms Z H MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr 0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaabaaaaaaaaape GaamOwa8aadaWgaaWcbaWdbiaadIeaa8aabeaaaaa@3812@ and Z F MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr 0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaabaaaaaaaaape GaamOwa8aadaWgaaWcbaWdbiaadAeaa8aabeaaaaa@3810@ to simplify the notation.
V HHH = n H Z H ( 1+λ ) 1−σ [ 1− ( a HFH a HHH ) k−( σ−1 ) ] MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr 0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaabaaaaaaaaape GaamOva8aadaWgaaWcbaWdbiaadIeacaWGibGaamisaaWdaeqaaOWd biabg2da9iaad6gapaWaaSbaaSqaa8qacaWGibaapaqabaGcpeGaai iOaiaadQfapaWaaSbaaSqaa8qacaWGibaapaqabaGcpeGaaiiOamaa bmaapaqaa8qacaaIXaGaey4kaSIaeq4UdWgacaGLOaGaayzkaaWdam aaCaaaleqabaWdbiaaigdacqGHsislcqaHdpWCaaGcdaWadaWdaeaa peGaaGymaiabgkHiTmaabmaapaqaa8qadaWcaaWdaeaapeGaamyya8 aadaWgaaWcbaWdbiaadIeacaWGgbGaamisaaWdaeqaaaGcbaWdbiaa dggapaWaaSbaaSqaa8qacaWGibGaamisaiaadIeaa8aabeaaaaaak8 qacaGLOaGaayzkaaWdamaaCaaaleqabaWdbiaadUgacqGHsisldaqa daWdaeaapeGaeq4WdmNaeyOeI0IaaGymaaGaayjkaiaawMcaaaaaaO Gaay5waiaaw2faaaaa@5E74@ (39)
V HFH = n H Z H ( τ F τ H +λ w F w H τ H ) 1−σ ( a HFH a HHH ) k−( σ−1 ) MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr 0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaabaaaaaaaaape GaamOva8aadaWgaaWcbaWdbiaadIeacaWGgbGaamisaaWdaeqaaOWd biabg2da9iaad6gapaWaaSbaaSqaa8qacaWGibaapaqabaGcpeGaai iOaiaadQfapaWaaSbaaSqaa8qacaWGibaapaqabaGcpeWaaeWaa8aa baWdbiabes8a09aadaWgaaWcbaWdbiaadAeaa8aabeaak8qacaGGGc GaeqiXdq3damaaBaaaleaapeGaamisaaWdaeqaaOWdbiabgUcaRiab eU7aSnaalaaapaqaa8qacaWG3bWdamaaBaaaleaapeGaamOraaWdae qaaaGcbaWdbiaadEhapaWaaSbaaSqaa8qacaWGibaapaqabaaaaOWd biaacckacqaHepaDpaWaaSbaaSqaa8qacaWGibaapaqabaaak8qaca GLOaGaayzkaaWdamaaCaaaleqabaWdbiaaigdacqGHsislcqaHdpWC aaGcdaqadaWdaeaapeWaaSaaa8aabaWdbiaadggapaWaaSbaaSqaa8 qacaWGibGaamOraiaadIeaa8aabeaaaOqaa8qacaWGHbWdamaaBaaa leaapeGaamisaiaadIeacaWGibaapaqabaaaaaGcpeGaayjkaiaawM caa8aadaahaaWcbeqaa8qacaWGRbGaeyOeI0YaaeWaa8aabaWdbiab eo8aZjabgkHiTiaaigdaaiaawIcacaGLPaaaaaaaaa@68CF@ (40)
V FFH = n F Z H ( w F w H ( 1+λ ) τ H ) 1−σ ( a FFH a HHH ) k−( σ−1 ) MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr 0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaabaaaaaaaaape GaamOva8aadaWgaaWcbaWdbiaadAeacaWGgbGaamisaaWdaeqaaOWd biabg2da9iaad6gapaWaaSbaaSqaa8qacaWGgbaapaqabaGcpeGaai iOaiaadQfapaWaaSbaaSqaa8qacaWGibaapaqabaGcpeWaaeWaa8aa baWdbmaalaaapaqaa8qacaWG3bWdamaaBaaaleaapeGaamOraaWdae qaaaGcbaWdbiaadEhapaWaaSbaaSqaa8qacaWGibaapaqabaaaaOWd biaacckadaqadaWdaeaapeGaaGymaiabgUcaRiabeU7aSbGaayjkai aawMcaaiaacckacqaHepaDpaWaaSbaaSqaa8qacaWGibaapaqabaaa k8qacaGLOaGaayzkaaWdamaaCaaaleqabaWdbiaaigdacqGHsislcq aHdpWCaaGcdaqadaWdaeaapeWaaSaaa8aabaWdbiaadggapaWaaSba aSqaa8qacaWGgbGaamOraiaadIeaa8aabeaaaOqaa8qacaWGHbWdam aaBaaaleaapeGaamisaiaadIeacaWGibaapaqabaaaaaGcpeGaayjk aiaawMcaa8aadaahaaWcbeqaa8qacaWGRbGaeyOeI0YaaeWaa8aaba Wdbiabeo8aZjabgkHiTiaaigdaaiaawIcacaGLPaaaaaaaaa@6522@ (41)
Z H = ϕ E H ( n H ( 1+λ ) 1−σ [ 1− ( a HFH a HHH ) k−( σ−1 ) ]+ n H ( τ F τ H +λ w F w H τ H ) 1−σ ( a HFH a HHH ) k−( σ−1 ) + n F ( w F w H ( 1+λ ) τ H ) 1−σ ( a FFH a HHH ) k−( σ−1 ) ) −1 MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr 0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaabaaaaaaaaape GaamOwa8aadaWgaaWcbaWdbiaadIeaa8aabeaak8qacqGH9aqpcaGG GcGaeqy1dyMaaiiOaiaadweapaWaaSbaaSqaa8qacaWGibaapaqaba GcpeWaaeWaa8aabaWdbiaad6gapaWaaSbaaSqaa8qacaWGibaapaqa baGcpeGaaiiOamaabmaapaqaa8qacaaIXaGaey4kaSIaeq4UdWgaca GLOaGaayzkaaWdamaaCaaaleqabaWdbiaaigdacqGHsislcqaHdpWC aaGcdaWadaWdaeaapeGaaGymaiabgkHiTmaabmaapaqaa8qadaWcaa WdaeaapeGaamyya8aadaWgaaWcbaWdbiaadIeacaWGgbGaamisaaWd aeqaaaGcbaWdbiaadggapaWaaSbaaSqaa8qacaWGibGaamisaiaadI eaa8aabeaaaaaak8qacaGLOaGaayzkaaWdamaaCaaaleqabaWdbiaa dUgacqGHsisldaqadaWdaeaapeGaeq4WdmNaeyOeI0IaaGymaaGaay jkaiaawMcaaaaaaOGaay5waiaaw2faaiabgUcaRiaad6gapaWaaSba aSqaa8qacaWGibaapaqabaGcpeGaaiiOamaabmaapaqaa8qacqaHep aDpaWaaSbaaSqaa8qacaWGgbaapaqabaGcpeGaaiiOaiabes8a09aa daWgaaWcbaWdbiaadIeaa8aabeaak8qacqGHRaWkcqaH7oaBdaWcaa WdaeaapeGaam4Da8aadaWgaaWcbaWdbiaadAeaa8aabeaaaOqaa8qa caWG3bWdamaaBaaaleaapeGaamisaaWdaeqaaaaak8qacaGGGcGaeq iXdq3damaaBaaaleaapeGaamisaaWdaeqaaaGcpeGaayjkaiaawMca a8aadaahaaWcbeqaa8qacaaIXaGaeyOeI0Iaeq4WdmhaaOWaaeWaa8 aabaWdbmaalaaapaqaa8qacaWGHbWdamaaBaaaleaapeGaamisaiaa dAeacaWGibaapaqabaaakeaapeGaamyya8aadaWgaaWcbaWdbiaadI eacaWGibGaamisaaWdaeqaaaaaaOWdbiaawIcacaGLPaaapaWaaWba aSqabeaapeGaam4AaiabgkHiTmaabmaapaqaa8qacqaHdpWCcqGHsi slcaaIXaaacaGLOaGaayzkaaaaaOGaey4kaSIaamOBa8aadaWgaaWc baWdbiaadAeaa8aabeaak8qacaGGGcWaaeWaa8aabaWdbmaalaaapa qaa8qacaWG3bWdamaaBaaaleaapeGaamOraaWdaeqaaaGcbaWdbiaa dEhapaWaaSbaaSqaa8qacaWGibaapaqabaaaaOWdbiaacckadaqada WdaeaapeGaaGymaiabgUcaRiabeU7aSbGaayjkaiaawMcaaiaaccka cqaHepaDpaWaaSbaaSqaa8qacaWGibaapaqabaaak8qacaGLOaGaay zkaaWdamaaCaaaleqabaWdbiaaigdacqGHsislcqaHdpWCaaGcdaqa daWdaeaapeWaaSaaa8aabaWdbiaadggapaWaaSbaaSqaa8qacaWGgb GaamOraiaadIeaa8aabeaaaOqaa8qacaWGHbWdamaaBaaaleaapeGa amisaiaadIeacaWGibaapaqabaaaaaGcpeGaayjkaiaawMcaa8aada ahaaWcbeqaa8qacaWGRbGaeyOeI0YaaeWaa8aabaWdbiabeo8aZjab gkHiTiaaigdaaiaawIcacaGLPaaaaaGccaqGGcaacaGLOaGaayzkaa WdamaaCaaaleqabaWdbiabgkHiTiaaigdaaaaaaa@BA73@ (42)
