United States

Department

of Agriculture

www.ers.usda.gov

A Report from the Economic Research Service

Abstract

Before 2000, the United States was the largest supplier of bone-in chicken to South 

Africa. But in 2000, alarmed by rapidly rising imports, the South African Government 

imposed antidumping duties on U.S. bone-in chicken, following which U.S. exports 

to South Africa fell almost to zero. Faced with possible suspension of trade preferences under the recently renewed African Growth and Opportunity Act (AGOA), 

South Africa agreed in June 2015 to allow a quota of 65,000 tons of U.S. chicken legs 

at a tariff rate of 37 percent. The first U.S. chicken entered the South African market 

in March 2016. This study analyzes the long-term impact of the removal of the antidumping duty. Findings suggest that with the 37-percent tariff, but without the quota, 

South Africa would import close to 71,000 tons of U.S. bone-in chicken, only slightly 

above the quota now in effect. Longrun negative impacts on the South African poultry 

industry are minimal. 

Keywords: South Africa, poultry, U.S. poultry exports, leg quarters, antidumping 

duties, AGOA.

Acknowledgments

The authors thank the following technical peer reviewers: Getachew Nigatu, U.S. 

Department of Agriculture, Economic Research Service; Sharon Sydow, USDA, 

Office of the Chief Economist; Jamilah Cassagnol, USDA, Foreign Agricultural 

Service; and H.L. Goodwin, Jr., University of Arkansas. The report was reviewed and 

cleared by Seth Meyer of USDA’s World Agricultural Outlook Board. Thanks also to 

ERS editor Mark Farrell and ERS designer Lori A. Fields.

AES-96

November 2016

Nancy Cochrane, James Hansen, and Ralph Seeley

Poultry Production and Trade 

in the Republic of South Africa: 

A Look at Alternative Trade 

Policy Scenarios

Approved by USDA’s 

World Agricultural 

Outlook Board
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Poultry Production and Trade in the Republic of South Africa: A Look at Alternative Trade Policy Scenarios, AES-96

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Contents

Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1

Background: South African Poultry Output Fails To Keep Pace With Demand . . . . . . . . . . . . . . . . . . . 3

The Structure of South African Poultry Trade . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6

Antidumping Duties Froze U.S. Poultry Out of the South African Market . . . . . . . . . . . . . . . . . . . . . . . 8

Long-Term Outlook: Poultry Imports Will Continue To Grow . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10

Scenario Analysis: Reduction of Duties on U.S. Bone-In Exports . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13

Conclusions: Outlook Remains Uncertain . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15

References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16

Appendix A: What Does AGOA Mean for South Africa? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18

Appendix B: The Country-Commodity Linked System (CCLS) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21

Appendix C: Armington-Cline Model Description . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22

Elasticities. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22

Linear-nonlinear model equations. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23

Prices. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23

Base trade levels used to calculate linear responsiveness. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23

Export and import expansion. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24

Export and import substitution. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24

Export and import totals. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25

Derivation of simple substitution response from Armington demand equation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25
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Poultry Production and Trade 

in the Republic of South Africa: 

A Look at Alternative Trade 

Policy Scenarios 

Introduction

Consumer demand for poultry meat more than doubled in the past 20 years in South Africa, 

reflecting rising income and population growth. Domestic poultry output grew more slowly and 

imports increased. During the last 15 years, the South African Government used a variety of 

trade restricting measures on the United States and other exporters to limit imports and support 

the domestic poultry industry. While restrictive trade policies have changed the mix of countries 

exporting to South Africa, they have not prevented import growth. Internal production constraints 

limit the growth of South Africa’s domestic industry, and the 2015/16 USDA baseline projects 

continued import growth over the next decade. 

Before 2000, the United States was the largest supplier of leg quarters to the South African market. 

In 1997, the United States shipped 37,192 tons under the affected tariff lines, and South Africa 

was the sixth-largest U.S. market.1 But in 2001, South Africa imposed antidumping duties on 

U.S. chicken leg quarters, after which U.S. exports dropped nearly to zero. In 2010, U.S. exports 

of bone-in chicken to South Africa began to rise, reaching 9,665 tons in 2012. In response, South 

Africa raised the antidumping duty in 2013, once again shutting off U.S. exports.

The U.S. poultry industry argued that the method used by South Africa to justify the antidumping 

duties violated the rules of the World Trade Organization (WTO). The method used by the South 

Africans was a calculation of a weighted cost of production that ignored the fact that white meat 

in the United States commands a higher price than dark meat. The United States did not take the 

case to the WTO. Instead, the U.S. poultry industry pursued bilateral negotiations in the context of 

the 2015 debate over the renewal of the African Growth and Opportunity Act (AGOA) in the U.S. 

Congress. Under pressure from the U.S. poultry industry, Congress threatened to exclude South 

Africa from AGOA trade preferences unless South Africa provided greater market access to U.S. 

poultry. South Africa had a strong interest in remaining in the AGOA, which has provided duty-free 

access for significant exports of wine and citrus fruit, as well as automobiles and other manufactured 

products, to the United States. (See Appendix A: What Does AGOA Mean for South Africa?) 

AGOA was renewed for an additional 10 years in June 2015, with the proviso that the United States 

Trade Representative (USTR) undertake an out-of-cycle review of South African trade policies 

1The bulk of U.S. poultry exports to South Africa before 2000 fell under two 10-digit tariff codes: 0207.14.0010 

(leg quarters) and 0207.14.0090 (other chicken portions not including offals). Tariff codes are harmonized across countries 

to the 6-digit level, but each country has the option of supplementing the codes with greater detail to meet its own needs. 

The United States adopted a 10-digit code system and began using it for U.S. trade on January 1, 1989. South Africa uses 

8-digit codes, and South African trade statistics classify chicken under both the U.S. codes as 0207.14.90.
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and report on its compliance with AGOA trade requirements. The review raised concerns about 

continued lack of access for U.S. poultry and other meats. Finally, in January 2016, following an 

intense round of negotiations, South Africa agreed to allow up to 65,000 tons of U.S. chicken legs at 

the Most Favored Nation (MFN) tariff of 37 percent, with exports over that quota still subject to the 

antidumping duty. The first shipment of U.S. chicken arrived in South Africa in March 2016. 

