Technical Report 

An Analysis of EPA Renewable Fuel Scenarios 

with the FAPRI-CARD International Models 

By CARD Staff 

December, 2009 
2

1. Introduction 

 United States Environmental Protection Agency (EPA) contracted with the Center for 

Agricultural and Rural Development (CARD) at Iowa State University of the Food and 

Agricultural Policy Research Institute (FAPRI) to examine various renewable fuel scenarios 

using the FAPRI-CARD U.S. and global agricultural models.1

 This report outlines the models 

and assumptions used for the analysis, the scenarios performed, and the results derived from the 

analysis. 

2. The FAPRI-CARD Agricultural Models 

The FAPRI-CARD Agricultural Models are a set of multi-market, partial-equilibrium, 

and non-spatial econometric models.i

 The models cover all major temperate crops, sugar, 

ethanol, dairy, and livestock and meat products for all major producing and consuming countries 

and calibrated on the most recently available data (see Table 2 for a summary description of the 

model coverage). The models are used extensively for generating ten-year baseline projections 

for agricultural markets and for policy analysis based on the baseline projections in the last 25 

years. The individual commodity models or the full set of models have been employed for 

numerous studies, such as Abler et al. (2007),ii Elobeid et al.(2006),iii Fabiosa et al. (2007),iv

Fabiosa et al. (2005),v Tokgoz et al. (2008),vi Hayes et al. (2009),vii Fabiosa et al. (2009)viii, and 

Fabiosa et al. (2009).ix The FAPRI models have been used by several organizations (e.g., the 

U.S. Congress)x to develop baselines as well as for policy analysis purposes. In particular, it was 

used to examine world market impacts of alternative proposals during the Uruguay Round 

Agreement on Agriculture, several Farm Bill rounds, and the current WTO Doha Round. 

Recently, research on renewable fuels that used the FAPRI-CARD model was supported by the 

USDA and several commodity groups.xi 

These models capture the biological, technical, and economic relationships among key 

variables within a particular commodity and across commodities. They are based on historical 

data analysis, current academic research, and a reliance on accepted economic, agronomic, and 

biological relationships in agricultural production and markets. The links between the U.S. and 

international models are made through commodity prices and net trade equations. 

In general, for each commodity sector, the economic relationship that quantity supplied 

equals quantity demanded is achieved through a market-clearing price for the commodity. In 

many countries domestic prices are modeled as a function of the world price using a price 

transmission equation. Since econometric models for each sector can be linked, changes in one 

commodity sector will impact the other sectors. 

 

1

 The Food and Agricultural Policy Research Institute (FAPRI) is a unique, dual-university research program, 

established in 1984 by a grant from the U.S. Congress. The Center for Agricultural and Rural Development (CARD) 

at Iowa State University develops the international side of the models, and the Center for National Food and 

Agricultural Policy (CNFAP) at the University of Missouri-Columbia develops the U.S. domestic component. This 

model is called the Food and Agricultural Policy Research Institute (FAPRI) model system when the work is 

performed by Iowa State and its partner institution at the University of Missouri. When Iowa State runs the model 

on its own, especially when changes in structure, parameters, and specifications are introduced, the model system is 

called the FAPRI-CARD Model. 
3

The model for each commodity consists of a number of countries/regions, including a 

rest-of-the-world aggregate to close the model. The models specify behavioral equations for 

production, use, stocks, and trade between countries/regions. The models solve for 

representative world prices by equating excess supply and demand across countries. Using price 

transmission equations, the domestic price for each country is linked with the representative 

world price through exchange rates and other price policy wedges.2

In general, data for supply and utilization of agricultural commodities were obtained from 

the F.O. Lichts Online Database;xii the Food and Agricultural Organization (FAO) of the United 

Nations (FAOSTAT Online);xiii and the Production, Supply and Distribution View (PS&D) of 

the U.S. Department of Agriculture (USDA).xiv Macroeconomic data were gathered from 

various sources, including the International Monetary Fund (IMF) and IHS Global Insight. 

Additional details on exchange rate estimates, international population growth, international 

GDP growth, and other factors for key countries can be found at: 

http://www.fapri.iastate.edu/outlook/2009/. 

2. 1 Structure of the Domestic Model 

The U.S. (domestic) model is part of a customized version of the FAPRI-CARD 

modeling system (see Figure 1). This system includes models of supply and demand for all 

important, temperate agricultural products in major producing and consuming countries. The 

models are a set of multi-market, partial-equilibrium, econometric, and non-spatial models. 

Agricultural and trade policies are included in the models to the extent that they affect the supply 

and demand decisions of the economic agents. The models assume that existing domestic and 

trade policy variables will remain unchanged in the outlook period. 

 

2

 This may include border duties, export taxes, and domestic price supports. 
4

Figure 1: Model Interactions 

The U.S. Crops Model is a partial-equilibrium model, which includes behavioral 

equations that determine crop planted acreage, domestic feed, food and industrial uses, trade, and 

ending stocks in marketing years. Figure 2 shows the basic structure of a crop model. The 

model solves for the set of prices that brings annual supply and demand into balance in all 

markets. The U.S. Crops Model is divided into regions with equations for each crop grown 

within each region. Table 1 provides a detailed list of the regions and crops covered in the 

Model. 

 

Table 1: Regions and Crops in the U.S. Crops Model 

Regions Crops 

Corn Belt 

Central Plains 

Delta States 

Far West 

Lake States 

Northeast 

Northern Plains 

Southeast 

Southern Plains 

Corn 

Soybeans 

Wheat 

Upland Cotton 

Sorghum 

Barley 

Oats 

Rice 

Sunflowers 

Peanuts 

Canola 

Sugar beet 

Sugarcane 
5

For crops with by-products, behavioral equations for the by-products are also included 

(i.e., high fructose corn syrup, ethanol and corn oil, and soybean meal, soybean oil and biodiesel 

from soybeans). For each commodity, a market-clearing price is achieved by equating quantity 

supplied to quantity demanded. The market linkages imply that changes in one commodity 

sector will have impacts on the other sectors. 

In the U.S. ethanol sub-model, total ethanol production is the sum of ethanol produced 

from corn through the dry- and wet-milling processes, ethanol produced from non-corn sources, 

and ethanol produced from cellulosic feedstock. Ethanol production is based on production 

capacity and capacity utilization which are both driven net revenue from ethanol production. 

The amount of corn that is required for the level of ethanol production is derived by dividing the 

ethanol production with the ethanol yield. On the demand side, there are three major 

components for ethanol: the additive, voluntary E-10, and E-85 markets. In the ethanol additive 

market, which is currently the largest component, oxygenation requirements and blend mandates 

determine the ethanol demand. Net trade is based on the relative price of U.S. and world 

ethanol. However, for these sets of runs the U.S. ethanol sub-model has not been utilized since 

the EPA volume requirements have been imposed exogenously in the model. These 

predetermined renewable fuel requirements have been used to estimate feedstocks going into 

ethanol production and are incorporated into the crop demand module to determine the response 

of the U.S. agricultural sector to the renewable fuel requirements. 

In the interest of evaluating the agriculture sector impacts of individual fuel requirements, 

certain adjustments to the FAPRI-CARD modeling framework were undertaken. For example, 

we decoupled the ethanol sub-model from fully interacting with the rest of the FAPRI-CARD 

models. This enabled the observation of agriculture sector impacts of the change in a specific 

fuel volume, ceteris paribus (i.e., without allowing market impacts to affect changes in fuel 

volumes). Market outcomes would be different if the ethanol sub-model is not decoupled. For 

example, in the Control Case the U.S. ethanol sector still has excess profit in 2022. If arbitrage 

was allowed in the model this would have provided enough incentive for the sector to expand 

production, strengthening demand for more corn feedstock and resulting to higher prices of corn. 

Holding all else constant, prices of other crops are expected to increase as their supplies tighten 

with corn becoming more competitive in attracting the limited resource – land. Likewise, 

livestock prices are expected to follow as feeding becomes more expensive. Mixed influences 

make it difficult to predict likely outcomes in the world ethanol market. On the one hand, like 

the other crops, sugar feedstock for ethanol will be more expensive as land is bid-away in favor 

of corn, but import demand in the U.S. may decline as more ethanol is domestically produced, on 

the other. 