V FFF = n F Z F ( w F w H ( 1+λ ) ) 1−σ MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr 0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaabaaaaaaaaape GaamOva8aadaWgaaWcbaWdbiaadAeacaWGgbGaamOraaWdaeqaaOWd biabg2da9iaad6gapaWaaSbaaSqaa8qacaWGgbaapaqabaGcpeGaai iOaiaacckacaWGAbWdamaaBaaaleaapeGaamOraaWdaeqaaOWdbmaa bmaapaqaa8qadaWcaaWdaeaapeGaam4Da8aadaWgaaWcbaWdbiaadA eaa8aabeaaaOqaa8qacaWG3bWdamaaBaaaleaapeGaamisaaWdaeqa aaaak8qacaGGGcWaaeWaa8aabaWdbiaaigdacqGHRaWkcqaH7oaBai aawIcacaGLPaaaaiaawIcacaGLPaaapaWaaWbaaSqabeaapeGaaGym aiabgkHiTiabeo8aZbaaaaa@517D@ (43)
V HFF = n H Z F ( τ F +λ w F w H ) 1−σ ( a HFF a FFF ) k−( σ−1 ) MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr 0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaabaaaaaaaaape GaamOva8aadaWgaaWcbaWdbiaadIeacaWGgbGaamOraaWdaeqaaOWd biabg2da9iaad6gapaWaaSbaaSqaa8qacaWGibaapaqabaGcpeGaai iOaiaacckacaWGAbWdamaaBaaaleaapeGaamOraaWdaeqaaOWdbmaa bmaapaqaa8qacqaHepaDpaWaaSbaaSqaa8qacaWGgbaapaqabaGcpe Gaey4kaSIaeq4UdW2aaSaaa8aabaWdbiaadEhapaWaaSbaaSqaa8qa caWGgbaapaqabaaakeaapeGaam4Da8aadaWgaaWcbaWdbiaadIeaa8 aabeaaaaaak8qacaGLOaGaayzkaaWdamaaCaaaleqabaWdbiaaigda cqGHsislcqaHdpWCaaGcdaqadaWdaeaapeWaaSaaa8aabaWdbiaadg gapaWaaSbaaSqaa8qacaWGibGaamOraiaadAeaa8aabeaaaOqaa8qa caWGHbWdamaaBaaaleaapeGaamOraiaadAeacaWGgbaapaqabaaaaa GcpeGaayjkaiaawMcaa8aadaahaaWcbeqaa8qacaWGRbGaeyOeI0Ya aeWaa8aabaWdbiabeo8aZjabgkHiTiaaigdaaiaawIcacaGLPaaaaa aaaa@6193@ (44)
V HHF = n H Z F ( ( 1+λ ) τ F ) 1−σ [ ( a HHF a FFF ) k−( σ−1 ) − ( a HFF a FFF ) k−( σ−1 ) ] MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr 0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaabaaaaaaaaape GaamOva8aadaWgaaWcbaWdbiaadIeacaWGibGaamOraaWdaeqaaOWd biabg2da9iaad6gapaWaaSbaaSqaa8qacaWGibaapaqabaGcpeGaai iOaiaacckacaWGAbWdamaaBaaaleaapeGaamOraaWdaeqaaOWdbmaa bmaapaqaa8qacaGGGcWaaeWaa8aabaWdbiaaigdacqGHRaWkcqaH7o aBaiaawIcacaGLPaaacaGGGcGaeqiXdq3damaaBaaaleaapeGaamOr aaWdaeqaaaGcpeGaayjkaiaawMcaa8aadaahaaWcbeqaa8qacaaIXa GaeyOeI0Iaeq4WdmhaaOWaamWaa8aabaWdbmaabmaapaqaa8qadaWc aaWdaeaapeGaamyya8aadaWgaaWcbaWdbiaadIeacaWGibGaamOraa WdaeqaaaGcbaWdbiaadggapaWaaSbaaSqaa8qacaWGgbGaamOraiaa dAeaa8aabeaaaaaak8qacaGLOaGaayzkaaWdamaaCaaaleqabaWdbi aadUgacqGHsisldaqadaWdaeaapeGaeq4WdmNaeyOeI0IaaGymaaGa ayjkaiaawMcaaaaakiabgkHiTmaabmaapaqaa8qadaWcaaWdaeaape Gaamyya8aadaWgaaWcbaWdbiaadIeacaWGgbGaamOraaWdaeqaaaGc baWdbiaadggapaWaaSbaaSqaa8qacaWGgbGaamOraiaadAeaa8aabe aaaaaak8qacaGLOaGaayzkaaWdamaaCaaaleqabaWdbiaadUgacqGH sisldaqadaWdaeaapeGaeq4WdmNaeyOeI0IaaGymaaGaayjkaiaawM caaaaaaOGaay5waiaaw2faaaaa@7538@ (45)
Z F =ϕ E F ( n F ( w F w H ( 1+λ ) ) 1−σ + n H ( τ F +λ w F w H ) 1−σ ( a HFF a FFF ) k−( σ−1 ) + n H ( ( 1+λ ) τ F ) 1−σ [ ( a HHF a FFF ) k−( σ−1 ) − ( a HFF a FFF ) k−( σ−1 ) ] ) −1 MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr 0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaabaaaaaaaaape GaamOwa8aadaWgaaWcbaWdbiaadAeaa8aabeaak8qacqGH9aqpcqaH vpGzcaGGGcGaamyra8aadaWgaaWcbaWdbiaadAeaa8aabeaak8qaca GGGcWaaeWaa8aabaWdbiaad6gapaWaaSbaaSqaa8qacaWGgbaapaqa baGcpeGaaiiOamaabmaapaqaa8qadaWcaaWdaeaapeGaam4Da8aada WgaaWcbaWdbiaadAeaa8aabeaaaOqaa8qacaWG3bWdamaaBaaaleaa peGaamisaaWdaeqaaaaak8qacaGGGcWaaeWaa8aabaWdbiaaigdacq GHRaWkcqaH7oaBaiaawIcacaGLPaaaaiaawIcacaGLPaaapaWaaWba aSqabeaapeGaaGymaiabgkHiTiabeo8aZbaakiabgUcaRiaad6gapa WaaSbaaSqaa8qacaWGibaapaqabaGcpeGaaiiOamaabmaapaqaa8qa cqaHepaDpaWaaSbaaSqaa8qacaWGgbaapaqabaGcpeGaey4kaSIaeq 4UdW2aaSaaa8aabaWdbiaadEhapaWaaSbaaSqaa8qacaWGgbaapaqa baaakeaapeGaam4Da8aadaWgaaWcbaWdbiaadIeaa8aabeaaaaaak8 qacaGLOaGaayzkaaWdamaaCaaaleqabaWdbiaaigdacqGHsislcqaH dpWCaaGcdaqadaWdaeaapeWaaSaaa8aabaWdbiaadggapaWaaSbaaS qaa8qacaWGibGaamOraiaadAeaa8aabeaaaOqaa8qacaWGHbWdamaa BaaaleaapeGaamOraiaadAeacaWGgbaapaqabaaaaaGcpeGaayjkai aawMcaa8aadaahaaWcbeqaa8qacaWGRbGaeyOeI0YaaeWaa8aabaWd biabeo8aZjabgkHiTiaaigdaaiaawIcacaGLPaaaaaGccqGHRaWkca WGUbWdamaaBaaaleaapeGaamisaaWdaeqaaOWdbiaacckadaqadaWd aeaapeGaaiiOamaabmaapaqaa8qacaaIXaGaey4kaSIaeq4UdWgaca GLOaGaayzkaaGaaiiOaiabes8a09aadaWgaaWcbaWdbiaadAeaa8aa beaaaOWdbiaawIcacaGLPaaapaWaaWbaaSqabeaapeGaaGymaiabgk HiTiabeo8aZbaakmaadmaapaqaa8qadaqadaWdaeaapeWaaSaaa8aa baWdbiaadggapaWaaSbaaSqaa8qacaWGibGaamisaiaadAeaa8aabe aaaOqaa8qacaWGHbWdamaaBaaaleaapeGaamOraiaadAeacaWGgbaa paqabaaaaaGcpeGaayjkaiaawMcaa8aadaahaaWcbeqaa8qacaWGRb GaeyOeI0YaaeWaa8aabaWdbiabeo8aZjabgkHiTiaaigdaaiaawIca caGLPaaaaaGccqGHsisldaqadaWdaeaapeWaaSaaa8aabaWdbiaadg gapaWaaSbaaSqaa8qacaWGibGaamOraiaadAeaa8aabeaaaOqaa8qa caWGHbWdamaaBaaaleaapeGaamOraiaadAeacaWGgbaapaqabaaaaa GcpeGaayjkaiaawMcaa8aadaahaaWcbeqaa8qacaWGRbGaeyOeI0Ya aeWaa8aabaWdbiabeo8aZjabgkHiTiaaigdaaiaawIcacaGLPaaaaa aakiaawUfacaGLDbaacaqGGcaacaGLOaGaayzkaaWdamaaCaaaleqa baWdbiabgkHiTiaaigdaaaaaaa@B416@ (46)