Research results presented in this report suggest that even without the quota, U.S. exports at the 

MFN rate would not rise very much above the 65,000-ton quota because U.S. poultry now faces stiff 

competition from the European Union (EU) as a result of the Trade, Development and Co-operation 

Agreement signed by South Africa and the EU in 1999. The agreement established a free trade area 

that covers 90 percent of bilateral trade between the EU and South Africa, and the full liberalization of trade went into effect in 2012. Among other goods traded between the two countries, tariffs 

on poultry imported from the EU were eliminated. Immediately, there was a significant rise in 

poultry imports from the EU, particularly for bone-in portions, which rose from 1,487 tons in 2011 

to 62,000 tons in 2012 and 113,000 tons in 2013. The EU’s rising share has come principally at the 

expense of Brazil, whose exports remained subject to the MFN tariffs, all of which were raised in 

2013 (the new tariffs are still within the maximum allowed under WTO rules).

What is likely to happen to the South African poultry industry now that U.S. poultry is once again 

entering the country? The industry faces a number of internal constraints to expansion, including 

high feed costs, labor costs, labor regulations, infrastructure weaknesses, limited electricity and 

water supplies, and a lack of a supportive environment for productivity-enhancing investments 

(NAMC, 2015b). A severe drought has hampered South Africa’s poultry market by reducing the 

corn crop by 40 percent and increasing feed prices. USDA baseline projections (presented below) 

suggest that throughout the next decade, under normal weather conditions, South Africa’s industry 

will continue to be unable to meet demand through domestic production. As in the past, trade policies can shift the source, but not the existence, of poultry imports. 

In this report, we present a set of alternative trade-policy scenarios of liberalized imports, using an 

Armington-Cline spreadsheet-based model to simulate a reduction in the tariff on U.S. chicken. We 

then use the 2015/16 USDA Baseline modeling framework to analyze the impact of the resulting 

increase in imports on the entire agricultural sector. We model two scenarios:

• Elimination of the antidumping duty on U.S. exports of leg quarters. The 2015/16 USDA 

Baseline model assumes that the antidumping duty remains in place. Under this scenario, U.S. 

exports enter South Africa at the most favored nation (MFN) tariff rate of 37 percent, but without 

a quota. Imports from all other partners would enter at the duty rates they are now subject to.

• U.S. leg quarters enter South Africa at the MFN rate, again without a quota, and duty-free 

access for EU leg quarters is eliminated, so that EU legs also face the MFN tariff. This is a 

measure that the South African poultry industry has recently requested. This scenario can also 

reveal the market share that the United States has lost as a result of this agreement.

The scenarios presented in this analysis do not represent a full liberalization of South African 

poultry trade. We focus on one tariff line—bone-in chicken—and both scenarios reduce the tariff 

to the MFN rate of 37 percent, not to zero. Our results suggest that this tariff change will not seriously impact the South African poultry sector. It is quite possible that a reduction of all tariffs to 

zero would have a more serious impact. But the focus of this analysis is the long term impacts of the 

recent opening of the South African market to U.S. poultry; we do not address the implications of 

full trade liberalization.
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Background: South African Poultry Output 

Fails To Keep Pace With Demand

Like many middle-income countries, South Africa’s rising income has been accompanied by significant increases in per capita meat consumption (fig. 1). Poultry meat, being cheaper than other meats, 

accounts for most of the growth. Per capita poultry consumption more than doubled from 17 kilograms in 1994/95 to 40 in 2013/14 (DAFF, 2016). In recent years, beef consumption has also risen, 

but poultry consumption remains dominant. Consumption of other meats has remained constant.

Domestic output has also increased rapidly, but has failed to keep pace with demand growth, 

resulting in rising imports (fig. 2). The South African Poultry Association (SAPA) has long advocated greater protection against imports. Significant protection has been put in place, including 

imposing antidumping duties on U.S. leg quarters in 2001, as well as increases in tariffs on poultry 

supplied by other exporters such as Brazil and Argentina (see details in the next section). Despite 

increasing levels of protection, imports have continued to rise. In 2000, the country was nearly selfsufficient in poultry production; by 2015 imports made up 22 percent of domestic consumption.

Figure 1

Per capita poultry consumption rises with per capita income

Kilograms 2005 U.S. dollars

Source: USDA, Economic Research Service, using data from USDA’s Foreign Agricultural Service Production, 

Supply, and Distribution (PS&D) database.

0

1,000

2,000

3,000

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6,000

7,000

8,000

0

10

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30

40

50

60

70

1970/71 1975/76 1980/81 1985/86 1990/91 1995/96 2000/01 2005/06 2010/2011

Poultry Beef Pork Lamb and goat Per capita income, real
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The South African poultry industry is highly concentrated—two large firms control slightly over 

50 percent of the market, while five medium-sized firms control 31 percent (NAMC, 2015b). The 

industry is considered to be technically efficient, with feed conversion ratios reported to be around 

1.6, comparable to other major producing countries (NAMC, 2015a), but South African producers 

face high production costs and have difficulty competing with lower priced imports. 

The highest cost faced by poultry producers is feed. Feed makes up 70 percent of total production 

costs (NAMC, 2015b). Feed costs are high because of the need to import soybean meal and highly 

variable corn yields and prices (NAMC, 2015f). As a result of large corn yield fluctuations, South 

Africa alternates between being a net exporter and a net importer of corn. In most years, the country 

is a net exporter, but when yields are extremely low, it becomes a net importer. Prices thus fluctuate 

between “export parity” and “import parity.” Import parity is the international price plus the cost of 

unloading at the port and transporting to the major markets. Export parity is the international price 

minus the costs of transporting to the port of Durbin and loading onto a ship. If the country has 

an exportable surplus, the market price tends to fall toward export parity; conversely, if there is a 

production shortfall, the price rises to approach import parity. As a result, the domestic corn price 

has risen rapidly even though world prices are stable or even falling. This phenomenon was especially acute in 2015/16, as a severe drought forced South Africa to import large volumes of corn. 

In recent months, the U.S. Gulf price of corn declined slightly, but the price on the South African 

Futures Exchange (SAFEX) has been rising toward import parity (fig. 3). The variability in yields 

thus leads to extreme price volatility, which raises costs for users of corn. 

Figure 2

Poultry production rises, but does not keep pace with demand

1,000 metric tons

Source: USDA, Economic Research Service, using data from USDA’s Foreign Agricultural Service Production, 

Supply, and Distribution (PS&D) database.