2.2 Structure of the International Model 

The FAPRI-CARD international module is based on multi-market, partial-equilibrium, 

econometric, non-spatial models. The models cover all major temperate crops, sugar, ethanol, 

dairy, and livestock and meat products for all major producing and consuming countries and 

calibrated on most recently available data (see Table 2 for a detailed list of commodity and 

country coverage). In these models, extensive market linkages exist, reflecting derived demand 

for feed in livestock and dairy sectors, competition for land in production, and consumer 

substitution possibilities for close substitutes such as vegetable oils and meat types. 
6

Table 2: Model Description 

Exogenous Variables Population, GDP, GDP Deflators, Exchange Rates, Policy Variables 

Endogenous Variables Production, Consumption, Exports, Imports, Stocks, World and Domestic 

Prices 

Commodity Coverage Grains: Corn, Wheat, Sorghum, Barley, Oats, and Other Grains 

Oilseeds: Soybeans, Rapeseed, Sunflower, Palm, and Other Oilseeds 

Livestock: Beef, Pork, Poultry, and Other Livestock Products 

Dairy: Milk, Cheese, Butter, and Other Dairy Products 

Sugar 

Biofuels: Ethanol, Biodiesel 

Major Countries/Regions North America: United States, Canada, Mexico 

South America: Argentina, Brazil, etc. 

Asia: China, Japan, India, Malaysia, etc. 

Africa: South Africa, Egypt, Nigeria, etc. 

Europe: European Union, Russia, Ukraine, etc. 

Oceania: Australia, New Zealand 

Output by Commodity and 

Country 

World Prices, Domestic Prices, Production, Consumption, Net Trade, 

Stocks, Area Harvested, Yield 

2.3 Grains and Livestock Descriptions 

To provide more detail on the internal dynamics of the individual sector models, we have 

outlined the structure of the International Grains Model and the International Livestock and 

Poultry Model below. The International Grains Model is a non-spatial, multi-market model that 

covers several countries/regions and includes a rest-of-the world aggregate. It has links to other 

models in the modeling framework, such as the U.S. Crops Model, as well as the international 

Cotton, Dairy, Livestock, Oilseeds, Rice, and Sugar Models. The data sources included in the 

model are the USDA-Foreign Agricultural Service PSD data set,xv the International Monetary 

Funds' (IMF) International Financial Statistics (IFS) macroeconomic data set, USDA Attaché 

Reports,xvi and other sources for commodity prices. 

The Grains Model interacts with the Dairy and Livestock Models that provide 

information on animal production that are primary determinants in the feed demand in the 

countries, and with Oilseeds and Rice Models that provide information on the relative 

profitability and area harvested for the competing crops. Each country sub-Model consists of at 

least one commodity depending on the relative importance of the commodity and the relative 

importance of the country in the world markets as a supplier or a buyer. 

Figure 2 shows the basic structure of a crops model. In terms of the structure of the 

Models, the following identity is satisfied for each country/region and the world: Beginning 

Stock + Production + Imports = Ending Stock + Consumption + Exports. Production is a 

product of yield and area equations, while consumption is divided into feed and non-feed 
7

demand (which can be further disaggregated into food and industrial use). To satisfy the 

identity, two different methods are used. In most of the countries, domestic price is modeled as a 

function of the world price with a price transmission equation, and the identity is satisfied with 

one of the variables set as the residual (usually the net trade). In other cases, prices are solved to 

satisfy the identity. 

Figure 2: Basic Crop Sector Model Structure 

International

Prices

Beginning

Stocks

Yield

Area

Domestic Supply

Price

Transmission

Feed

Demand

Food

Demand

Ending

Stocks

Other

Demand

Domestic Demand

Net Exports

Exports

Imports

Trade Policy

Content

Agricultural and trade policies in each country are included in the model to the extent that 

they affect the supply and demand decisions of the economic agents. Examples of these include 

taxes on exports and imports, tariffs, tariff rate quotas, export subsidies, intervention prices, and 

set-aside rates. 

The International Grains Model assumes that the existing agricultural and trade policy 

variables will remain unchanged in the outlook period. Macroeconomic variables, such as GDP, 

population, and exchange rates, are exogenous variables that drive the projections of the Model. 

The Model also includes an adjustment for marketing-year differences by including a residual 

that is equal to world exports minus world imports, which ensures that world demand equals 

world supply. 

Like all the other international models, the International Livestock and Poultry Model is a 

partial equilibrium, econometric, non-spatial policy model. That is, all other sectors of the 

economy outside of the relevant commodities are considered as given; parameters in the Model 

are either directly estimated, surveyed from the literature, or obtained from consensus of expert 

opinion; and country sources and destinations of trade are not specified. 
8

The structure of the model considers carefully the biological processes involved in 

livestock and meat production and richly captures the investment, production, and consumption 

decisions of significant economic agents. Figure 3 provides a schematic description of the stock 

of live animals (e.g., breeding inventory) as well as their changes (i.e., flow of animals, e.g., 

number slaughtered). Figure 4 provides the supply and use of meat products. Both figures show 

the relationship of the biological processes and economic decisions as well as the relationship of 

stock and flow variables in the evolution of animal and meat production and consumption. In 

general, the demand side is driven by relevant prices, income, and population, while the supply 

side is driven by relevant prices, cost of production, and technology. When it is not a residual, 

trade is expressed as a function of the domestic price relative to the world price. 

The specification of the Model is based on five principles. The first is a clear 

differentiation of stock and flow variables. Animal inventory is an example of a stock variable, 

while animals slaughtered is a flow variable. Second, in the specification of the model, except 

for the breeding herd, all stock variables are derived in an accounting identity from the changes 

in the flow variables. Third, flow variables are generally the only ones with behavioral 

specification representing economic decisions of significant agents in the sector. Fourth, flow 

variables are specified in terms of rates rather than levels. Rates normally give a more stable 

behavior to the model compared with levels and lend easily to comparison across countries and 

time periods. Finally, price determination in individual country sub-models is specified as either 

price transmission from the world price or market clearing when there are significant restrictions 

in trade flow. The entire Model solves with a market-clearing world price that balances world 

trade and equates supply and demand in individual countries. 
9

Figure 3: Cattle Production and Use 

Figure 4: Beef Production and Consumption 
10

The Model strives to capture policy instruments that influence the incentives faced by 

economic agents. This includes domestic policies (for example, price support) and border 

policies (for example, duties, tariff rate quotas, export subsidies). Other policies that are difficult 

to represent quantitatively, such as environmental regulations, are accounted for exogenously. 

2.4 New Yield Specification 

Three specific aspects of the yield specification are new in the current version of the 

FAPRI-CARD models, including the parameter associated with the trend, sensitivity of yield 

response to price and cost changes, and yield impact of extensification. Supporting equation and 

tables are given in Annex 1.The yield of crop i is expressed as a function of trend, ratio of total 

revenue to variable cost in period t, moving average of the ratio of total revenue to variable cost, 

and total crop area planted. The first two explanatory variables capture the effect of 

intensification, and the last explanatory variable captures the effect of extensification on yield 

from the additional new land brought into production. The elasticities related to intensification 

in the case of corn in the U.S. model (specifically, the corn belt region) is 0.013 in the short-run 

and 0.074 in the long-run. The elasticity to additional land brought into production is -0.023. 

The same structure of the yield equations in the U.S. model is used for all the other 

countries covered by the models. Since we are constrained by data limitations to estimate the 

parameters, we use the U.S. parameters as the base values and calibrate country-specific 

parameters based on the following assumptions. First, we consider the response of yield to price 

in the short-run as primarily an allocative adjustment and we assume that it is the same across all 

countries. Second, the response of yield to long-run price trend involves some adjustment in 

technology. As such, we assume that a country whose actual yield is far from its yield frontier 

(or potential) has more opportunities to adjust its technology in response to long-term price 

changes. For example, Brazil’s corn yield of 2.91 is far from the U.S. yield of 8.55 (which we 

consider as the frontier for Brazil) so we use the ratio of the two yield at 2.95 as the adjustment 

factor to calibrate the price response of corn yield in Brazil to changes in long term price trends, 

giving an elasticity of 0.181 for Brazil. For the yield drag due to the increasing use of marginal 

lands we use the relative proportion of available land as basis of establishing a calibration factor. 

For example, Brazil’s permanent meadow and pasture, which we assume as potential source of 

new land for crop production is 0.92 of total available land compared to 0.75 that of the U.S. 

The ratio of the two is 0.81. We use this to calibrate the extensification elasticity of -0.23 in the 

U.S. to only -0.018 in Brazil. The same procedure is applied to the rest of the countries covered 

by the FAPRI-CARD model.3

2.5 New Brazil Model 

A new Brazil model was developed by CARD in 2009 and integrated into the FAPRI 

system.4

 Because of Brazil’s importance in world agriculture we provide here an extended 

 

3

 In a limited exception, the elasticity suggested by this method is only partially implemented when it results to 

unrealistic time paths of endogenous variables of interest. 