2.6 Effect of Import Costs on the Value of Trade Flows
Finally, we use the equilibrium conditions in equations (39) through (46) to calculate the percentage changes in economic outcomes in response to the increase in import costs in Home. For this calculation, we assume that wages and aggregate expenditure levels do not change with the industry-specific increase in import costs. Producer prices also do not change, since they are at a constant mark-up over marginal costs. This partial equilibrium approach is an appropriate simplifying assumption for an industry that is small relative to the aggregate national economies. In this case, and assuming that there is no change in the costs of importing into Foreign ( τ ^ F =0 MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr 0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaabaaaaaaaaape GafqiXdq3dayaajaWaaSbaaSqaa8qacaWGgbaapaqabaGcpeGaeyyp a0JaaGimaaaa@3AE0@ ), there is no change in the global chains that supply Foreign.
V ^ FFF = V ^ HFF = V ^ HHF = Z ^ F =0 MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr 0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaabaaaaaaaaape GabmOva8aagaqcamaaBaaaleaapeGaamOraiaadAeacaWGgbaapaqa baGcpeGaeyypa0JabmOva8aagaqcamaaBaaaleaapeGaamisaiaadA eacaWGgbaapaqabaGcpeGaeyypa0JabmOva8aagaqcamaaBaaaleaa peGaamisaiaadIeacaWGgbaapaqabaGcpeGaeyypa0JabmOwa8aaga qcamaaBaaaleaapeGaamOraaWdaeqaaOWdbiabg2da9iaaicdaaaa@4852@ (47)
On the other hand, there are adjustments in the global value chains that supply Home, represented in percentage changes in equations (48) through (53). To simplify the notation, we define Home market shares β ijH ≡ V ijH /( V HFH + V HHH + V FFH ) MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr 0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaabaaaaaaaaape GaeqOSdi2damaaBaaaleaapeGaamyAaiaadQgacaWGibaapaqabaGc peGaeyyyIORaamOva8aadaWgaaWcbaWdbiaadMgacaWGQbGaamisaa WdaeqaaOWdbiaac+cadaqadaWdaeaapeGaamOva8aadaWgaaWcbaWd biaadIeacaWGgbGaamisaaWdaeqaaOWdbiabgUcaRiaadAfapaWaaS baaSqaa8qacaWGibGaamisaiaadIeaa8aabeaak8qacqGHRaWkcaWG wbWdamaaBaaaleaapeGaamOraiaadAeacaWGibaapaqabaaak8qaca GLOaGaayzkaaaaaa@4FC8@ for regions i MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr 0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaabaaaaaaaaape GaamyAaaaa@36FA@ and j MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr 0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaabaaaaaaaaape GaamOAaaaa@36FB@ , and the ratios of the cutoff unit labor requirements for supplying Home r ijH ≡ a ijH / a HHH MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr 0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaabaaaaaaaaape GaamOCa8aadaWgaaWcbaWdbiaadMgacaWGQbGaamisaaWdaeqaaOWd biabggMi6kaadggapaWaaSbaaSqaa8qacaWGPbGaamOAaiaadIeaa8 aabeaak8qacaGGVaGaamyya8aadaWgaaWcbaWdbiaadIeacaWGibGa amisaaWdaeqaaaaa@4448@ .[10]
V ^ HHH = Z ^ H −( β HFH β HHH ) ( τ F τ H +λ τ H ( w F w H ) 1+λ ) σ−1 ( k−( σ−1 ) ) r ^ HFH MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr 0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaabaaaaaaaaape GabmOva8aagaqcamaaBaaaleaapeGaamisaiaadIeacaWGibaapaqa baGcpeGaeyypa0JaaiiOaiqadQfapaGbaKaadaWgaaWcbaWdbiaadI eaa8aabeaak8qacqGHsisldaqadaWdaeaapeWaaSaaa8aabaWdbiab ek7aI9aadaWgaaWcbaWdbiaadIeacaWGgbGaamisaaWdaeqaaaGcba Wdbiabek7aI9aadaWgaaWcbaWdbiaadIeacaWGibGaamisaaWdaeqa aaaaaOWdbiaawIcacaGLPaaacaGGGcWaaeWaa8aabaWdbmaalaaapa qaa8qacqaHepaDpaWaaSbaaSqaa8qacaWGgbGaaiiOaaWdaeqaaOWd biabes8a09aadaWgaaWcbaWdbiaadIeaa8aabeaak8qacqGHRaWkcq aH7oaBcaGGGcGaeqiXdq3damaaBaaaleaapeGaamisaaWdaeqaaOWd biaacckadaqadaWdaeaapeWaaSaaa8aabaWdbiaadEhapaWaaSbaaS qaa8qacaWGgbaapaqabaaakeaapeGaam4Da8aadaWgaaWcbaWdbiaa dIeaa8aabeaaaaaak8qacaGLOaGaayzkaaaapaqaa8qacaaIXaGaey 4kaSIaeq4UdWgaaaGaayjkaiaawMcaa8aadaahaaWcbeqaa8qacqaH dpWCcqGHsislcaaIXaaaaOGaaiiOamaabmaapaqaa8qacaWGRbGaey OeI0YaaeWaa8aabaWdbiabeo8aZjabgkHiTiaaigdaaiaawIcacaGL PaaaaiaawIcacaGLPaaacaGGGcGabmOCa8aagaqcamaaBaaaleaape GaamisaiaadAeacaWGibaapaqabaaaaa@7819@ (48)
V ^ HFH = Z ^ H +( 1−σ ) τ ^ H −( k−( σ−1 ) ) r ^ HFH MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr 0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaabaaaaaaaaape GabmOva8aagaqcamaaBaaaleaapeGaamisaiaadAeacaWGibaapaqa baGcpeGaeyypa0JaaiiOaiqadQfapaGbaKaadaWgaaWcbaWdbiaadI eaa8aabeaak8qacqGHRaWkdaqadaWdaeaapeGaaGymaiabgkHiTiab eo8aZbGaayjkaiaawMcaaiqbes8a09aagaqcamaaBaaaleaapeGaam isaaWdaeqaaOWdbiabgkHiTmaabmaapaqaa8qacaWGRbGaeyOeI0Ya aeWaa8aabaWdbiabeo8aZjabgkHiTiaaigdaaiaawIcacaGLPaaaai aawIcacaGLPaaacaGGGcGabmOCa8aagaqcamaaBaaaleaapeGaamis aiaadAeacaWGibaapaqabaaaaa@55A4@ (49)