0

200

400

600

800

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2,000

Production Imports Consumption

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2009

2010

2011

2012

2013

2014

20152016
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Figure 3

U.S. Gulf corn price compared to South African SAFEX price, 2012-16

Source: USDA, Economic Research Service and the South African Futures Exchange (SAFEX).

0

50

100

150

200

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300

350

Apr-12

Jun-12

Aug-12

Oct-12

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Apr-16

U.S. dollars per metric ton

U.S. Gulf South African Futures Exchange
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The Structure of South African Poultry Trade

The bulk of South Africa poultry imports falls under six tariff lines, described below and in table 1. 

In 2013, the South African Government, alarmed at the rapid rise in poultry imports, raised tariffs 

on five of the tariff lines. Most new tariffs are still below the bound rates agreed on with the WTO, 

but the tariff on frozen whole birds was raised to the maximum allowed under WTO rules. At the 

same time, however, tariffs for the EU on all tariff lines fell to zero as a result of the 1999 agreement with the EU. The new tariffs apply only to non-EU countries. 

1. Mechanically deboned meat (MDM, tariff code 0207.12.10): this product accounts for nearly 

half of imports by volume and comes in at a zero tariff (fig. 3). Brazil is the main supplier. The 

motivation behind the zero tariff is a desire on the part of the South African Government to 

provide a source of low-cost meat to lower-income households.

2. Carcasses (0207.12.20): this product has a relatively small share—around 5 percent by volume. 

The tariff was raised from 27 percent to 31 percent in 2013. Argentina and the EU are the main 

suppliers.

3. Frozen whole birds (0207.12.90): this product also accounted for a small share. The tariff was 

raised to 82 percent (the maximum allowed under WTO rules) in 2013, and imports of this tariff 

line dropped almost to zero after that.

4. Boneless cuts (0207.14.10): this a product lso accounts for a small share. The tariff was raised 

from 5 percent to 12 percent in 2013. Brazil is the largest supplier, and imports have dropped 

since the tariff was raised.

5. Offal (0207.14.20): the tariff on offal went from 27 percent to 30 percent. Brazil was historically 

the largest supplier, but starting in 2013, it has lost share to the EU. In 2014, the EU was the 

largest supplier.

6. Bone-in portions (0207.14.90): this product accounts for about half of South Africa’s imports 

by volume. This tariff line is also the most contentious on the part of the South African poultry 

industry. The antidumping duty on the United States applies to this tariff line. 

Table 1

South African tariffs on poultry imports by tariff code 

Tariff code Product Old tariff New tariff* EU** United States 2014 share by 

volume

0207.12.10 Mechanically 

deboned meat 0 0 0 0 0.37

0207.12.20 Carcasses 0.27 0.31 0 0.31 0.05

0207.12.90 Frozen whole birds 0.27 0.82 0 0.82 0.01

0207.14.10 Boneless cuts 0.05 0.12 0 0.12 0.03

0207.14.20 Offal 0.27 0.30 0 0.30 0.09

0207.14.90 Bone-in portions 0.18 0.37 0 9.4 rand/kg.*** 0.40

*New tariffs took effect October 2013.

**As of July 2014, antidumping duties on EU bone-in portions were imposed: 73% for Germany, 22.8% for the Netherlands, 

and 22% for the United Kingdom. These lapsed in January 2015.

***This rate went into effect February 2012; previous duties were 2.24 to 6.96 rand per kilogram.

Note: EU = European Union.

Source: USDA, Economic Research Service, and USDA, Foreign Agricultural Service.
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Imports have continued to grow, but there was a shift in suppliers from Brazil toward the EU

(fig. 4). Until 2014, Brazil was losing share to the EU as a result of the South Africa-EU trade agreement. However, in 2015, imports rose, and Brazil captured nearly the entire increase. There was 

an increase in imports of MDM, for which Brazil is the main supplier, but Brazil also managed to 

increase shipments of bone-in (fig. 5).

Figure 4

South African poultry imports by country of origin

Source: USDA, Economic Research Service, using data from the Global Trade Atlas.

1,000 metric tons

0

50

100

150

200

250

300

350

400

450

500

2012 2013 2014 2015

Other United States Argentina European Union Brazil

Figure 5

Composition of South Africa’s poultry imports1

1

Total imports depicted in this chart are slightly less than what is shown in figure 4. Figure 4 depicts all poultry imports, 

including turkeys and ducks, which are not included in this chart.

Source: USDA, Economic Research Service, using data from the Global Trade Atlas.

1,000 metric tons

Bone-in cuts Boneless cuts Offal

Frozen whole birds Carcasses Mechanically deboned meat

0

50

100

150

200

250

300

350

400

450

500

2011 2012 2013 2014 2015
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Antidumping Duties Froze U.S. Poultry 

Out of the South African Market

Before 2000, the United States was the largest supplier of leg quarters to the South African market; 

but South Africa imposed antidumping duties on U.S. leg quarters in 2000, ranging from 2.24 to 

6.96 rand per kilogram, depending on the U.S. supplier. The following year, U.S. exports dropped 

nearly to zero (fig. 6). In 2013, after U.S. exports began to rise, the duty was raised to 9.4 rand per 

kilogram and was imposed uniformly on all U.S. suppliers.

Following South Africa’s imposition of antidumping tariffs on the United States, Brazil became the 

largest supplier of leg quarters to South Africa. South Africa attempted to introduce antidumping 

duties on Brazil as well, but was forced to back off after Brazil filed a request for consultation 

under the WTO dispute settlement procedures. However, South Africa signed a trade agreement 

with the EU in 1999, and full liberalization of trade between South Africa and the EU took effect in 

2012. Under this agreement, tariffs on EU poultry were eliminated. Starting in 2011, the EU took 

a growing share of the market for bone-in leg quarters, displacing Brazil (fig. 6). South Africa now 

accounts for nearly a third of total EU exports of bone-in chicken parts.

Rest of world European Union United States Brazil Argentina

Figure 6

Suppliers of bone-in chicken legs to South Africa market (tariff code 0207.14.90) 

shift with changing tariff regimes

Source: USDA, Economic Research Service, using data from the Global Trade Atlas.