4

 The CARD and ICONE (Institute for International Trade Negotiations) collaborated in the development of the new 

Brazil model, including data collection, model specification, and parameter calibration. The model was integrated to 

the FAPRI-CARD models and used by CARD for the EPA analysis. 
11

overview of salient features of the new model. Detailed equations representing new specification 

features in the Brazil model are given in Annex 2. 

Due to its size and geographical location, Brazil encompasses widely varying 

ecosystems, ranging from grassland and crops associated with temperate climates in the South to 

tropical forests in the North and semiarid areas in the Northeast. The different regions also 

present enormous developmental disparities in terms of infrastructure, logistics, and strategies 

available to increase production. Thus, while rapid expansion of production of some 

commodities may only be achieved by taking area away from other agricultural activities in land 

constrained regions, increases in area used by all activities may be observed in other parts of the 

country; which points to distinct dynamics in the competition for land across space. Therefore, it 

is becoming increasingly important to recognize the spatial dimension of the agricultural 

expansion as its impacts are likely to be dependent on the way in which it occurs as well as on 

the resources of the location in which production takes place. 

We developed a spatially disaggregated partial equilibrium model of Brazilian 

agricultural production constructed at the regional level, incorporating major crops, biofuels and 

livestock interacting and competing for agricultural resources, in particular land. Outputs from 

the model include projections of production and utilization variables, and the amount of land 

allocated to the activities considered. On the crops side, we consider corn (1st and 2nd crop), the 

soybeans complex (including soybean meal, soybean oil, and biodiesel), the sugarcane complex 

(including sugar and ethanol), rice, cotton, and dry beans (multiple cropping depending on the 

region). The modeled animal products are beef, pork, poultry, and dairy. In terms of land 

allocation, and as will be discussed with more detail in the next section, the area used by a given 

activity depends on its expected real returns in comparison to expected returns of activities that 

compete for the resource. The strategy followed to model livestock activities closely follows the 

one utilized in the international livestock model of FAPRI, with the additional layer of explicitly 

modeling land used by beef and dairy production. Since not all the regions considered are 

equally suited for different activities, the competition for land is contingent on the location. As 

such not all activities compete with each other with the same intensity in all regions. 

Through the use of spatially disaggregated information on historical production activities 

and natural resource availability, the model is able to determine the relative profitability of 

different activities at the local level, which as mentioned will drive regional supply curves for 

relevant commodities and their associated land use. For this modeling effort Brazil is divided 

into 6 regions; South, Southeast, Central-West Cerrados, North-Northeast Cerrados, Amazon 

Biome, and Northeast Coast (see figure 5). The model is able to capture the regional differences 

in terms of capabilities and consequences of the expansion. As such, the impacts of land use 

changes derived from increasing demand for agricultural products can be more precisely 

established. A general overview of the structure of the model follows. 

a. General Model Structure 

Since a large goal of the model is to be able to project land use (and changes) at a 

regional level, production functions are modeled at that spatial scale. However, the demand side 

of the model is built at the aggregate (country) level. 
12

FIGURE 5. Regions in the FAPRI-CARD Brazil Model 

The degree of details included in this note varies widely across commodities. More 

detailed information and formulas are included for the crops sector, as the land use projections is 

where the largest departures from other models in the system are. 

 

i. Crops 

As already described in the previous section, crops currently included in the Brazilian 

regional model are: corn, soybeans, cotton, rice, dry beans, wheat, barley, and sugarcane. These 

crops are further separated according whether they are competing for land with each other. 

Crops that do not compete for land include (a) a second crop of corn (commonly known as 

“safrinha” or little season) from the main crop, (b) a second crop of dry beans, and (c) winter 

crops such as wheat and barley from the other crops. 

 

Prices drive production and consumption equations in the model. The endogenous prices 

in this sector of the model are those of: corn, soybeans, soybean meal, soybean oil, cotton, rice, 

dry beans, wheat, barley, sugar, and ethanol. Prices for livestock and dairy products drive the 

livestock section. A solution for the model is a set of prices such that supply equals demand in 

all markets. 
13

The supply of a crop comes from two main sources, namely production and beginning 

stocks. Beginning stocks are not explicitly modeled, but derived from the ending stocks of the 

previous period. Ending stocks are modeled at the “country level” as a demand component. 

Crop production of a region is the product of the area planted and crop yield. Yields for each 

crop and region is projected including a time trend, returns to the crops (intensification), and area 

used for production of major competing activities (extensification). The area of activities (crops 

and pasture) competing for land in space and time is projected following a two step approach. 

The first step determines the total amount of land to be used by these activities combined. The 

second step shares that area out to the different activities. An agriculture-wide expected returns 

function is a determining factor in the first step. The second step of this procedure follows 

closely the method published by Holt (1999)5 consisting of sharing that area out to the different 

activities, based on own returns, and returns of competing activities. 

ii. Livestock 

As in the crops section, whereas the supply side of the livestock model is divided into 6 

regions, the demand is modeled at an aggregate level. The products modeled are broilers, dairy, 

pork, and beef. The structure of the supply side of livestock depends on the product considered. 

For the case of poultry, production is modeled directly. For these products, output levels are 

projected based on their regional prices and costs of production (mostly feed costs). 

In the case of other commodities, such as beef, dairy, and pork, both the stocks of animals 

and production levels consistent with these stocks are modeled. Milk production levels are 

calculated by multiplying the number of milking cows and milk yield per animal. A slightly 

more involved structure is used for both beef and pork projections. 

The stocks of cattle and hogs are mainly driven by the modeled stocks of cows and sows. 

Given these stocks, and the projected birth rates, the crop size (calves and piglets) can be 

obtained. Adult animals not part of the breeding herd are allocated to an "other" (cattle or hogs) 

category. The supplies of beef and pork meat are calculated by multiplying the number of 

animals slaughtered (given by stocks and slaughter rates) by the average slaughter weight. 

 

The modeling of the stock of beef cows in the Brazil model warrants some more 

explanation, as it differs from the structure used in other countries. The evolution of the beef 

cattle herd is (in the Brazil model) linked to the area of pastureland available, as beef production 

is the largest user of pasture. As mentioned, this is a departure from the other models in the 

system which do not model pastureland directly. A link between pasture availability and the size 

of the cattle herd is introduced by modeling the stocking rate (number of cows per hectare of 

pasture) directly. Drivers of this stocking rate include returns to beef production, and the lagged 

stocking rate. Pastureland area varies by region as each region has its own land limit and has 

unique elasticity of total land to the sector-wide aggregate revenue. Moreover, the set of other 

enterprises that compete for land and their elasticities vary by region. Both factors drive 

differential evolution of pasture intensification across Brazil. 

 

5

 Holt, M. T. 1999. "A Linear Approximate Acreage Allocation Model." Journal of Agricultural and Resource 

Economics 24 (2): 383-397. 
14

3. Description of Scenario Simulations for EPA 

 Nine scenarios were run for the EPA analysis. The first established a reference case 

based on the AEO 2007 projected renewable fuel volumes (labeled “Reference Case”), which 

includes 12.3 billion gallons (Bgal) of corn ethanol, 0.4 Bgal of biodiesel, and 0.6 Bgal of 

imported sugarcane ethanol by 2022. In order to match the AEO renewable fuel projections, the 

ethanol demand module was turned off, and the specific volume mandates were imposed on the 

FAPRI-CARD models. The renewable fuel requirements were specifically imposed in the U.S. 

Crops Model’s ethanol module with the connections to the rest of the model maintained such that 

the rest of the Model was allowed to respond to the U.S renewable fuel requirements. In 

addition, the dry and wet mill yields were capped at the levels provided by EPA (i.e., 2.71 and 

2.5 gallons of ethanol per bushel of corn, respectively). The amount of corn used for fuel ethanol 

was then derived based on the volumes requirements and the dry and wet mill yields. 

The second scenario (labeled “Control Case”) incorporates the renewable fuels that EPA 

assumed would contribute to meet the EISA requirements, which include 15 Bgal of corn 

ethanol, 1 .7 Bgal of biodiesel, and 2.24 Bgal of imported ethanol by 2022. A series of 

additional fuel specific volumes were also run, which looked at the incremental change due to 

the increase in a single renewable fuel, holding all other renewable fuels at the Control Case 

levels. A corn ethanol case analyzed only the increase of 2.7 Bgal of corn ethanol (labeled 

“Corn Only Case”), the biodiesel case analyzed only the increase of 0.8 Bgal of biodiesel 

(labeled “Biodiesel Only Case”). Table 4 outlines the ethanol and biodiesel volumes for these 

four scenarios. The fifth scenario was the imported ethanol case, which analyzed only an 

increase of 1.6 Bgal of imported ethanol (labeled "Import Only").6

The FAPRI-CARD models do not include cellulosic ethanol sources; however we 

attempted to approximate the impact of an increase in switchgrass ethanol by modeling a 

scenario that displaces area for agricultural crops to be used for switchgrass ethanol (labeled 

“Switchgrass Only Case”), and compared it to a scenario that did not allow these acres to be used 

for switchgrass production. The number of acres diverted from agricultural crops modeled in the 

U.S. Crops Model was determined from the output of the FASOM model.7

 

6

 The Import Only Case has the Control Case volumes with Reference Case volumes for imported ethanol. 