V ^ FFH = Z ^ H +( 1−σ ) τ ^ H −( k−( σ−1 ) ) r ^ FFH MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr 0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaabaaaaaaaaape GabmOva8aagaqcamaaBaaaleaapeGaamOraiaadAeacaWGibaapaqa baGcpeGaeyypa0JaaiiOaiqadQfapaGbaKaadaWgaaWcbaWdbiaadI eaa8aabeaak8qacqGHRaWkdaqadaWdaeaapeGaaGymaiabgkHiTiab eo8aZbGaayjkaiaawMcaaiqbes8a09aagaqcamaaBaaaleaapeGaam isaaWdaeqaaOWdbiabgkHiTmaabmaapaqaa8qacaWGRbGaeyOeI0Ya aeWaa8aabaWdbiabeo8aZjabgkHiTiaaigdaaiaawIcacaGLPaaaai aawIcacaGLPaaacaGGGcGabmOCa8aagaqcamaaBaaaleaapeGaamOr aiaadAeacaWGibaapaqabaGcpeGaaiiOaaaa@56DE@ (50)
Z ^ H =( k−( σ−1 ) )( β HFH [ ( τ F τ H +λ τ H ( w F w H ) 1+λ ) σ−1 −1 ] r ^ HFH − β FFH r ^ FFH )−( 1−σ )( β HFH + β FFH ) τ ^ H MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr 0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaabaaaaaaaaape GabmOwa8aagaqcamaaBaaaleaapeGaamisaaWdaeqaaOWdbiabg2da 9maabmaapaqaa8qacaWGRbGaeyOeI0YaaeWaa8aabaWdbiabeo8aZj abgkHiTiaaigdaaiaawIcacaGLPaaaaiaawIcacaGLPaaadaqadaWd aeaapeGaeqOSdi2damaaBaaaleaapeGaamisaiaadAeacaWGibaapa qabaGcpeGaaiiOamaadmaapaqaa8qadaqadaWdaeaapeWaaSaaa8aa baWdbiabes8a09aadaWgaaWcbaWdbiaadAeacaGGGcaapaqabaGcpe GaeqiXdq3damaaBaaaleaapeGaamisaaWdaeqaaOWdbiabgUcaRiab eU7aSjaacckacqaHepaDpaWaaSbaaSqaa8qacaWGibaapaqabaGcpe GaaiiOamaabmaapaqaa8qadaWcaaWdaeaapeGaam4Da8aadaWgaaWc baWdbiaadAeaa8aabeaaaOqaa8qacaWG3bWdamaaBaaaleaapeGaam isaaWdaeqaaaaaaOWdbiaawIcacaGLPaaaa8aabaWdbiaaigdacqGH RaWkcqaH7oaBaaaacaGLOaGaayzkaaWdamaaCaaaleqabaWdbiabeo 8aZjabgkHiTiaaigdaaaGccqGHsislcaaIXaaacaGLBbGaayzxaaGa aiiOaiqadkhapaGbaKaadaWgaaWcbaWdbiaadIeacaWGgbGaamisaa WdaeqaaOWdbiabgkHiTiabek7aI9aadaWgaaWcbaWdbiaadAeacaWG gbGaamisaaWdaeqaaOWdbiaacckaceWGYbWdayaajaWaaSbaaSqaa8 qacaWGgbGaamOraiaadIeaa8aabeaaaOWdbiaawIcacaGLPaaacqGH sisldaqadaWdaeaapeGaaGymaiabgkHiTiabeo8aZbGaayjkaiaawM caamaabmaapaqaa8qacqaHYoGypaWaaSbaaSqaa8qacaWGibGaamOr aiaadIeaa8aabeaak8qacqGHRaWkcqaHYoGypaWaaSbaaSqaa8qaca WGgbGaamOraiaadIeaa8aabeaaaOWdbiaawIcacaGLPaaacaGGGcGa aiiOaiqbes8a09aagaqcamaaBaaaleaapeGaamisaaWdaeqaaaaa@916D@ (51)
The cutoff unit labor requirements in equation (12), (14), and (16) imply the following changes in r FFH MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr 0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaabaaaaaaaaape GaamOCa8aadaWgaaWcbaWdbiaadAeacaWGgbGaamisaaWdaeqaaaaa @39C0@ and r HFH MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr 0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaabaaaaaaaaape GaamOCa8aadaWgaaWcbaWdbiaadIeacaWGgbGaamisaaWdaeqaaaaa @39C2@ in response to the increase in import costs:
r ^ FFH =− τ ^ H MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr 0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaabaaaaaaaaape GabmOCa8aagaqcamaaBaaaleaapeGaamOraiaadAeacaWGibaapaqa baGcpeGaeyypa0JaeyOeI0IafqiXdq3dayaajaWaaSbaaSqaa8qaca WGibaapaqabaaaaa@3ED9@ (52)
r ^ HFH =( ( τ F τ H +λ ( w F w H ) τ H ) 1−σ ( 1+λ ) 1−σ − ( τ F τ H +λ ( w F w H ) τ H ) 1−σ ) τ ^ H MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr 0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaabaaaaaaaaape GabmOCa8aagaqcamaaBaaaleaapeGaamisaiaadAeacaWGibaapaqa baGcpeGaeyypa0ZaaeWaa8aabaWdbmaalaaapaqaa8qadaqadaWdae aapeGaeqiXdq3damaaBaaaleaapeGaamOraaWdaeqaaOWdbiaaccka caGGGcGaeqiXdq3damaaBaaaleaapeGaamisaaWdaeqaaOWdbiaacc kacqGHRaWkcqaH7oaBcaGGGcWaaeWaa8aabaWdbmaalaaapaqaa8qa caWG3bWdamaaBaaaleaapeGaamOraaWdaeqaaaGcbaWdbiaadEhapa WaaSbaaSqaa8qacaWGibaapaqabaaaaaGcpeGaayjkaiaawMcaaiaa cckacqaHepaDpaWaaSbaaSqaa8qacaWGibaapaqabaaak8qacaGLOa GaayzkaaWdamaaCaaaleqabaWdbiaaigdacqGHsislcqaHdpWCaaaa k8aabaWdbmaabmaapaqaa8qacaaIXaGaey4kaSIaeq4UdWgacaGLOa GaayzkaaWdamaaCaaaleqabaWdbiaaigdacqGHsislcqaHdpWCaaGc cqGHsisldaqadaWdaeaapeGaeqiXdq3damaaBaaaleaapeGaamOraa WdaeqaaOWdbiaacckacaGGGcGaeqiXdq3damaaBaaaleaapeGaamis aaWdaeqaaOWdbiaacckacqGHRaWkcqaH7oaBcaGGGcWaaeWaa8aaba Wdbmaalaaapaqaa8qacaWG3bWdamaaBaaaleaapeGaamOraaWdaeqa aaGcbaWdbiaadEhapaWaaSbaaSqaa8qacaWGibaapaqabaaaaaGcpe GaayjkaiaawMcaaiaacckacqaHepaDpaWaaSbaaSqaa8qacaWGibaa paqabaaak8qacaGLOaGaayzkaaWdamaaCaaaleqabaWdbiaaigdacq GHsislcqaHdpWCaaaaaaGccaGLOaGaayzkaaGafqiXdq3dayaajaWa aSbaaSqaa8qacaWGibaapaqabaaaaa@83AF@ (53)
The increase in import costs can lead to significant restructuring of the global value chains of the industry, including a change in whether some firms offshore. In the terminology of the literature on trade with firm heterogeneity, there are adjustments on the extensive margin of trade as well as the intensive margin of trade.