1,000 metric tons

0

20

40

60

80

100

120

140

160

180

19961997199819992000200120022003200420052006200720082009201020112012201320142015

200

Antidumping duties 

imposed on U.S. poultry

South Africa - European Union

trade agreement went into effect
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Since the EU agreement went into effect, the EU has captured most of this market. EU exports of 

bone-in portions rose steadily. In reaction, in July 2014, South Africa imposed antidumping duties 

on exports of leg quarters from three EU member countries: 72 percent for Germany, 22.8 percent 

for the Netherlands, and 22 percent for the United Kingdom. 

The antidumping duties on the EU lapsed in January 2015, giving rise to vigorous ongoing 

discussion about reimposing these duties. However, it appears that the antidumping duties had 

little effect on total imports from the EU. Imports of bone-in portions from the EU fell in July and 

August 2014 but then picked up; by November 2014 imports were at similar levels as those in 

previous years (fig. 7). Imports from Germany, the Netherlands, and the United Kingdom stayed 

down, but other EU member countries—principally Spain, Belgium, Hungary, and Denmark—

apparently picked up the slack. Following the resumption of imports from the United States and 

greater short-term pressures on the South African poultry sector, the industry is again demanding 

some sanctions on imports from the EU.

Figure 7

Monthly imports of bone-in portions: Antidumping duties lead to 

shift in suppliers within the European Union, 2012-15

Source: USDA, Economic Research Service, using data from the Global Trade Atlas.

1,000 metric tons

Ireland Denmark Hungary Belgium Spain

Netherlands United Kingdom Germany

0

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Jan 2012

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Mar 2014

May 2014

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Sep 2014

Nov 2014

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Mar 2015

May 2015
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Long-Term Outlook: Poultry Imports Will Continue To Grow

We used the 2015/16 USDA Baseline model to project the 10-year outlook for South Africa’s 

poultry production and trade (described in Appendix B). The South African country model used to 

make the baseline projections is a partial equilibrium model that includes behavioral equations for 

production, consumption, and stocks. The model covers 24 commodity markets, including beef, 

pork, poultry, wheat, corn, other feed grains, oilseeds, protein meals, and vegetable oils. For most 

commodities, imports or exports are residual; however, poultry is modeled with a market-clearing 

producer price and behavioral imports and exports. The model makes 10-year projections under 

neutral assumptions, including normal weather and a continuation of the current policy and institutional environment. The South African model with scenario tariff changes was run in the countrycommodity linked system, which links 41 country and regional models to derive a new set of 

equilibrium world prices (see Appendix B). 

The 2015/16 country model assumes a continuation of the antidumping duties on U.S. chicken 

exports, since at the time the model was finalized (December 2015), it was not certain whether 

the duties would be lifted. Model results show that under the baseline scenario with no change 

in the 2015 policy regime, poultry consumption continues to rise (fig. 8). The key factor driving 

this consumption growth is 2.1-percent annual growth in real per capita income combined with a 

2.1-percent annual decline in real prices. Poultry continues to be lower priced than other meats. 

Domestic production also rises but fails to keep pace with demand, leading to rising imports. By the 

end of the projection period, imports make up 33 percent of domestic consumption.

Figure 8

South African poultry output grows but does not keep pace with demand

Source: USDA, Economic Research Service (2016).

1,000 metric tons

0

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Consumption

Production

Imports

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2023

2024

2025

2026
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Results also show a continuation of increases in soybean and soymeal output. In recent years, area 

planted to soybeans expanded as a result of favorable prices relative to corn and wheat. Soybean 

area continues to expand at the expense of corn and wheat (fig. 9).

Even as soybean area and production rise, South Africa has been constrained by a shortage of 

crushing capacity. Between 2007/08 and 2011/12, South Africa found itself exporting soybeans 

even as it continued importing soymeal, due to the inability to crush the entire crop. But crushing 

capacity has increased rapidly, soymeal production has increased, and exports dropped to zero in 

2013/14 (fig. 10).

This trend is projected to continue. South Africa’s soymeal production and use continue to increase 

while imports fall (fig. 11).

Figure 9

South African soybean area expands at the expense of corn and wheat

Source: USDA, Economic Research Service (2016).

1,000 metric tons

Corn Soybean Wheat

0

1,000

2,000

3,000

4,000

5,000

6,000

95/9696/9797/9898/9999/0000/0101/0202/0303/0404/0505/0606/0707/0808/0909/1010/1111/1212/1313/1414/1515/1616/1717/1818/1919/2020/2121/2222/2323/2424/2525/26
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Figure 10

Soybean crush in South Africa expands rapidly

Source: USDA, Economic Research Service (2016).

1,000 metric tons

Crush Food use Feed and waste

Exports Ending stocks

95/96

97/98

99/00

01/02

03/0405/0607/0809/1011/1213/1415/16

17/18

19/2021/2223/2425/26

0

200

400

600

800

1,000

1,200

1,400

1,600

1,800

2,000

Figure 11

South African domestic soymeal output expands while imports decline

Source: USDA, Economic Research Service (2016).

1,000 metric tons

0

200

400

600

800

1,000

1,200

1,400

Total Consumption Production Imports

95/96

97/98

99/00

01/0203/0405/0607/08

09/10

11/12

13/14

15/1617/18

19/2021/22

23/24

25/26
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Scenario Analysis: Reduction of Duties on 

U.S. Bone-In Exports

We used a two-step process to model a reduction or elimination of the antidumping duties currently 

imposed on imports of bone-in portions (tariff code 0207.14.90) from the United States. The first 

step was to use a spreadsheet-based framework, which we refer to as a “modified Armington Cline 

framework,” to model changes in trade at one point in time (see Appendix C for details). Then we 

used the USDA baseline modeling framework to model the impact of the trade changes on the entire 

agricultural sector of South Africa over the 10-year projections period.

The model used in this analysis draws on what is known in the literature as the “Armington assumption”: that demand for an internationally traded product is differentiated by country of origin 

(Armington, 1969). This is an approach that is commonly used to model changes in bilateral trade 

flows. Our objective was to model South Africa’s substitution among import partners in response to 

tariff changes. The model consists of a set of equations (referred to in Appendix C as “Armington 

equations” and “Cline equations”) that calculate changes in trade in response to relative changes in 

effective prices, including ad valorem tariffs (Cline, 1978). 