7

 Beach, Robert; McCarl, Bruce, U.S. Agricultural and Forestry Impacts of the Energy Independence and Security 

Act: FASOM Results and Model Description, RTI International, January, 2010. 
15

Table 4: Renewable Fuel Specific Mandates 

2010 2011 2012 2013 2014 2015 2016 2017 2018 2019 2020 2021 2022

Reference Case 

Ethanol 

Dry Mill Corn Ethanol 9.33 9.50 9.61 9.71 9.78 9.87 9.92 10.05 10.21 10.39 10.62 10.84 11.04

Wet Mill Corn Ethanol 1.16 1.19 1.20 1.21 1.22 1.23 1.24 1.25 1.28 1.30 1.21 1.23 1.25

Imported Ethanol 0.29 0.16 0.18 0.19 0.20 0.39 0.51 0.53 0.54 0.58 0.60 0.63 0.64

Cellulosic Ethanol (Offline) 0.12 0.19 0.25 0.25 0.25 0.25 0.25 0.25 0.25 0.25 0.25 0.25 0.25

Total Ethanol 10.91 11.03 11.24 11.37 11.45 11.74 11.92 12.08 12.28 12.52 12.67 12.94 13.18

Biodiesel 

Soybean Oil Biodiesel 0.08 0.09 0.09 0.09 0.10 0.10 0.10 0.10 0.11 0.11 0.11 0.12 0.12

Yellow Grease Biodiesel 0.24 0.24 0.24 0.24 0.14 0.15 0.25 0.25 0.26 0.26 0.26 0.26 0.27

Total Biodiesel 0.32 0.33 0.33 0.33 0.23 0.25 0.35 0.36 0.36 0.37 0.37 0.38 0.39

Control Case 

Ethanol 

Dry Mill Corn Ethanol 10.02 10.80 11.51 12.09 12.74 13.42 13.61 13.61 13.61 13.61 13.61 13.61 13.61

Wet Mill Corn Ethanol 1.22 1.28 1.31 1.33 1.35 1.37 1.39 1.39 1.39 1.39 1.39 1.39 1.39

Imported Ethanol 0.29 0.16 0.18 0.19 0.20 0.39 0.63 1.07 1.51 1.96 1.88 1.81 2.24

Cellulosic Ethanol (Offline) 0.03 0.08 0.15 0.31 0.54 0.92 1.31 1.69 2.15 2.61 3.23 4.15 4.92

Total Ethanol 11.56 12.31 13.16 13.92 14.82 16.10 16.93 17.76 18.67 19.57 20.11 20.96 22.16

Biodiesel 

Soybean Oil Biodiesel 0.42 0.44 0.52 0.60 0.62 0.66 0.66 0.66 0.66 0.66 0.66 0.66 0.66

Corn Oil Biodiesel 0.08 0.14 0.22 0.30 0.39 0.49 0.51 0.54 0.57 0.60 0.62 0.65 0.68

Fats, Oils, Greases Biodiesel 0.38 0.38 0.38 0.38 0.38 0.38 0.38 0.38 0.38 0.38 0.38 0.38 0.38

Cellulosic Diesel (Offline) 0.04 0.10 0.20 0.41 0.71 1.22 1.73 2.24 2.85 3.46 4.28 5.50 6.52

Algae/Cam (Offline) 0.00 0.00 0.00 0.00 0.00 0.01 0.01 0.02 0.03 0.04 0.06 0.08 0.10

Total Biodiesel 0.91 1.07 1.32 1.69 2.10 2.75 3.29 3.84 4.49 5.14 6.00 7.27 8.34

Corn Only Case 

Ethanol 2010 2011 2012 2013 2014 2015 2016 2017 2018 2019 2020 2021 2022

Dry Mill Corn Ethanol 8.92 9.27 9.56 9.67 9.74 9.83 9.90 10.02 10.21 10.40 10.53 10.76 10.97

Wet Mill Corn Ethanol 1.22 1.28 1.31 1.33 1.35 1.37 1.39 1.39 1.39 1.39 1.39 1.39 1.39

Imported Ethanol 0.29 0.16 0.18 0.19 0.20 0.39 0.63 1.07 1.51 1.96 1.88 1.81 2.24

Total Ethanol 10.44 10.70 11.05 11.19 11.29 11.59 11.91 12.48 13.11 13.75 13.81 13.97 14.61

Biodiesel 

Fats, Oils, Greases Biodiesel 0.38 0.38 0.38 0.38 0.38 0.38 0.38 0.38 0.38 0.38 0.38 0.38 0.38

Corn Oil Biodiesel 0.07 0.12 0.18 0.24 0.30 0.36 0.38 0.41 0.44 0.46 0.49 0.52 0.56

Soybean Oil Biodiesel 0.42 0.44 0.52 0.60 0.62 0.66 0.66 0.66 0.66 0.66 0.66 0.66 0.66

Total Biodiesel 0.86 0.95 1.08 1.22 1.30 1.40 1.42 1.45 1.48 1.50 1.53 1.56 1.60

Biodiesel Only Case 

Ethanol 2010 2011 2012 2013 2014 2015 2016 2017 2018 2019 2020 2021 2022

Dry Mill Corn Ethanol 10.02 10.80 11.51 12.09 12.74 13.42 13.61 13.61 13.61 13.61 13.61 13.61 13.61

Wet Mill Corn Ethanol 1.22 1.28 1.31 1.33 1.35 1.37 1.39 1.39 1.39 1.39 1.39 1.39 1.39

Imported Ethanol 0.29 0.16 0.18 0.19 0.20 0.39 0.63 1.07 1.51 1.96 1.88 1.81 2.24

Total Ethanol 11.53 12.23 13.01 13.61 14.29 15.17 15.63 16.07 16.51 16.96 16.88 16.81 17.24

Biodiesel 

Fats, Oils, & Greases Biodiesel 0.38 0.38 0.38 0.38 0.38 0.38 0.38 0.38 0.38 0.38 0.38 0.38 0.38

Corn Oil Biodiesel 0.08 0.14 0.22 0.30 0.39 0.49 0.51 0.54 0.57 0.60 0.62 0.65 0.68

Soybean Oil Biodiesel 0.082 0.086 0.089 0.092 0.095 0.098 0.101 0.104 0.107 0.110 0.113 0.117 0.120

Total Biodiesel 0.54 0.61 0.69 0.77 0.86 0.96 0.99 1.02 1.06 1.09 1.12 1.15 1.18
16

Finally, three more scenarios were run as a sensitivity study, with higher yield 

assumptions for corn and soybeans in the U.S. and the top five international producers 

(Argentina, Brazil, China, the EU and Mexico). The high-yield assumptions were implemented 

in the Control Case, the Corn Only Case and the Biodiesel Only Case (labeled “Control Case 

with High Yield”, “Corn Only Case with High Yield”, and “Biodiesel Only with High Yield”, 

respectively). Corn yields were assumed to be 27% higher and soybeans 30% higher by 2022 

relative to the standard Control Case. The higher yield is achieved with a linear improvement in 

technology. As Table 5 shows, the higher corn and soybean yields were implemented by region 

in the U.S. and Brazil. 