2.7 Effect on the Employment of Production Workers in Home
The increase in import costs does not change the value of sales in Foreign ( V HHF MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr 0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaabaaaaaaaaape GaamOva8aadaWgaaWcbaWdbiaadIeacaWGibGaamOraaWdaeqaaaaa @39A6@ and V HFF MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr 0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaabaaaaaaaaape GaamOva8aadaWgaaWcbaWdbiaadIeacaWGgbGaamOraaWdaeqaaaaa @39A4@ ) in the partial equilibrium analysis, but it does change the value of sales in Home ( V HHH MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr 0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaabaaaaaaaaape GaamOva8aadaWgaaWcbaWdbiaadIeacaWGibGaamisaaWdaeqaaaaa @39A8@ and V HFH MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr 0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaabaaaaaaaaape GaamOva8aadaWgaaWcbaWdbiaadIeacaWGgbGaamisaaWdaeqaaaaa @39A6@ ). In the model, the labor income of production workers in the HHH supply chain is a fixed fraction of V HHH MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr 0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaabaaaaaaaaape GaamOva8aadaWgaaWcbaWdbiaadIeacaWGibGaamisaaWdaeqaaaaa @39A8@ , given the fixed mark-up of price over wages.[11]
V HHH =( σ σ−1 ) w H L HHH MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr 0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaabaaaaaaaaape GaaiiOaiaadAfapaWaaSbaaSqaa8qacaWGibGaamisaiaadIeaa8aa beaak8qacqGH9aqpdaqadaWdaeaapeWaaSaaa8aabaWdbiabeo8aZb WdaeaapeGaeq4WdmNaeyOeI0IaaGymaaaaaiaawIcacaGLPaaacaGG GcGaam4Da8aadaWgaaWcbaWdbiaadIeaa8aabeaak8qacaGGGcGaam ita8aadaWgaaWcbaWdbiaadIeacaWGibGaamisaaWdaeqaaaaa@4B27@ (54)
Equation (54) implies the following equation for Home employment of production workers in this purely domestic supply chain:
L HHH = V HHH w H ( σ−1 σ ) MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr 0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaabaaaaaaaaape Gaamita8aadaWgaaWcbaWdbiaadIeacaWGibGaamisaaWdaeqaaOWd biabg2da9maalaaapaqaa8qacaWGwbWdamaaBaaaleaapeGaamisai aadIeacaWGibaapaqabaaakeaapeGaam4Da8aadaWgaaWcbaWdbiaa dIeaa8aabeaaaaGcpeGaaiiOamaabmaapaqaa8qadaWcaaWdaeaape Gaeq4WdmNaeyOeI0IaaGymaaWdaeaapeGaeq4WdmhaaaGaayjkaiaa wMcaaaaa@4928@ (55)
Therefore, the percentage change in Home employment of production workers in the HHH supply chain is equal to the percentage change in V HHH MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr 0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaabaaaaaaaaape GaamOva8aadaWgaaWcbaWdbiaadIeacaWGibGaamisaaWdaeqaaaaa @39A8@ , since wages do not adjust in the partial equilibrium analysis.
L ^ HHH = V ^ HHH MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr 0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaabaaaaaaaaape Gabmita8aagaqcamaaBaaaleaapeGaamisaiaadIeacaWGibaapaqa baGcpeGaeyypa0JabmOva8aagaqcamaaBaaaleaapeGaamisaiaadI eacaWGibaapaqabaaaaa@3E7A@ (56)
Likewise, the labor income of Home production workers in the HFH supply chain is a fixed fraction of revenue in that supply chain, given the fixed mark-ups and the assumption that there are fixed factor proportions in production:
V HFH =( σ σ−1 ) ( w H τ F + λ w F ) τ H L HFH MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr 0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaabaaaaaaaaape GaaiiOaiaadAfapaWaaSbaaSqaa8qacaWGibGaamOraiaadIeaa8aa beaak8qacqGH9aqpdaqadaWdaeaapeWaaSaaa8aabaWdbiabeo8aZb WdaeaapeGaeq4WdmNaeyOeI0IaaGymaaaaaiaawIcacaGLPaaacaGG GcWaaeWaa8aabaWdbiaadEhapaWaaSbaaSqaa8qacaWGibaapaqaba GcpeGaaiiOaiabes8a09aadaWgaaWcbaWdbiaadAeaa8aabeaak8qa cqGHRaWkcaGGGcGaeq4UdWMaaiiOaiaadEhapaWaaSbaaSqaa8qaca WGgbaapaqabaGcpeGaaiiOaaGaayjkaiaawMcaaiaacckacqaHepaD paWaaSbaaSqaa8qacaWGibaapaqabaGcpeGaaiiOaiaacckacaWGmb WdamaaBaaaleaapeGaamisaiaadAeacaWGibaapaqabaaaaa@5E7E@ (57)
Equation (57) implies the following equation for Home employment of production workers in the HFH supply chain:
L HFH = V HFH ( w H τ F + λ w F ) τ H ( σ−1 σ ) MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr 0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaabaaaaaaaaape Gaamita8aadaWgaaWcbaWdbiaadIeacaWGgbGaamisaaWdaeqaaOWd biabg2da9maalaaapaqaa8qacaWGwbWdamaaBaaaleaapeGaamisai aadAeacaWGibaapaqabaaakeaapeWaaeWaa8aabaWdbiaadEhapaWa aSbaaSqaa8qacaWGibaapaqabaGcpeGaaiiOaiabes8a09aadaWgaa WcbaWdbiaadAeaa8aabeaak8qacaGGGcGaey4kaSIaaiiOaiabeU7a SjaacckacaWG3bWdamaaBaaaleaapeGaamOraaWdaeqaaaGcpeGaay jkaiaawMcaaiaacckacqaHepaDpaWaaSbaaSqaa8qacaWGibaapaqa baGcpeGaaiiOaiaacckaaaGaaiiOamaabmaapaqaa8qadaWcaaWdae aapeGaeq4WdmNaeyOeI0IaaGymaaWdaeaapeGaeq4WdmhaaaGaayjk aiaawMcaaaaa@5DA3@ (58)
Therefore, the percentage change in Home employment of production workers in the HFH supply chain is equal to the percentage change in V HFH MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr 0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaabaaaaaaaaape GaamOva8aadaWgaaWcbaWdbiaadIeacaWGgbGaamisaaWdaeqaaaaa @39A6@ minus the percent change in τ H MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr 0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaabaaaaaaaaape GaeqiXdq3damaaBaaaleaapeGaamisaaWdaeqaaaaa@38F8@ .
L ^ HFH = V ^ HFH − τ ^ H MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr 0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaabaaaaaaaaape Gabmita8aagaqcamaaBaaaleaapeGaamisaiaadAeacaWGibaapaqa baGcpeGaeyypa0JabmOva8aagaqcamaaBaaaleaapeGaamisaiaadA eacaWGibaapaqabaGcpeGaeyOeI0IafqiXdq3dayaajaWaaSbaaSqa a8qacaWGibaapaqabaaaaa@4279@ (59)
According to the accounting identity in equation (60), the percentage change in total employment of production workers in Home is a share-weighted average of the percentage changes in the production workers employed in the two affected supply chains.