The first step was to construct a 6-by-6 trade matrix, averaged over the 2012-14 period. The trade 

matrix shows bilateral trade in poultry meat among six trading partners: South Africa, the United 

States, the EU, Brazil, Argentina, and rest of world (ROW). In the base period, Brazil, Argentina, 

and ROW faced the most favored nation (MFN) tariff of 37 percent; the EU faced a zero tariff, 

and the United States faced an ad valorem equivalent tariff of 65 percent.2 The model can then be 

shocked by changing the tariff rate faced by one or more trading partners. The results reflect what 

2012-14 average trade would have been under different tariff regimes. 

We used the Armington-Cline framework to evaluate trade changes under two tariff reduction 

scenarios. Under the first, the tariff on U.S. exports was reduced to the MFN rate of 37 percent, 

while tariffs on other suppliers remained unchanged. Results suggest that under this scenario, a 

reduction of the antidumping duties on U.S. poultry to the MFN rate of 37 percent would enable 

the United States to capture on average 35 percent of the South African market for bone-in quarters 

exports to South Africa during 2012-14 (table 2). Exports rise from less than 1,000 tons to nearly 

71,000 tons, slightly above the 65,000 quota that is now in effect. The United States takes some 

share away from the EU, but the EU remains the dominant supplier.

2The ad valorem equivalent was calculated by dividing the specific tariff of 9.4 rand per kilogram by the import unit 

value of that tariff line.

Table 2

South African bone-in poultry trade 2012-14 average: Following tariff changes, 

the United States gains share at the expense of the EU

Base Scenario 1 Absolute change Scenario 2 Absolute change

1,000 metric tons

U.S. exports to RSA 0.8 70.7 69.9 81.9 81.1

EU exports to RSA 124.2 105.6 -18.6 16.7 -107.4

Total RSA imports 155.0 200.7 45.7 130.0 -25.0

Note: RSA = Republic of South Africa. 

Source: USDA, Economic Research Service, using data from the Global Trade Atlas.
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The second scenario assumes that the EU loses its preferential access, and all suppliers, including 

the EU, face a 37-percent tariff. In response to financial pressures resulting from the 2016 drought, 

SAPA requested the South African Government impose a 37-percent safeguard duty on bone-in 

poultry from the EU. Under this scenario, U.S. poultry is not subject to a quota, so this scenario also 

provides an estimate of the market share lost to the United States as a result of that trade agreement. 

The U.S. share rises to 63 percent, the EU loses substantial share, and total South African imports 

fall. If the South Africa-EU trade agreement were not in place, and if U.S. poultry could enter 

without a quota, the United States would come closer to regaining its pre-2000 position in the South 

African market. However, the market structure has changed, and under current conditions, elimination of the antidumping duty brings substantial benefits to the U.S. poultry sector, but does not bring 

it back to its earlier dominance in the market.

To analyze the impact of the tariff change on the entire South African poultry/feed complex over 

the 10-year projection period, we created two tariff shocks within the baseline framework. Under 

scenario 1, average 2012-14 South African poultry imports rise by 46,000 tons; under scenario 2 

imports decrease by 25,000 tons. We ran several iterations of the baseline model to determine how 

much the trade-weighted tariff on all poultry products would need to change in order to generate 

these changes in import quantities in the first year of the projections period.3 Before the tariff 

change, the trade-weighted tariff on all poultry cuts was 34 percent (NAMC, 2015e). Under scenario 

1, we determined that lowering this tariff to 31 percent would bring the desired increase in imports; 

under the second scenario, raising the tariff to 35 percent was found to generate a 25,000- ton 

decline in imports. We then created two scenarios to simulate the long-term impact of these tariff 

changes. The new tariffs were assumed to remain constant throughout the projection period. 

South African poultry production in 2026 is 2.3 percent lower in scenario 1 than in the baseline, 

but is 1.2 percent higher under scenario 2 (fig. 12). But the changes in South African poultry output 

are very small under both scenarios. The bottom line is that the tariff changes do not appear to have 

serious long-term impacts on the South African poultry sector.

3The USDA Baseline model does not disaggregate poultry meat by cut.

Figure 12

South Africa’s 2016 poultry output is lower than the base under scenario 1, 

but higher under scenario 2

Source: USDA, Economic Research Service, authors’ analysis using results from USDA (2016).

1,000 metric tons

0

500

1,000

1,500

2,000

2,500

Base Scenario 1

Scenario 2

Base Scenario

1

Scenario

2

Base Scenario

1

Scenario

2

Production Consumption Net trade
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Conclusions: Outlook Remains Uncertain

In June 2015, the U.S. and South African industries agreed on a tariff rate quota: imports of U.S. 

bone-in leg quarters would be allowed at the MFN tariff of 37 percent, up to a quota of 65,000 tons, 

and over-quota imports would be subject to the antidumping duty. Implementation was delayed, 

however. Even though the South African industry agreed to reduce the tariff on U.S. poultry, the 

market remained closed to U.S. poultry for several months. South Africa maintained a blanket ban 

on U.S. poultry due to ongoing outbreaks of highly pathogenic avian influenza. It was only after 

President Obama issued a formal threat to suspend South Africa’s trade preferences under AGOA 

that South Africa finally agreed, on January 6, 2016, to end its ban on U.S. poultry as well as pork 

and beef, which were also banned due to sanitary concerns. 

Our results suggest that the resumption of U.S. poultry exports to South Africa will not cause 

serious harm to the country’s poultry industry. But the tariff changes analyzed in this report are 

relatively small; greater liberalization of South African poultry trade could bring more dramatic 

impacts. The South African poultry industry remains concerned about its ability to compete in 

the world market without the current tariff protection. SAPA has warned that the industry could 

lose as much as $72 million and suffer job losses approaching 6,500 as a result of the resumption of imports from the United States (Reuters, 2015). South African analysis, using a computable general equilibrium model, estimates that reduction of the average tariff to zero would 

bring job losses of 22,693 jobs per year (NAMC, 2015g). The scenarios presented in this report 

are more moderate—reducing the tariff on just one tariff line to the MFN level. Our results 

suggest that reducing the tariff on U.S. poultry would not seriously impact the South African 

poultry industry. In any case, estimated job gains from AGOA far outnumber any losses that 

might be suffered by the poultry industry.