Table 5: Corn and Soybean Yield Increases in High-Yield Scenarios 

Corn Corn Soybeans Soybeans 

Control Case High Yield Control Case High Yield 

United States 

 Corn Belt bu/ac 196.67 249.71 50.64 66.01

 Central Plains bu/ac 168.35 213.75 48.93 63.78

 Delta States bu/ac 162.56 206.41 41.67 54.32

 Far West bu/ac 204.03 259.06 0.00 

 Lake States bu/ac 185.09 235.01 45.04 58.71

 Northeast bu/ac 143.54 182.25 41.18 53.68

 Northern Plains bu/ac 157.52 200.00 37.51 48.90

 Southeast bu/ac 151.97 192.96 37.74 49.19

 Southern Plains bu/ac 150.80 191.47 25.61 33.38

Brazil 

First crop corn 

 Region 1 mt/ha 5.83 7.40 2.74 3.58

 Region 2 mt/ha 6.41 8.14 3.32 4.33

 Region 3 mt/ha 6.57 8.34 3.17 4.14

 Region 4 mt/ha 2.61 3.32 3.56 4.64

 Region 5 mt/ha 1.10 1.40 

 Region 6 mt/ha 2.20 2.79 3.53 4.60

 Brazil mt/ha 4.66 5.92 3.11 4.05

Corn Safrinha 

 Region 1 mt/ha 5.21 6.61 

 Region 2 mt/ha 3.83 4.86 

 Region 3 mt/ha 5.07 6.44 

 Region 4 mt/ha 5.03 6.38 

 Region 5 mt/ha 

 Region 6 mt/ha 1.63 2.06 

 Brazil mt/ha 4.82 6.12 

Argentina mt/ha 8.40 10.67 3.10 4.04

China mt/ha 6.42 8.15 2.01 2.62

EU mt/ha 6.94 8.81 

Mexico mt/ha 3.50 4.45 

4. Assumptions and Model Adjustments 

 The FAPRI-CARD models were customized to simulate EISA according to EPA’s 

specifications. Customized scenarios were developed by making certain model adjustments and 

adding assumptions about renewable fuel production, which are described below. 
17

4.1 Model Extension 

As mentioned above, one of the major model adjustments was to extend the projection 

period of the models. The FAPRI-CARD models were originally built to project out over a tenyear time horizon. For this project, the models were extended to generate projections until the 

2022 calendar and marketing years when all the Energy Independence and Security Act (EISA) 

RFS2 levels are reached. This necessitated extending all the behavioral equations in the models, 

as well as the exogenous variables including macroeconomic projections and all the policy 

variables. Also, the trend was extended which affected some variables reflecting technical 

relationships such as crop yields. Calibration and solution of the models remain the same. 

4.2 Model Calibration and Data Sources 

The models are typically calibrated to match data from a variety of sources, such as the 

United States Department of Agriculture USDA, IHS Global Insight, F.O. Licht, and the 

Renewable Fuels Association (RFA). For the Reference Case, renewable fuel volumes were 

calibrated to the U.S. DOE’s Annual Energy Outlook for 2007 (AEO 2007) levels. 

Data for 2006 were matched up with United States Departments of Energy (U.S. DOE) 

and Agriculture sources. For these runs, under the baseline, the (AEO 2007)xvii projects 

reneweable fuel supplies and renewable fuel usage throughout the projection period. Energy 

prices, such as crude oil prices, gasoline prices and renewable fuel prices were calibrated to AEO 

2009 Reference case prices, April Release. 

4.3 Policy Assumptions 

The FAPRI-CARD models include agricultural and energy policies such as trade 

agreements, tariffs, and subsidies. Generally the FAPRI-CARD models extend provisions in the 

2002 Farm Bill through the end of the period of analysis. 

Bioenergy mandates continue to be key drivers in the current market outlook. Major 

energy policies included in the baseline are the U.S. Energy Independence and Security Act 

(EISA) of 2007, the 2003 Renewable Fuels Directive of the EU, fuel mandates and regulations 

for Argentina and Brazil, Indonesia’s newly implemented biodiesel consumption mandate, and 

producer incentives in Canada. Specifically, in the modeling conducted for EPA, agricultural 

and energy policies in place as of January 2009, were maintained through 2022. Policies set to 

sunset, such as the $0.54/gallon U.S. ethanol import tariff, the $0.45/gallon ethanol blenders tax 

credit, and the $1.00/gallon tax credit for biodiesel, were assumed to be extended over the full 

projection period, since these incentives have consistently been renewed in the past. The 

European Union moved from the indicative targets proposed under directive 2003/30/EC toward 

a mandatory biofuel usage of 10% of the energy used for transport by 2020. In the Control Case, 

total EU biofuels consumption from first generation feedstock reaches 4% of transport fuels in 

2022. 
18

4.4 Yields of Key Crops

 As described in section 2.4, the trend parameters in the yield equation were updated with 

recent data up to 2008 in most commodities. This trend parameter captures the growth in yield 

under average weather conditions. The models in this analysis also include price-induced yield 

changes from intensification of agricultural practices and some yield drag impact when marginal 

land is brought into production. Three new scenarios run as a sensitivity analysis assumed 

significant yield improvements in some crops for several countries. 

4.5 Key Commodity By-Products 

 To be consistent with other areas of the EPA rulemaking, the average dry mill ethanol 

yield was set to 2.71 gallons of pure ethanol per bushel and the average wet mill ethanol yield 

was set to 2.50 gallons. The models also assumed that the distillers grains not consumed 

domestically in the U.S. would be exported to the international markets. The amount of the 

Distillers Grains (DG) that would be exported changed depending on each scenario. 

Use of DG in animal feed is highest in the beef cattle sector (62 to 65% share), followed 

by the dairy sector (11 to 13%), and then pork (12 to 13%) and poultry (10 to 13%) sectors. The 

differential use of DG in animal feed is a function of the adoption rate of DG by livestock and 

poultry producers and the inclusion rate of DG in their feed rations. A major concern of 

livestock and poultry producers in the adoption of DG as a feed ingredient is on its quality 

including stability of its nutritional content, storability, and ease of transport. In particular, the 

variability of the nutritional content of DG products may discourage full adoption by animal 

producers. This is particularly true to non-ruminant animals such as swine and poultry where 

specific amino acid requirement are critical because these animals are unable to metabolize on 

their own some amino acid in adequate amounts. Ruminant animal feed ration, on the other 

hand, can use DG in wet form, which bypasses the cost of drying, thereby, enabling this sector to 

be competitive in attracting DG compared to monogastric animals which have to use DG in dry 

form. For these reasons, adoption rate is highest in dairy cattle at 64 to 93%, followed by beef 

cattle at 53 to 79%, then pork at 28 to 43%, and poultry at 22 to 37%. 

There are other considerations in the use of DG in feed ration such as the issue of 

storability. Because DGs contain unstable fatty acids it is subject to rancidity in a short span of 

time. Furthermore, mycotoxins from molds, if present in the feedstock corn can spillover into 

the co-products, and can have serious adverse repercussions on animal production performance. 

These technical factors can potentially discourage the use of DG as a feed ingredient, even if 

economic considerations appear favorable. 

The inclusion of DG in the animal feed ration has been researched extensively. The 

maximum allowable inclusion rate of DG in animal feed ration has been examined in many 

studies, including Nollxviii for poultry, Shursonxix and Thalerxx for swine, Trenklexxi and Tjardes 

and Wrightxxii for cattle, and Schingoethexxiii for dairy. These studies establish inclusion rates 

that avoid compromising animal production performance (i.e., reduced daily weight gain), as 

well as final product quality (i.e., meat quality). Beef cattle feed ration has the highest inclusion 
19

rate at 41 to 50%. The maximum inclusion rate for dairy follows at 27 to 30%, for hogs 22 to 

25%, and for poultry 22 to 25%. 

In the U.S., livestock and poultry industry corn is the main source of energy and soymeal 

is the main source of protein. DG can be used as a substitute for corn and soymeal. The use of 

DG in feed ration is determined by both technical (energy and protein content of DG relative to 

corn and soymeal) and economic (price of DG, corn, and soymeal) considerations. As described 

in the previous paragraphs, there are currently several challenges associated with the quality and 

transport of DGs that prevent higher inclusion rates in animal feed. However, as DG markets 

mature, increases in efficiency, quality, and transport of DGs are likely to improve. With recent 

feeding trials showing improvement in feed efficiency in the use of DGS, for the analysis 

conducted for EPA, it assumed that DG efficiency gains will eventually reach the potential 

identified in these trials. Specifically, we assume feed efficiency gains when DG is used in 

ruminants but none when used in monogastric animals. Cost minimization of feed ration with 

DG suggests that DG can displace corn as a source of energy from 1.028 in 2009 and increasing 

to 1.196 by 2022 in beef cattle, from 0.564 and increasing to 0.731 in dairy cattle, 0.89 in swine, 

and 0.79 in poultry. Displacement of soymeal as a source of protein increases from 0.488 in 

2009 to 0.633 by 2022 in dairy cattle, 0.110 for pork, and 0.21 for poultry. 

 Furthermore, we assumed that the proportion of dry mills (in terms of volume) that 

extract corn oil from the DGs increases from 10 to 70%, and the proportion of dry mills that 

adopt fractionation increases from 3 to 20%, such that by 2022 only 10% of the dry mills do not 

produce corn oil as a by-product, based on the EPA’s engineering analysis conducted as part of 

the RFS2.. 