L ^ H =( L HHH L H )( L ^ HHH )+( L HFH L H ) ( L ^ HFH ) MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr 0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaabaaaaaaaaape Gabmita8aagaqcamaaBaaaleaapeGaamisaaWdaeqaaOWdbiabg2da 9maabmaapaqaa8qadaWcaaWdaeaapeGaamita8aadaWgaaWcbaWdbi aadIeacaWGibGaamisaaWdaeqaaaGcbaWdbiaadYeapaWaaSbaaSqa a8qacaWGibaapaqabaaaaaGcpeGaayjkaiaawMcaamaabmaapaqaa8 qaceWGmbWdayaajaWaaSbaaSqaa8qacaWGibGaamisaiaadIeaa8aa beaaaOWdbiaawIcacaGLPaaacqGHRaWkdaqadaWdaeaapeWaaSaaa8 aabaWdbiaadYeapaWaaSbaaSqaa8qacaWGibGaamOraiaadIeaa8aa beaaaOqaa8qacaWGmbWdamaaBaaaleaapeGaamisaaWdaeqaaaaaaO WdbiaawIcacaGLPaaacaGGGcWaaeWaa8aabaWdbiqadYeapaGbaKaa daWgaaWcbaWdbiaadIeacaWGgbGaamisaaWdaeqaaaGcpeGaayjkai aawMcaaaaa@5528@ (60)
Equation (61) substitutes equations (56) and (59) into equation (60).
L ^ H =( L HHH L H )( V ^ HHH )+( L HFH L H ) ( V ^ HFH − τ ^ H ) MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr 0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaabaaaaaaaaape Gabmita8aagaqcamaaBaaaleaapeGaamisaaWdaeqaaOWdbiabg2da 9maabmaapaqaa8qadaWcaaWdaeaapeGaamita8aadaWgaaWcbaWdbi aadIeacaWGibGaamisaaWdaeqaaaGcbaWdbiaadYeapaWaaSbaaSqa a8qacaWGibaapaqabaaaaaGcpeGaayjkaiaawMcaamaabmaapaqaa8 qaceWGwbWdayaajaWaaSbaaSqaa8qacaWGibGaamisaiaadIeaa8aa beaaaOWdbiaawIcacaGLPaaacqGHRaWkdaqadaWdaeaapeWaaSaaa8 aabaWdbiaadYeapaWaaSbaaSqaa8qacaWGibGaamOraiaadIeaa8aa beaaaOqaa8qacaWGmbWdamaaBaaaleaapeGaamisaaWdaeqaaaaaaO WdbiaawIcacaGLPaaacaGGGcWaaeWaa8aabaWdbiqadAfapaGbaKaa daWgaaWcbaWdbiaadIeacaWGgbGaamisaaWdaeqaaOWdbiabgkHiTi qbes8a09aagaqcamaaBaaaleaapeGaamisaaWdaeqaaaGcpeGaayjk aiaawMcaaaaa@593F@ (61)
Finally, we approximate the employment shares in equation (61) using the status quo values of several industry statistics.[12]
L ^ H = ω H ( 1− α H ) ( V ^ HHH )+( α H γ H δ H ) ( V ^ HFH − τ ^ H ) MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr 0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaabaaaaaaaaape Gabmita8aagaqcamaaBaaaleaapeGaamisaaWdaeqaaOWdbiabg2da 9iabeM8a39aadaWgaaWcbaWdbiaadIeaa8aabeaak8qacaGGGcWaae Waa8aabaWdbiaaigdacqGHsislcqaHXoqypaWaaSbaaSqaa8qacaWG ibaapaqabaaak8qacaGLOaGaayzkaaGaaiiOamaabmaapaqaa8qace WGwbWdayaajaWaaSbaaSqaa8qacaWGibGaamisaiaadIeaa8aabeaa aOWdbiaawIcacaGLPaaacqGHRaWkdaqadaWdaeaapeGaeqySde2dam aaBaaaleaapeGaamisaaWdaeqaaOWdbiaacckacqaHZoWzpaWaaSba aSqaa8qacaWGibaapaqabaGcpeGaaiiOaiabes7aK9aadaWgaaWcba WdbiaadIeaa8aabeaaaOWdbiaawIcacaGLPaaacaGGGcWaaeWaa8aa baWdbiqadAfapaGbaKaadaWgaaWcbaWdbiaadIeacaWGgbGaamisaa WdaeqaaOWdbiabgkHiTiqbes8a09aagaqcamaaBaaaleaapeGaamis aaWdaeqaaaGcpeGaayjkaiaawMcaaaaa@623B@ (62)
The parameter ω H MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr 0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaabaaaaaaaaape GaeqyYdC3damaaBaaaleaapeGaamisaaWdaeqaaaaa@3900@ represents the share of Home’s domestic shipments (non-exports) that are competing directly with imports in the Home market, and the parameter α H MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr 0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaabaaaaaaaaape GaeqySde2damaaBaaaleaapeGaamisaaWdaeqaaaaa@38D2@ represents the share of Home production that is exported. Our default assumption is that ω H MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr 0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaabaaaaaaaaape GaeqyYdC3damaaBaaaleaapeGaamisaaWdaeqaaaaa@3900@ is equal to 1− α H MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr 0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaabaaaaaaaaape GaaGymaiabgkHiTiabeg7aH9aadaWgaaWcbaWdbiaadIeaa8aabeaa aaa@3A7A@ and all Home production is import-competing. However, we consider alternative assumptions in our sensitivity analysis of the model. The parameter γ H MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr 0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaabaaaaaaaaape Gaeq4SdC2damaaBaaaleaapeGaamisaaWdaeqaaaaa@38DA@ represents the share of exports from Home that are intermediate inputs into production within the same industry, and the parameter δ H MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr 0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaabaaaaaaaaape GaeqiTdq2damaaBaaaleaapeGaamisaaWdaeqaaaaa@38D8@ represents the share of these exported intermediate products that return Home after further manufacturing in Foreign.
The net employment effect in equation (62) combines a positive effect on Home employment due to the increased demand for domestic shipments and a negative effect on Home employment due to the reduced demand for Home exports for further manufacture in Foreign and shipment back to the Home market.
The model shows that the tariff has different effects on different supply chains. The increased import costs lead consumers to substitute to purely domestic producers, increasing employment in that supply chain. When a tariff is imposed ( τ ^ H >0 MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr 0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaabaaaaaaaaape GafqiXdq3dayaajaWaaSbaaSqaa8qacaWGibaapaqabaGcpeGaeyOp a4JaaGimaaaa@3AE4@ ), the model predicts that there will be an increase in domestic shipments ( V ^ HHH >0 MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr 0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaabaaaaaaaaape GabmOva8aagaqcamaaBaaaleaapeGaamisaiaadIeacaWGibaapaqa baGcpeGaeyOpa4JaaGimaaaa@3B94@ ) and associated labor demand ( L ^ HHH >0 MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr 0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaabaaaaaaaaape Gabmita8aagaqcamaaBaaaleaapeGaamisaiaadIeacaWGibaapaqa baGcpeGaeyOpa4JaaGimaaaa@3B8A@ ). However, the tariff increases costs in supply chains that involve offshoring, and this has a negative effect on Home employment. More formally, the tariff leads to a reduction in exports of intermediates for reimport ( V ^ HFH <0 MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr 0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaabaaaaaaaaape GabmOva8aagaqcamaaBaaaleaapeGaamisaiaadAeacaWGibaapaqa baGcpeGaeyipaWJaaGimaaaa@3B8E@ ) and associated labor demand ( L ^ HFH <0 MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr 0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaabaaaaaaaaape Gabmita8aagaqcamaaBaaaleaapeGaamisaiaadAeacaWGibaapaqa baGcpeGaeyipaWJaaGimaaaa@3B84@ ).