In the short term, however, the South African poultry industry is under serious stress because of the 

ongoing drought. The drought has reduced the corn crop by 40 percent, and the country is projected 

to import 3.5 million tons in 2015/16. Soybean output is down by 20 percent, and imports are 

projected by USDA to reach 250,000 tons. The result is rising feed costs and worsening financial 

pressures on the South African poultry industry. 

In response, SAPA is demanding a safeguard duty of 37 percent on EU chicken. Our model results 

suggest that the elimination of duty-free access for EU poultry would bring small increases in South 

African production, but would leave the country dependent on imports to meet the population’s 

rising demand. The South African poultry industry will continue to be challenged by high feed 

costs, the result of volatile corn prices and a continuing need to import soymeal. As long as U.S. 

poultry remains subject to the 65,000-ton quota, the United States would not benefit from such an 

action. The gap would most likely be filled by other suppliers such as Brazil. 
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References

AGOA.info–African Growth and Opportunity Act (AGOA). 2015. Stellenbosch, South Africa, 

available at http://agoa.info/.

Armington, Paul S. 1969. “A Theory of Demand for Products Distinguished by Place of 

Production.” IMF Staff Papers, 16. pp. 159-78.

Cline, William R., Noboru Kawanabe, Tom Kronsjö, and Thomas Williams. 1978. “Trade 

Negotiations in the Tokyo Round–A Quantitative Assessment.” The Brookings Institution, 

Washington, DC. p. 37.

Department of Agriculture, Forestry and Fisheries, Republic of South Africa (DAFF). 2016. 

Abstract of Agricultural Statistics, 2016.

Donelly, William A., Kyle Johnson, and Marinos Tsigas. 2004. “Revised Armington Elasticities 

of Substitution for the USITC Model and Concordance for Constructing a Consistent Set for 

the GTAP Model.” Office of Economics Research Note. U.S. International Trade Commission, 

Washington, DC.

Mevel, Simon, Zenia A. Lewis, Mwangi S. Kimenyi, Stephen Karingi, and Ann Kamau. 2013. 

The African Growth and Opportunity Act: an Empirical Analysis of the Possibilities Post-2015. 

African Growth Initiative at Brookings and the United Nations Economic Commission for 

Africa, Washington, DC.

National Agricultural Marketing Council (NAMC). 2015a. Evaluating the Southern African 

Poultry Food System, Report 1: Overview of the South African Broiler Industry. Pretoria, 

South Africa.

NAMC. 2015b. Evaluating the Southern African Poultry Food System, Report 2: The South 

African Broiler Value Chain, Stakeholder and Price Forming. Pretoria, South Africa.

NAMC. 2015c. Evaluating the Southern African Poultry Food System, Report 3: Factors 

Affecting the Competitiveness of the South African Poultry Feed Industry. Pretoria, 

South Africa.

NAMC. 2015d. Evaluating the Southern African Poultry Food System, Report 4: 

Factors Affecting the Competitiveness of the South African Broiler Industry. 

Pretoria, South Africa.

NAMC. 2015e. Evaluating the Southern African Poultry Food System, Report 6: The Effect 

of Policy on the South African Broiler Industry. Pretoria, South Africa.

NAMC. 2015f. Comparisons of the South African Broiler Industry with Global Role 

Players and Outlook. Pretoria. South Africa.

NAMC. 2015g. Macroeconomic Impact of the South African Broiler Industry Applying the 

South African Inforum Model (SAFRIM). Pretoria. South Africa.
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NAMC. 2015h. Analysis of the South African Poultry Food System: Major Findings, Challenges, 

and Concluding Remarks. Pretoria. South Africa.

Reuters. 2015. “South Africa’s Poultry Industry Says U.S. Imports Could Cost 6500 Jobs,” 

June 10, 2015.

Schneidman, Witney, and Zenia A. Lewis. 2012. The African Growth and Opportunity 

Act: Looking Back, Looking Forward. African Growth Initiative at Brookings. 

Washington, DC.

Schneidman, Witney. 2014. “AGOA: Economic Effects of Providing Duty-Free Treatment 

for Imports.” Testimony before the U.S. International Trade Commission, January 14, 

2014. Available at http://www.brookings.edu/research/testimony/2014/01/14-agoarenewal-schneidman. Washington, DC.

Seeley. Ralph. 2015. “Bilateral-Bilateral Model – Endogenous Exporter Prices, Prohibitive 

Tariffs, Transportation Costs, and TRQs.” World Outlook Conference, Washington, DC. 

United States Department of Agriculture (USDA). 2016. International Long-Term Projections to 

2025. http://www.ers.usda.gov/data-products/international-baseline-data.aspx.

Williams, Brock. 2015. Africa Growth and Opportunity Act (AGOA): Background and 

Reauthorization. Congressional Research Service, Washington DC.
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Appendix A: What Does AGOA Mean for South Africa?

Enacted in 2000, the African Growth and Opportunity Act (AGOA) is aimed at expanding 

U.S. trade and investment with sub-Saharan Africa. Combined with the Generalized System of 

Preferences (GSP), nearly all goods produced in AGOA-eligible countries enter the U.S. duty-free. 

The agreement potentially covers 49 countries, but each of the 49 countries must undergo an annual 

review by USTR to determine whether it continues to meet the eligibility criteria, which include 

market-based economic policies, reduced barriers to U.S. trade and investment, efforts to battle 

corruption, protected internationally recognized labor rights, and policies promoting economic 

development (Williams, 2015). As of the end of 2015, 39 countries, out of 49 total, were eligible for 

AGOA benefits. 

South Africa is part of both GSP and AGOA; it is the third-largest exporter under AGOA to the 

United States (numbers one and two are Nigeria and Angola, respectively). AGOA, combined with 

GSP, are very important to South Africa. Combined U.S. imports from South Africa under AGOA 

and GSP totaled $3.1 billion in 2014; imports under AGOA alone totaled $1.7 billion, roughly 21 

percent of all South African exports to the United States. South Africa is the top exporter of nonenergy products under AGOA. Most products are manufactured goods. The largest category of 

imports under AGOA are automobiles, totaling $1.3 billion in 2014. Agricultural imports under 

AGOA totaled $176 million, 56 percent of total U.S. agricultural imports from South Africa, 

consisting mainly of wine and citrus (appendix table 1).