4.6 Crop Production Patterns 

Changes in international production capacity and, in turn, international land use changes 

are based on the response of the international crop models to commodity price changes. Land 

use changes depend not only on own price (i.e., gross returns) elasticities but also on cross-price 

elasticities. This set up allows country models to respond to relative price (i.e., gross return) 

changes in each crop separately. The new Brazil model allows direct inclusion of limits on land. 

The rest of the countries do not incorporate limits on land availability, but the inclusion of crossprice elasticities allows total crop area to respond to changes in a consistent manner. Countries 

respond to increases in crop prices by increasing their supply through area expansion and by 

decreasing their domestic demand. Which crop area increases is determined by the relative 

prices of each crop to competing crops which are country specific. FAPRI-CARD does not 

explicitly model land conversion costs, however the international production supply curves used 

by the FAPRI-CARD model implicitly take into account conversion costs. FAPRI-CARD's 

supply curves are based on historical responses to price changes, which take into account the 

conversion costs of land, based on expected future returns associated with land conversion. 
20

5. Summary of Results 

In this section, some of the key results of the alternative renewable fuel scenarios are 

presented. The key results for this analysis include change in crop acreage, crop production, 

livestock production, international trade patterns, and commodity prices. 

5.1 Crop Acreage Changes 

Table 6 shows crop area changes for the 2022 crop year as we move from each individual 

case to the Control Case, which represents higher renewable fuel volumes as outlined in the 

EISA RFS2 requirements. This means that the table shows percentage change as we move from 

Reference Case to the Control Case, Corn Only Case to the Control Case, etc. The only 

exception is with respect to Switchgrass Only Case where we move from Control Case to 

Switchgrass Only case with its higher renewable fuel volume. As such, Switchgrass Only Case 

results are discussed separate from all the other cases. 

Under the Control Case, corn acreage for the 2022 crop year is 80.9 million acres in the 

U.S., 8.4 million acres in Argentina, 36.7 million acres in Brazil, and 79.5 million acres in China. 

In general, corn area increases for all these countries as we move to Control Case from the 

Reference Case, the Corn Only Case, and the Import Only Case. The exception is that corn area 

in Brazil declines in the Import Only Case as sugar becomes more competitive with the higher 

import demand of sugar ethanol in the U.S. Also, crop area declines slightly for U.S., Argentina, 

and Brazil in the Biodiesel Only Case. As we move from the Control Case to the Switchgrass 

Only Case, area increases for Argentina, Brazil, and China as land for crop production decreases 

in the U.S. to plant for more switchgrass. 

Corn area declines for the U.S., Argentina, Brazil, and China from the standard Control 

Case to the Control High Yield Case (table 6A). There is the same pattern of higher corn area in 

all countries of interest as we move from the Corn Only High Yield Case to the Control High 

Yield Case, and lower corn area when we move from the Biodiesel Only High Yield Case to the 

Control High Yield Case. 
21

Table 6. Changes in Crop Acreage 

Table 6A. Changes in Crop Acreage with High Yield 

Control Reference Corn Only Biodiesel Only Import Only Switchgrass Only

Case Case Case Case Case Case

Corn (000 acres) (percent) (percent) (percent) (percent) (percent)

United States 80,892 2.24 1.87 -0.25 0.17 -1.72

Argentina 8,379 1.25 1.07 -0.13 0.07 0.51

Brazil 36,717 2.72 3.63 -0.26 -1.21 1.42

China 79,469 0.55 0.46 -0.05 0.03 0.26

Soybeans

United States 77,425 -1.09 -1.08 0.42 -0.06 -4.53

Argentina 52,737 -0.21 -0.17 0.11 -0.09 0.06

Brazil 70,225 1.09 0.12 1.92 0.04 3.07

Wheat

United States 48,060 -0.45 -0.36 -0.19 -0.04 -3.33

Argentina 13,615 -0.23 -0.17 -0.08 -0.01 0.07

Australia 33,203 0.00 0.02 -0.01 -0.01 0.05

Canada 22,046 -0.15 -0.04 -0.14 -0.03 0.11

Russia 65,648 0.01 0.00 0.02 0.01 0.11

Sugarcane

Australia 1,011 0.53 0.05 0.02 0.46 0.04

Brazil 28,213 3.62 -0.11 -0.03 3.77 -0.07

India 12,825 0.12 -0.03 -0.02 0.16 -0.06

Thailand 2,718 0.02 -0.05 0.00 0.08 -0.02

Note: These are percentage changes calculated based on moving from each case to the Control Case except the Swichgrass Only Case.

Control Corn Only Biodiesel Only

Case Case Case

Corn (000 acres) (percent) (percent)

United States 65,737 2.42 -0.07

Argentina 7,980 1.33 -0.05

Brazil 31,007 3.44 -0.06

China 76,897 0.55 -0.01

Soybeans

United States 76,648 -1.09 0.34

Argentina 50,895 -0.15 0.09

Brazil 36,112 0.77 3.79

Wheat

United States 51,611 -0.30 -0.24

Argentina 13,827 -0.25 -0.12

Australia 33,108 0.00 -0.02

Canada 22,772 -0.13 -0.20

Russia 65,305 0.01 0.02

Sugarcane

Australia 1,007 0.04 0.02

Brazil 28,265 -0.07 -0.04

India 12,952 -0.03 -0.01

Thailand 2,736 -0.05 0.00

Note: These are percentage changes calculated based on moving from each case to the Control Case except the Switchgrass Only Case.
22

Soybean plantings for the 2022 crop year under the Control Case are 77.4 million acres in 

the U.S., 52.7 million acres in Argentina and 70.2 million acres in Brazil. Soybean area 

increases for Brazil in the Reference, Corn Only, and Import Only Cases. In contrast, soybean 

area decreases in Argentina for all these cases. Soybean area increases for all three countries in 

the Biodiesel Only Case. As in the case for corn acreage, the impact of the Import Only Case is 

lower relative to the other cases. As we move from the Control Case to the Switchgrass Only 

Case, soybean area increases in both Argentina and Brazil but decreases in the U.S. 

For wheat, plantings for 2022 under Control Case are 48.1 million acres in the U.S., 13.6 

million acres in Argentina, 33.2 million acres in Australia, 22.0 million acres in Canada, and 

65.6 million acres in Russia. Wheat area declines for most of the countries in almost all of the 

Cases. The exceptions are Australia and Russia for the Reference and Corn Only; and Russia for 

Biodiesel Case and Import Only Case. As we move from the Control Case to the Switchgrass 

Only Case, wheat area increases in Argentina, Australia, Canada, and Russia, but decreases in 

the U.S. 

Australia is projected to have 1.0 million acres devoted to sugarcane production by 2022. 

Brazil is projected to have 28.3 million acres; India is projected to have 12.9 million acres; and 

Thailand is projected to have 2.7 million acres. The changes in the sugarcane area are small in 

all cases, except in the case of Brazil, where sugarcane area increases by over 3% in both the 

Reference and Import Only Cases. 

 The direction of impact for soybeans, wheat, and sugarcane in the High Yield sensitivity 

scenarios is the same as that of the standard scenarios with slight differences in magnitudes in the 

Corn Only and Biodiesel Only cases. 

5.2 U.S. Trade Changes 

The projected amounts and changes in selected U.S. commodity trade for the year 2022 

are given in Table 7. U.S. corn exports are lower in the Reference and Corn Only Cases, 

whereas, they are higher in the Biodiesel Only, and Import Only Cases. A similar pattern holds 

for U.S. sorghum net exports. In all the cases, U.S. wheat net exports decline with the largest 

impact seen between the Control Case and the Reference Case. Soybean net exports decreases in 

all cases. The impact on soybean oil net trade is the largest with a decline of 26% in the 

Biodiesel Only Case and followed by the Reference Case. On the other hand, soybean meal net 

exports increase by more than 3% in the Reference and Corn Only Cases. Trade in all selected 

commodity of interest decline as we move from the Control Case to the Switchgrass Only Case. 

In general, a similar pattern of trade changes is shown in the High Yield sensitivity cases, 

where U.S. net trade for commodities of interest declined with the exception of soybean meal 

and soybean oil in the Corn Only Case (table 7). In the Biodiesel Only Case, the decline in net 

trade now includes corn and sorghum as well. 
23

Table 7. U.S. Trade Patterns 

Table 7A. U.S. Trade Patterns with High Yield 

5.3 Ethanol Trade Changes 

Projected ethanol trade and the changes under the scenarios for the year 2022 are shown 

in Table 8. Negative values in the first column of the table indicate net imports. As can be seen 

for the countries listed, only Brazil is projected to export ethanol while the others import. The 

renewable fuel requirements have rather different impacts for ethanol trade. The largest impacts 

can be seen in the Reference and Import Only Cases, where U.S. net imports increase by nearly 

236%. Brazil increases its net exports by 37.8% to meet the increased import demand from the 

U.S. in both cases. The impact of the Corn Only and Biodiesel Only, and Switchgrass Only 

Cases are negligible for all countries since they are driven mostly by second round impacts to 

changes in feedstock prices. For almost all cases, net imports of ethanol decline for the rest of the 

countries, especially in the Reference and Import Only Cases. 