3.1 Example Simulation of the Model
We use simple numerical simulations to illustrate the magnitudes of the net employment effects for different values of the industry data that are inputs of the model. As a benchmark case, we assume that α H =0.50 MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr 0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaabaaaaaaaaape GaeqySde2damaaBaaaleaapeGaamisaaWdaeqaaOWdbiabg2da9iaa icdacaGGUaGaaGynaiaaicdaaaa@3CD7@ , β HFH =1/3 MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr 0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaabaaaaaaaaape GaeqOSdi2damaaBaaaleaapeGaamisaiaadAeacaWGibaapaqabaGc peGaeyypa0JaaGymaiaac+cacaaIZaaaaa@3DB7@ , β FFH =1/3 MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr 0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaabaaaaaaaaape GaeqOSdi2damaaBaaaleaapeGaamOraiaadAeacaWGibaapaqabaGc peGaeyypa0JaaGymaiaac+cacaaIZaaaaa@3DB5@ , β HHH =1/3 MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr 0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaabaaaaaaaaape GaeqOSdi2damaaBaaaleaapeGaamisaiaadIeacaWGibaapaqabaGc peGaeyypa0JaaGymaiaac+cacaaIZaaaaa@3DB9@ , γ H =0.9 MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr 0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaabaaaaaaaaape Gaeq4SdC2damaaBaaaleaapeGaamisaaWdaeqaaOWdbiabg2da9iaa icdacaGGUaGaaGyoaaaa@3C29@ , δ H =1/4 MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr 0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaabaaaaaaaaape GaeqiTdq2damaaBaaaleaapeGaamisaaWdaeqaaOWdbiabg2da9iaa igdacaGGVaGaaGinaaaa@3C24@ , ω H =1 MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr 0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaabaaaaaaaaape GaeqyYdC3damaaBaaaleaapeGaamisaaWdaeqaaOWdbiabg2da9iaa igdaaaa@3ADB@ , σ=5 MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr 0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaabaaaaaaaaape Gaeq4WdmNaeyypa0JaaGynaaaa@3994@ , λ=1/2 MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr 0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaabaaaaaaaaape Gaeq4UdWMaeyypa0JaaGymaiaac+cacaaIYaaaaa@3AF0@ , τ H =1 MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr 0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaabaaaaaaaaape GaeqiXdq3damaaBaaaleaapeGaamisaaWdaeqaaOWdbiabg2da9iaa igdaaaa@3AD3@ , τ F =1 MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr 0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaabaaaaaaaaape GaeqiXdq3damaaBaaaleaapeGaamOraaWdaeqaaOWdbiabg2da9iaa igdaaaa@3AD1@ , w F w H =1/2 MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr 0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaabaaaaaaaaape WaaSaaa8aabaWdbiaadEhapaWaaSbaaSqaa8qacaWGgbaapaqabaaa keaapeGaam4Da8aadaWgaaWcbaWdbiaadIeaa8aabeaaaaGcpeGaey ypa0JaaGymaiaac+cacaaIYaaaaa@3DE3@ , and k=5 MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr 0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaabaaaaaaaaape Gaam4Aaiabg2da9iaaiwdaaaa@38C1@ .
The tariff has different effects on different supply chains. These effects are summarized in table 1. The tariff increases costs in the HFH and FFH supply chains. The sales of the competing HHH supply chain increase. This leads to an increase in the number of Home production workers in HHH and a decrease in the number of U.S. production workers in HFH. There is no Home employment in FFH, so there would be no impact there.
Table 1: Effect of the Tariff on Different Supply Chains
Location of Intermediate Production
Location of Final Production
Supply Chain in the Model?
Change in Domestic Employment
5 FHH
6 FHF
7 FFH
If τ ^ H =0.05 MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr 0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaabaaaaaaaaape GafqiXdq3dayaajaWaaSbaaSqaa8qacaWGibaapaqabaGcpeGaeyyp a0JaaGimaiaac6cacaaIWaGaaGynaaaa@3D0D@ (a 5% increase in import prices), then there is a 21 percent increase in the domestic shipments of Home producers ( V ^ HHH =0.2132 MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr 0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaabaaaaaaaaape GabmOva8aagaqcamaaBaaaleaapeGaamisaiaadIeacaWGibaapaqa baGcpeGaeyypa0JaaGimaiaac6cacaaIYaGaaGymaiaaiodacaaIYa aaaa@3F34@ ) and an 11 percent increase in associated production workers ( L ^ HHH =0.1066 MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr 0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaabaaaaaaaaape Gabmita8aagaqcamaaBaaaleaapeGaamisaiaadIeacaWGibaapaqa baGcpeGaeyypa0JaaGimaiaac6cacaaIXaGaaGimaiaaiAdacaaI2a aaaa@3F2F@ ). There is a 13 percent decline in imports from offshored final production ( V ^ HFH =−0.1299 MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr 0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaabaaaaaaaaape GabmOva8aagaqcamaaBaaaleaapeGaamisaiaadAeacaWGibaapaqa baGcpeGaeyypa0JaeyOeI0IaaGimaiaac6cacaaIXaGaaGOmaiaaiM dacaaI5aaaaa@402C@ ) and a 2 percent decline in associated production workers ( L ^ HFH =−0.0202 MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr 0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaabaaaaaaaaape Gabmita8aagaqcamaaBaaaleaapeGaamisaiaadAeacaWGibaapaqa baGcpeGaeyypa0JaeyOeI0IaaGimaiaac6cacaaIWaGaaGOmaiaaic dacaaIYaaaaa@4011@ ). There is an almost 9 percent net increase in the total number of production workers in the industry in Home ( L ^ H =0.0864 MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr 0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaabaaaaaaaaape Gabmita8aagaqcamaaBaaaleaapeGaamisaaWdaeqaaOWdbiabg2da 9iaaicdacaGGUaGaaGimaiaaiIdacaaI2aGaaGinaaaa@3D9A@ .)
If all Home exports were final products that did not return to the Home market, then we would have only the positive effect from the increase in domestic shipments. However, since there is significant trade in intermediate products and offshoring in the example, then there is also a negative effect of the increase in import costs on the number of Home production workers.
The values of different parameters affect the net change in industry employment. Table 2 lists the effects of each of the model’s parameters on net employment changes in the industry.
Table 2: Effects of the Model Parameters
Effect of an Increase in the Parameter on the Net Employment Change
α H MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr 0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaabaaaaaaaaape GaeqySde2damaaBaaaleaapeGaamisaaWdaeqaaaaa@38D2@
Home export share
β HHH MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr 0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaabaaaaaaaaape GaeqOSdi2damaaBaaaleaapeGaamisaiaadIeacaWGibaapaqabaaa aa@3A6E@
Domestic market share of supply chain HHH
β HFH MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr 0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaabaaaaaaaaape GaeqOSdi2damaaBaaaleaapeGaamisaiaadAeacaWGibaapaqabaaa aa@3A6C@
Domestic market share of supply chain HFH
β FFH MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr 0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaabaaaaaaaaape GaeqOSdi2damaaBaaaleaapeGaamOraiaadAeacaWGibaapaqabaaa aa@3A6A@
Domestic market share of supply chain FFH
γ H MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr 0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaabaaaaaaaaape Gaeq4SdC2damaaBaaaleaapeGaamisaaWdaeqaaaaa@38DA@
Share of exports that are used as intermediate inputs
δ H MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr 0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaabaaaaaaaaape GaeqiTdq2damaaBaaaleaapeGaamisaaWdaeqaaaaa@38D8@
Share of Foreign production that re-enters the Home market
k MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr 0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaabaaaaaaaaape Gaam4Aaaaa@36FC@
Pareto shape parameter
σ MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr 0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaabaaaaaaaaape Gaeq4Wdmhaaa@37CF@
Consumer elasticity of substitution between each firms’ variety
Relative unit labor requirement in the final production stage
w F w H MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr 0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaabaaaaaaaaape WaaSaaa8aabaWdbiaadEhapaWaaSbaaSqaa8qacaWGgbaapaqabaGc peGaaeiOaaWdaeaapeGaam4Da8aadaWgaaWcbaWdbiaadIeaa8aabe aaaaaaaa@3BDB@
Ratio of wages in Foreign and Home
ω H MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr 0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaabaaaaaaaaape GaeqyYdC3damaaBaaaleaapeGaamisaaWdaeqaaaaa@3900@
Share of Home’s domestic
shipments that are import-competing
There is a specific reason why each of the parameters affects employment impacts in the manner it does. The net effect on Home employment in the industry is greater if its export share ( α H MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr 0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaabaaaaaaaaape GaeqySde2damaaBaaaleaapeGaamisaaWdaeqaaaaa@38D2@ ) is small, because the negative effect on exports accounts for a small share of total industry employment. It is also greater if the import penetration ratios ( β HFH MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr 0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaabaaaaaaaaape GaeqOSdi2damaaBaaaleaapeGaamisaiaadAeacaWGibaapaqabaaa aa@3A6C@ and β FFH MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr 0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaabaaaaaaaaape GaeqOSdi2damaaBaaaleaapeGaamOraiaadAeacaWGibaapaqabaaa aa@3A6A@ ) are large or the domestic share is small ( β HHH ) MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr 0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaabaaaaaaaaape GaeqOSdi2damaaBaaaleaapeGaamisaiaadIeacaWGibaapaqabaGc peGaaiykaaaa@3B35@ , because the tariff provides more protection for the domestic industry, and this has a positive impact on industry employment. The net effect is greater if the share of exports that are used as intermediate inputs ( γ H MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr 0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaabaaaaaaaaape Gaeq4SdC2damaaBaaaleaapeGaamisaaWdaeqaaaaa@38DA@ ) and the share of these exports that returns to Home ( δ H MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr 0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaabaaaaaaaaape GaeqiTdq2damaaBaaaleaapeGaamisaaWdaeqaaaaa@38D8@ ) are small, because the negative employment effect from the reduction in exports is less important. The net effect is greater if the Pareto shape parameter of the productivity distribution ( k MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr 0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaabaaaaaaaaape Gaam4Aaaaa@36FC@ ) is large and the elasticity of substitution ( σ MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr 0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaabaaaaaaaaape Gaeq4Wdmhaaa@37CF@ ) is small, because trade flows are more sensitive to prices. It is greater if the relative unit labor requirement in the final stage of production (λ) is small or the ratio of the wage in Foreign to wage in Home ( w F / w H MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr 0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaabaaaaaaaaape Gaam4Da8aadaWgaaWcbaWdbiaadAeaa8aabeaak8qacaGGVaGaam4D a8aadaWgaaWcbaWdbiaadIeaa8aabeaaaaa@3B1D@ ) is large, because under either of those conditions, the role for offshoring final production is less important. Finally, the net effect on industry employment is greater if the share of Home’s domestic shipments that are import-competing ( ω H MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr 0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaabaaaaaaaaape GaeqyYdC3damaaBaaaleaapeGaamisaaWdaeqaaaaa@3900@ ) is large, because this magnifies the positive effect of protection on employment from domestic shipments.