According to a one study, South Africa had been able to add 62,395 jobs as of 2010 because 

of exports under AGOA (Schneidman and Lewis, 2012). Another study estimates that exclusion from AGOA would cost South Africa $260 million in lost exports (Mevel et al., 2013).4

South African media report concerns about the potential loss of jobs in South Africa’s auto 

industry, as well as jobs in the labor-intensive apparel and food processing sectors. According 

to the Brookings Institution, the South African automotive industry is the fifth-largest employer 

in the country, directly employing 36,000 people and indirectly supporting nearly 275,000 

(Schneidman, January 14, 2014).

4The 2013 Brookings study was conducted before the decision on AGOA renewal. It analyzed several alternative 

scenarios concerning both country eligibility and product coverage. The scenario cited here was one where middle income 

countries, including South Africa, are excluded from AGOA. Because other countries in addition to South Africa were 

excluded under this scenario, the results may not be identical to a scenario under which only South Africa is excluded.
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Appendix table 1

U.S. Imports from South Africa under AGOA

Sector Category 2012 2013 2014

Agricultural products $ Million U.S. 

Total U.S. imports from South Africa 306,465 301,535 315,443

Imports under AGOA 163,178 184,516 175,504

Forest products

Total U.S. imports from South Africa 26,181 35,567 40,538

Imports under AGOA 92 55 102

Chemicals and related products

Total U.S. imports from South Africa 831,922 773,786 794,386

Imports under AGOA 63,330 62,292 47,790

Energy-related products

Total U.S. imports from South Africa 74,170 104,956 64,701

Imports under AGOA 33 96 24

Textiles and apparel

Total U.S. imports from South Africa 24,686 26,501 25,251

Imports under AGOA 5,253 5,999 5,717

Footwear

Total U.S. imports from South Africa 1,354 1,052 1,074

Imports under AGOA 316 444 343

Minerals and metals

Total U.S. imports from South Africa 4,564,069 4,172,844 4,794,578

Imports under AGOA 221,245 202,839 209,132

Machinery

Total U.S. imports from South Africa 353,339 338,354 369,685

Imports under AGOA 6 2

Transportation equipment

Total U.S. imports from South Africa 2,160,564 2,313,838 1,528,956

Imports under AGOA 1,928,750 2,121,213 1,307,121

Electronic products

Total U.S. imports from South Africa 73,119 69,754 72,855

Imports under AGOA 16 16

Miscellaneous manufactures

Total U.S. imports from South Africa 131,697 144,549 136,556

Imports under AGOA 1,133 1,027 1,898

continued—
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Appendix table 1

U.S. Imports from South Africa under AGOA—continued

Sector Category 2012 2013 2014

Agricultural products $ Million U.S. 

Special provision

Total U.S. imports from South Africa 332,349 323,437 270,238

Imports under AGOA 147,891 109,398 125,542

All sectors

Total U.S. imports from South Africa 8,695,457 8,392,134 8,269,567

Imports under AGOA 2,383,352 2,578,496 1,747,633

Imports from all 

AGOA eligible 

countries

Billion U.S. dollars

Total U.S. imports 47,500 38,329 25,479

Imports under AGOA 32,476 24,800 11,813

South Africa share .07 .10 .15

Source: Data compiled from agoa.info using data from the U.S. Department of Commerce.
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Appendix B: The Country-Commodity 

Linked System (CCLS)

The country-commodity-linked system (CCLS) consists of 42 models, of which 32 are country 

models and 10 are regional models. The system simultaneously equilibrates prices and quantities for 24 world commodity markets, for each of the 10 projected years in the analysis. The 

commodities include four coarse grains (corn, sorghum, barley, and other coarse grains); two 

food grains (wheat and rice); four oilseeds and respective meals and oils (soybeans, rapeseed, 

sun seed, and other oilseeds); two other crops (cotton and sugar); and four animal products 

(beef, pork, poultry, and eggs). 

Each model contains commodity blocks with prices, policy variables, and supply and use variables, 

including production, imports, exports, consumption, and stocks. The quantities respond to prices, 

policy variables, and macroeconomic variables, or to other quantities. The modeling of different 

country-commodity blocks may vary in the level of detail, in the choice of residual variable, and so 

on. The number of commodity blocks varies by model, with less important country/commodity pairs 

aggregated into rest-of-regions models or rest-of-sector commodities, such as other oilseeds. The 

behavioral equations typically use a linearized growth-rate functional form.

The modeling system can introduce scenario shocks by incorporating reference-run and scenario 

versions of models. Alternatively, the system can introduce shocks into the reference-run versions 

of models. In the reference run, levels for a residual “region” are calculated to clear world 

markets. For most scenarios, the residual calculations are performed for all years, so the world 

will be in balance prior to the introduction of scenario shocks. The modeling software includes 

Excel for individual models, and Fortran, Visual Basic, and Access for the modeling system. 
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Appendix C: Armington-Cline Model Description

To analyze shifts in bilateral trade resulting from eliminating the antidumping duty on U.S. poultry, 

we used a spreadsheet-based, modified Armington-Cline model. This method expands upon the 

“Armington assumption” that demand for an internationally traded product is differentiated by 

country of origin (Armington, 1969). 

The approach used here handles some limitations of Armington’s method. The Armington approach 

describes demand share changes by source for one importer, in response to relative source price 

changes, through an elasticity of substitution. The approach used here models simultaneous changes 

in destination shares by multiple exporters, in response to relative destination price changes, as well 

as source share changes by multiple importers, in response to relative source price changes. 

Since the Armington approach describes relative changes in source shares, in response to a change 

in relative source prices, a zero or small initial share leads to a zero or small change in that share. 

The bilateral-bilateral model provides a combined functional form that can allow a zero or small 

share to grow by a non-negligible amount, if the analyst determines that base trade was blocked 

by a prohibitive tariff. In that case, the analyst may cause the model to calculate a synthetic linear 

responsiveness for that bilateral trade level. 

The model has additional features that are not used in this analysis: it can adjust the synthetic 

responsiveness to reflect bilateral transportation costs; it can include bilateral tariff rate quotas 

(TRQs), by a simple but exact method; and it can use estimates of tariff water, the extent to which 

base tariffs are more than sufficient to prevent trade.

Accurate elasticities of trade substitution are important, but difficult to estimate. In this analysis, 

we assume that there is no water in the tariff; i.e., that the 65 percent ad valorem base tariff on U.S. 

poultry is exactly enough to stop exports.