With no change in the U.S. ethanol net imports for both the Corn Only and Biodiesel 

Only High Yield Cases, the impacts shown in table 8A are second round impacts, responding to 

changes in feedstock prices. As in the earlier scenarios, in general, net imports of ethanol 

decline. 

Control Reference Corn Only Biodiesel Only Import Only Switchgrass Only

Case Case Case Case Case Case

 (TMT) (percent) (percent) (percent) (percent) (percent)

Corn 55,034 -15.83 -15.04 0.03 1.33 -8.23

Sorghum 5,589 -1.70 -1.15 0.04 0.01 -6.09

Wheat 26,300 -1.53 -1.22 -0.19 -0.11 -5.88

Soybeans 28,091 -2.99 -2.29 -0.43 -0.11 -11.36

Soybean Meal 15,270 3.63 3.59 -0.34 -0.05 -2.95

Soybean Oil 4,051 -6.27 4.12 -26.28 -0.05 -2.82

Note: These are percentage changes calculated based on moving from each case to the Control Case except the Switchgrass Only Case.

Control Corn Only Biodiesel Only

Case Case Case

 (TMT) (percent) (percent)

Corn 43,046 -16.32 -0.82

Sorghum 7,429 -2.01 -0.29

Wheat 32,356 -0.96 -0.32

Soybeans 46,889 -1.93 -0.41

Soybean Meal 17,972 3.37 -2.15

Soybean Oil 5,156 3.78 -21.87

Note: These are percentage changes calculated based on moving from each case to the Control Case except the Switchgrass Only Case.
24

Table 8. Ethanol Trade 

Table 8A. Ethanol Trade with High Yield 

5.4 Vegetable Oil Trade Changes 

The projected vegetable oil trade figures and changes are shown in Table 9. Soybean oil 

exports are dominated by three countries: Argentina, Brazil, and the U.S. With the decline in 

U.S. net exports of soybean oil, Argentina and Brazil fill the gap, while China, EU, and India 

reduce their net imports in both the Reference and the Biodiesel Only Cases. The opposite 

happens in the Corn Only Case where U.S. net exports increase, displacing exports from 

Argentina and Brazil, while China, EU, and India absorbs some of the increase in net exports. 

For rapeseed/canola oil, Canada is the major exporter and it roughly maintains its export levels 

under the scenarios. The EU increases its import under the Reference, Biodiesel Only, and 

Import Only Cases, while U.S. imports decline including in the Corn Only Case. The impact on 

sunflower and palm oil trade is very small in all cases with the exception of the Biodiesel Only 

Case where the EU’s net imports of sunflower oil decreased. As we move from the Control Case 

to the Switchgrass Only Case, U.S. exports of of soybean oil declines. The exports from 

Argentina and Brazil increase, while the imports to China, EU, and India decline. 

The impact in the High Yield Cases in table 9A follow exactly the same pattern as in the 

standard cases. 

Control Reference Corn Only Biodiesel Only Import Only Switchgrass Only

Case Case Case Case Case Case

 (TMT) (percent) (percent) (percent) (percent) (percent)

U.S. -2,146 235.50 0.00 0.00 235.50 0.00

Brazil 5,331 37.79 0.02 0.00 37.77 0.02

China -142 -5.28 0.54 -0.03 -5.82 0.46

EU -714 -2.30 -0.03 -0.01 -2.24 -0.02

India -190 -7.38 -0.13 -0.06 -7.20 -0.20

Japan -580 -0.54 -0.01 0.00 -0.52 -0.02

South Korea -377 -0.43 -0.01 0.00 -0.42 -0.01

Note: These are percentage changes calculated based on moving from each case to the Control Case except the Switchgrass Only Case.

Control Corn Only Biodiesel Only

Case Case Case

 (TMT) (percent) (percent)

U.S. -2,146 0.00 0.00

Brazil 5,302 0.02 0.00

China -126 0.62 0.04

EU -712 -0.03 0.00

India -192 -0.13 -0.08

Japan -581 -0.01 -0.01

South Korea -377 -0.01 0.00

Note: These are percentage changes calculated based on moving from each case to the Control Case except the Switchgrass Only Case.
25

Table 9. Vegetable Oil Trade Impacts 

Table 9A. Vegetable Oil Trade Impacts with High Yields 

Control Reference Corn Only Biodiesel Only Import Only Switchgrass Only

Case Case Case Case Case Case

Soybean Oil (TMT) (percent) (percent) (percent) (percent) (percent)

Argentina 7,976 0.19 -0.23 1.24 0.00 0.11

Brazil 1,921 3.13 -2.76 27.55 -0.06 0.32

U.S. 4,051 -6.27 4.12 -26.28 -0.05 -2.82

China -4,535 -1.78 0.97 -8.38 -0.04 -0.93

EU -1,613 -1.68 0.16 -7.33 0.02 -0.82

India -2,200 -0.74 0.39 -3.76 -0.03 -0.52

Rapeseed/Canola Oil

Canada 2,191 -0.49 -0.12 0.04 0.01 0.03

EU -538 41.59 -5.14 2.57 0.24 0.66

U.S. -1,752 -18.29 -0.28 -1.26 0.00 -0.08

Sunflower Oil

Argentina 1,809 -0.20 -0.08 0.07 0.00 -0.02

Other CIS 993 -0.14 0.03 -0.67 0.00 -0.03

EU -1,613 0.20 -0.32 1.39 0.02 0.10

Palm Oil

Malaysia 20,424 -0.06 -0.06 0.42 0.00 0.04

Indonesia 25,275 -0.01 -0.03 0.23 0.00 0.02

China -10,914 -0.02 -0.02 0.19 0.00 0.02

EU -4,746 -0.08 -0.09 0.70 0.01 0.06

India -7,509 -0.03 -0.04 0.34 0.00 0.04

Note: These are percentage changes calculated based on moving from each case to the Control Case except the Switchgrass Only Case.

Control Corn Only Biodiesel Only

Case Case Case

Soybean Oil (TMT) (percent) (percent)

Argentina 8,031 -0.26 1.31

Brazil 2,203 -2.44 23.67

U.S. 5,156 3.78 -21.87

China -5,136 0.93 -7.52

EU -1,716 1.12 -6.40

India -2,532 0.37 -3.07

Rapeseed/Canola Oil

Canada 2,175 -0.04 0.13

EU -438 -0.41 10.24

U.S. -1,791 -0.37 -1.25

Sunflower Oil

Argentina 1,815 -0.03 0.10

Other CIS 1,001 0.05 -0.63

EU -1,580 -0.09 1.67

Palm Oil

Malaysia 20,261 -0.03 0.44

Indonesia 25,169 -0.01 0.24

China -10,867 -0.01 0.20

EU -4,687 -0.05 0.74

India -7,456 -0.02 0.35

Note: These are percentage changes calculated based on moving from each case to the Control Case exept the Switchgrass Only Case.
26

5.5 World Food Consumption Changes 

Due to the increase in crop prices in almost all cases, the cost of producing livestock and 

dairy products also increases. As seen in Table 10, given the higher renewable fuel target in the 

Control Case, livestock and dairy prices increase in all cases except the Biodiesel Only Case. 

Under the biodiesel case, feed prices become favorable as more of the by-product soybean meal 

is produced to meet higher biodiesel targets. As we move from the Control Case to the 

Switchgrass Case, feed grains and oilseed meal supplies tightens raising the price of meat and 

dairy products. With the Import Only Case largely impacting the sugar sector, the rate of 

increase in the prices of feed grains is small resulting in lower rate of increase in the cost of 

livestock and poultry production, and directly translating to lower rate of increases in meat and 

dairy prices. 

The direction of impacts in the High Yield sensitivity cases in table 10A is the same as 

the standard cases, but with slightly larger magnitudes. 
27

Table 10. Impact on Livestock and Dairy Prices 

Table 10A. Impact on Livestock and Dairy Prices with High Yield 

5.6 World Grain, Oilseed, and Renewable Fuel Price Changes 

 Table 11 outlines the world price impacts under the scenarios. The commodity prices 

increase in most of the scenarios. The impacts are largest in the Reference and Import Only 

Cases. Ethanol prices show an 8.5% increase between the Reference Case and the Control Case 

and 8.3% increase in the Import Only Case. Biodiesel price increases in the Biodiesel Only Case 

by 2.9%. All commodity prices increases as we move from the Control Case to the Switchgrass 

Only Case.8

 Table 11A shows that the same pattern holds in the High Yield cases as in the standard 

cases. 