The net change in industry employment also depends on the time period being examined. The model addresses the firms’ decisions about whether to participate in different markets and where to locate the various stages of production. However, these adjustments on the extensive margins of trade do not occur immediately, and so the model can be best described as a model of long-run effects. However, the model can be easily converted to one of short-run effects, by assuming that there are no adjustments on the extensive margins and that there are no changes in the relative cut-off rules in equations (52) and (53). Omitting adjustments on the extensive margin reduces the absolute value of the modeled percentage net changes in industry employment. This implies that the net changes in employment are magnified by the adjustments on the extensive margins.
Applying the model to a specific industry requires the following industry data:
· Market shares in the Home market
· Share of Home production that is exported
· Share of Home domestic shipments that are substitutes for the imported products
· Share of exports that are intermediate inputs subject to further processing
· Share of exports of intermediate inputs that return to Home
· Magnitude of initial variable trade costs
· Relative unit labor requirements of final production
· Wage in Foreign relative to the wage in Home
· Elasticity parameters σ MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr 0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaabaaaaaaaaape Gaeq4Wdmhaaa@37CF@ and k MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr 0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaabaaaaaaaaape Gaam4Aaaaa@36FC@ [13]
In this paper, we have developed an economic model of barriers to international trade in an industry with global value chains. We have derived from the model a relatively simple formula for employment effects that incorporates industry data on trade and production shares. The model demonstrates that there are positive and negative employment effects of impeding trade in global value chain, even within the same industry. The magnitudes of these effects, and even the sign of the net effect, will vary industry-by-industry depending on the data, and specifically the pattern of global value chains.
While the model focuses on employment effects, it can also be used to estimate the impact on the profitability of firms in the industry, for example to determine which firms are likely to gain or lose from the tariff. The sensitivity of each firm’s profits to the tariff depends on the firm’s global value chain, and specifically on the shares of V HHH MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr 0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaabaaaaaaaaape GaamOva8aadaWgaaWcbaWdbiaadIeacaWGibGaamisaaWdaeqaaaaa @39A8@ , V HFH MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr 0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaabaaaaaaaaape GaamOva8aadaWgaaWcbaWdbiaadIeacaWGgbGaamisaaWdaeqaaaaa @39A6@ , and V FFH MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr 0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaabaaaaaaaaape GaamOva8aadaWgaaWcbaWdbiaadAeacaWGgbGaamisaaWdaeqaaaaa @39A4@ in its global sales, since the firm’s variable profits are proportional to its revenue in the model. If the firm supplies the Home market from all domestic production (an HHH supply chain), then it would unambiguously gain from the increase in import costs. On the other hand, if the firm supplies the Home market by offshoring some of its production (HFH and FFH supply chains), then it would generally lose from the increase in import costs. If the firm utilizes a mix of these three supply chains, then gains or losses will depend on the weights in the mix.
Extensions of the model that include additional countries and stages of production could be especially useful for evaluating the economic effects of changes in industry-specific rules of origin in trade agreements or for looking at industries which complex value chains that cross international borders many times before reaching consumers.
Antras, P. and E. Helpman (2004): “Global Sourcing.” Journal of Political Economy 112(3): 552-80.
Di Giovanni, J., A.A. Levchenko, and R. Rancière (2011): “Power Laws in Firm Size and Openness to Trade: Measurement and Implications.” Journal of International Economics 85: 42-52.
Feenstra, R.C. and G. Hanson (1999): “The Impact of Outsourcing and High-Technology Capital on Wages: Estimates for the U.S., 1979-1990” Quarterly Journal of Economics 114(3): 907-940.
Feenstra, R. C. (2008): “Offshoring in the Global Economy.” Ohlin Lecture at the Stockholm School of Economics.
Feenstra, R.C. (2016): Advanced International Trade, 2nd Edition. Princeton, NJ: Princeton University Press.
Grossman, G.M. and E. Helpman (2005): “Outsourcing in a Global Economy.” Review of Economic Studies 72(1): 135-59.
Grossman, G.M. and E. Rossi-Hansberg (2008): “Trading Tasks: A Simple Theory of Offshoring.” American Economic Review 98 (5): 1978-97.
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[1] The model does not try to quantify the potential reductions in employment in other sectors of the economy if workers are drawn to a newly protected industry.
[2] Wright (2014) applies this model to a 2001-2007 panel dataset that includes a broad set of U.S. manufacturing industries. His measure of offshoring is the share of a U.S. industry’s intermediate inputs that are imported. He finds that a reduction in trade costs that increases offshoring had a negative direct displacement effect on U.S. employment but also a positive productivity effect.[2] He finds that the two effects mostly offset each other.
[3] Antras and Helpman (2004) and Grossman and Helpman (2005) are also important contributions to the literature on offshoring, though they focus on ownership structure and incomplete contracts rather than labor market impacts.
[4] The model focuses on the location of the different stages of production and the pattern of trade. It does not address ownership issues, e.g., the distinction between vertical integration and outsourcing of the production stages.
[5] In the context of our partial equilibrium model, there is no effect on supply chains that serve the foreign market.
[6] We assume that the firms have the technological capability to produce these varieties, but they may not find it profitable to participate in the market, given their firm-specific productivity. Their market participation decisions are explicitly addressed in the model.
[7] The gross trade cost factors are equal to one plus ad valorem charges.
[8] This assumption about inputs affects how we calculate the changes in the number of production workers.
[9] This assumption of complementarity in production is common in the trade literature on offshoring, including Feenstra and Hanson (1999).
[10] There are similar definitions for the market shares and ratios of cutoff levels for the other supply chains.
[11] This is the case because we have assumed that the fixed and variable trade costs involve a combination of materials and labor from outside of the industry and non-production workers within the industry, but not production workers within the industry.
[12] We assume that firms’ labor productivity is the same in their exports and domestic shipments.
[13] One data source for the Pareto shape parameter is Di Giovanni, Levchenko, and Rancière (2011). The authors estimate the parameter based on firm-level data on non-exporting French companies.