The source and destination choices are combinations of trade substitution and expansion. Trade 

expansion is based on linear equations (referred to here as “Cline equations”), which use elasticities 

to calculate relative changes in trade given relative changes in effective prices, including ad valorem 

tariffs (Cline, 1978). Use of relative price changes means that absolute price levels are not needed. 

If an unscaled import or export substitution level will increase, a linearized Armington calculation 

is used so substitution can grow significantly from small or zero initial trade levels. If an unscaled 

substitution level will decrease, a nonlinear Armington-based calculation is used; therefore, the 

solution is not vulnerable to a small unscaled-substitution sum. 

Elasticities

For individual models, implied expansion elasticities were derived by shocking the countrycommodity linked system of models. The import substitution elasticity for all countries was taken 

from Donelly et al. (2004). It is assumed that the substitution between export destinations is quite 

price-responsive, to the extent that further increases in the export substitution responsiveness would 

not change the results substantially.
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Linear-nonlinear model equations

To save space, the import expansion, substitution, and total equations are not shown; they are like 

the corresponding export equations. 

Tariffs here are expressed as fractions, to make the equations more compact. 

J and K = exporter subscripts; K is used for summation.

L and M = importer subscripts; M is used for summation.

Base = reference run; initial levels. Scen = scenario. Elast = elasticity.

Prices

ScenExportPriceLJ adjusts until ScenExportsLJ ≈ ScenImportsLJ.

Import prices are based on the corresponding export prices, adjusted by ad valorem tariffs. 

BaseImportPriceLJ = BaseExportPriceLJ * (1 + BaseTariffLJ). 

ScenImportPriceLJ = ScenExportPriceLJ * (1 + ScenTariffLJ). 

Base trade levels used to calculate linear responsiveness

In order to allow a bilateral trade level to grow significantly even if the base bilateral trade level is 

very small or zero, a synthetic base trade level may be used for calculating expansion responsiveness and for calculating linear substitution responsiveness when trade will grow. The synthetic base 

trade level is less likely to be very small or zero than is the actual base trade level. The synthetic 

base trade level is the prospective exporter’s base total exports times the prospective importer’s 

share in base world imports. 

If base bilateral trade levels allow trade to respond appropriately in a particular scenario, then those 

base trade levels should be used rather than synthetic levels. 

BaseTradeLinearLJ =

If {BaseTradeSwitchLJ = 0,

BaseExportsLJ,

∑M BaseExportsMJ * ∑K BaseImportsLK / ∑M ∑K BaseImportsMK}.
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Export and import expansion

The bilateral export expansion calculation includes the relative difference in the bilateral export 

price, the exporter’s expansion elasticity, and base trade for linear calculations. The import and 

export expansion equations are analogous.

ExportExpansionLJ = 

(ScenExportPriceLJ / BaseExportPriceLJ - 1) * ExportExpansionElastJ * BaseTradeLinearLJ.

Export and import substitution

If an unscaled export substitution level will rise, unscaled substitution depends on the base bilateral 

export level, the relative price difference, the export substitution elasticity, and base trade for linear 

calculations. If the unscaled export substitution level will decrease, unscaled substitution depends 

on the base bilateral export level, the scenario/base bilateral export price ratio, and the export substitution elasticity. The import and export equations are similar.

Use of the linear calculation with a synthetic base level can allow the level to grow significantly 

from a small or zero base export level. If the unscaled substitution level will decrease, use of a 

nonlinear Armington-derived calculation prevents the sum of unscaled substitution levels from 

approaching zero, which is relevant because the sum is used to scale export substitution. 

UnscaledExportSubstitutionLJ = 

If {(ScenExportPriceLJ - BaseExportPriceLJ) * ExportSubstitutionElastJ >= 0,

BaseExportsLJ + (ScenExportPriceLJ / BaseExportPriceLJ - 1) * ExportSubstitutionElastJ

 * BaseTradeLinearLJ,

BaseExportsLJ * (ScenExportPriceLJ / BaseExportPriceLJ) ^ ExportSubstitutionElastJ }.

Export substitution is calculated from the scenario-base difference in export shares, applied to the 

exporter’s total base exports. Again, the forms of the import and export equations are parallel. If the 

denominator sum in a ratio equals zero, the ratio is replaced by zero.

ExportSubstitutionLJ = ∑M BaseExportsMJ *

(UnscaledExportSubstitutionLJ / ∑M UnscaledExportSubstitutionMJ 

 – BaseExportsLJ / ∑M BaseExportsMJ ).
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Export and import totals

The import equation is similar to the export equation.

ScenExportsLJ = BaseExportsLJ + ExportExpansionLJ + ExportSubstitutionLJ.

Derivation of simple substitution response from 

Armington demand equation

The substitution equations above are based on the substitution derivation below. The derivation and 

result are simple because we only need scenario versus base shares, not levels.

x = Armington bilateral demand. X = Armington demand index. b = demand coefficient. 

p = bilateral price. P = Armington price index. σ = (-) elasticity of demand substitution. 

j and k = exporter subscripts. s = scenario. 0 = base or reference run. 

The first step is to define Armington scenario and base demand (Armington equation 9):

 xjs = bj

σ Xs

 (pjs / Ps)

-σ

 xj0 = bj

σ X0 (pj0 / P0)-σ.

Solve the scenario and base demand equations for bj

σ, and then solve for xjs. Move demand and 

price indices to the left:

 bj

σ = xjs / Xs (Ps

 / pjs)

-σ = xj0 / X0 (P0 / pj0)-σ.

 xjs = xj0 Xs / X0 (P0 / pj0)

-σ / (Ps

 / pjs)

-σ

= Xs / X0 (P0 / Ps)

-σ xj0 (pjs / pj0)-σ.

Calculate share. Note that the demand and price indices have no country subscripts, so they can be 

moved outside the summation and then canceled:

 xjs / ∑k xks 

= [ Xs / X0 (P0 / Ps)

-σ xj0 (pjs / pj0)-σ ] / [ ∑k Xs / X0 (P0 / Ps

)

-σ xk0 (pks / pk0)-σ]

= [ Xs / X0 (P0 / Ps)

-σ xj0 (pjs / pj0)-σ ] / [ Xs / X0 (P0 / Ps

)

-σ ∑k xk0 (pks / pk0)-σ ]

= xj0 (pjs / pj0)

-σ / ∑k xk0 (pks / pk0)-σ.