 

8

 The other industrial rapeseed oil use in the U.S. is higher in the reference case relative to the control case. As a 

result, the projected rapeseed oil price is higher in the reference case in the last couple of years of the projection 

period. Since rapeseed oil is the main feedstock used for biodiesel production in the EU, and with our world 

biodiesel price quoted as a Central Europe FOB price, it is also higher in the reference case. 

Control Reference Corn Only Biodiesel Only Import Only Switchgrass Only

Case Case Case Case Case Case

 ($ per MT) (percent) (percent) (percent) (percent) (percent)

Beef 2,821 0.38 0.12 -0.34 0.06 0.72

Pork 1,448 1.58 1.24 -1.19 0.15 1.30

Broiler 2,462 0.93 0.78 -1.84 0.12 1.23

Butter 2,595 0.14 0.10 -0.11 0.01 0.17

Cheese 3,617 0.18 0.16 -0.23 0.02 0.24

Non-Fat Dry Milk 2,816 0.37 0.23 -0.28 0.02 0.46

Whole Milk Powder 3,018 0.20 0.15 -0.22 0.02 0.20

Note: These are percentage changes calculated based on moving from each case to the Control Case except the Switchgrass Only Case.

Control Corn Only Biodiesel Only

Case Case Case

 ($ per MT) (percent) (percent)

Beef 2,501 0.40 -0.53

Pork 1,065 1.94 -1.52

Broiler 1,822 1.58 -2.97

Butter 2,536 0.10 -0.10

Cheese 3,459 0.23 -0.21

Non-Fat Dry Milk 2,681 0.19 -0.29

Whole Milk Powder 2,919 0.15 -0.20

Note: These are percentage changes calculated based on moving from each case to the Control Case except the Switchgrass Only Case.
28

Table 11. Impact on World Crops and Biofuel Prices 

Table 11A. Impact on World Crops and Biofuel Prices with High Yield 

5.7 For Further Information 

 See data tables included in the docket. 

Control Reference Corn Only Biodiesel Only Import Only Switchgrass Only

Case Case Case Case Case Case

 ($ per MT) (percent) (percent) (percent) (percent) (percent)

Corn 204 3.07 2.32 0.06 0.27 2.36

Sorghum 208 1.69 1.24 0.18 0.21 2.68

Barley 194 1.46 1.10 0.11 0.16 1.53

Wheat 269 1.08 0.77 0.18 0.15 1.94

Soybeans 402 0.86 0.22 0.89 0.17 2.01

Rapeseed 418 -0.69 -0.71 1.10 0.14 0.85

Sunflower 483 0.23 0.15 1.07 0.12 1.14

($ per gallon)

Ethanol 2.15 8.54 0.11 0.05 8.32 0.22

Biodiesel 6.78 -1.34 -0.77 2.87 0.05 0.28

Note: These are percentage changes calculated based on moving from each case to the Control Case except the Switchgrass Only Case.

Control Corn Only Biodiesel Only

Case Case Case

 ($ per MT) (percent) (percent)

Corn 114 4.23 0.60

Sorghum 145 2.38 0.44

Barley 152 1.39 0.25

Wheat 217 1.02 0.35

Soybeans 216 0.66 1.70

Rapeseed 361 0.13 2.31

Sunflower 380 0.64 1.59

($ per gallon)

Ethanol 2.12 0.12 0.08

Biodiesel 6.43 -0.21 3.69

Note: These are percentage changes calculated based on moving from each case to the Control Case except the Switchgrass Only Case.
29

 

i Standard validation of models are conducted when they are initially developed, usually with a single country and 

commodity group coverage. Sample publications on validation includes; Fabiosa, Jacinto, Xiaoting Qi, 1998, 

“A New General Conceptual Approach to Modeling the Livestock Sector: An Application to the Japanese SwinePork Sector”, CARD Working Paper 98-WP 204 ; Barrett, C., and Jacinto F. Fabiosa, 1998, “A Policy Model for the 

Livestock and Poultry Sectors of Mexico”, CARD Working Paper, 98-TR 39; Fuller, 1997, “Policy and Projection 

Model for the Meat Sector in the People's Republic of China”, CARD Working Paper 97-TR 36; Shaw, I., J. 

Shaffer, and V. Premakumar, 1997, “Policy and Forecasting Models for the Chinese, South Korean, Australian, and 

European Union Meat Sectors”, CARD Working Paper 97-TR 35 

ii Abler, David, John C. Beghin, David Blandford, and Amani Elobeid. “Changing the U.S. Sugar Program into a 

Standard Crop Program: Consequences under NAFTA and Doha.” Review of Agricultural Economics, Volume 

30(1):82-102, 2007. 

iii Elobeid, Amani, Simla Tokgoz, Dermot J. Hayes, Bruce A. Babcock and Chad E. Hart. “The Long-Run Impact of 

Corn-Based Ethanol on the Grain, Oilseed, and Livestock Sectors with Implications for Biotech Crops.” 

AgBioForum, 9(4): 1-8, 2006. 

iv Fabiosa, J.F, J. Beghin, F. Dong, A. Elobeid, F. Fuller, H. Matthey, S. Tokgöz, and E. Wailes. “The Impact of the 

European Enlargement and CAP Reforms On Agricultural Markets. Much Ado about Nothing?” Journal of 

International Agricultural Trade and Development, Volume 3, Number 1: 57-69, 2007. 

v

 Fabiosa, Jacinto, John Beghin, Stéphane De Cara, Amani Elobeid, Cheng Fang, Murat Isik, Holger Matthey, 

Alexander Saak (Iowa State University) and Pat Westhoff, D. Scott Brown, Brian Willott, Daniel Madison, Seth 

Meyer, and John Kruse (University of Missouri-Columbia). “The Doha Round of the WTO and Agricultural 

Markets Liberalization: Impacts on Developing Economies.” Review of Agricultural Economics, Volume 27, 

Number 3, pages 317-335, 2005. 

vi Tokgoz, Simla, Amani Elobeid, Jacinto Fabiosa, Dermot J. Hayes, Bruce A. Babcock, Tun-Hsiang (Edward) Yu, 

Fengxia Dong, and Chad E. Hart, “Bottlenecks, Drought and Oil Price Spikes: Impact on U.S. Ethanol and 

Agricultural Sectors.” Review of Agricultural Economics, Volume 30(4), 2008. 

vii Hayes, Dermot, Bruce Babcock, Jacinto Fabiosa, Simla Tokgoz, Amani Elobeid, Tun-Hsiang Yu, Fengxia Dong, 

Chad Hart, Wyatt Thompson, Seth Meyer, Edward Chavez, and Suwen Pan. “Biofuels: Potential Production 

Capacity, Effects on Grain and Livestock Sectors, and Implications for Food Prices and Consumers.” Journal of 

Agricultural and Applied Economics, 41(2) August 2009: 465-491. 

viii Fabiosa, Jacinto., John C. Beghin, Fengxia Dong, Amani Elobeid, Simla Tokgoz, Tun-Hsiang Yu. “Land 

Allocation Effects of the Global Ethanol Surge: Predictions from the International FAPRI Model.” Land Economics, 

Forthcoming 

ix Fabiosa, J.F., John C. Beghin, Fengxia Dong, Amani Elobeid, Simla Tokgoz, and Tun-Hsiang Yu. 2010. “The 

Global Bioenergy Expansion: How Large Are the Food–Fuel Trade-Offs?” Part II – Chapter 8. pp 113-132. Natural 

Resource Management and Policy Series: Handbook of Bioenergy Economics and Policy, , Vol. 33 Khanna, 

Madhu; Scheffran, Jürgen; Zilberman, David (Eds.) 2010, XIV, 439 p. Springer, USA 

x

 FAPRI Staff, 2008, FAPRI 2008 U.S. and World Agricultural Outlook, 08-FSR 1, and FAPRI Staff, 2001, “Impact 

of a 10 Percent Decrease in Planted Acreage of All U.S. Program Crops,” Briefing Paper 01-BP 33 

xi Tokgoz, S. A. Elobeid, J. Fabiosa, D. Hayes, B. Babcock, T. (Edward) Yu, F. Dong, C. Hart, and J. Beghin. 2007 

“Emerging Biofuels: Outlook of Effects on U.S. Grain, Oilseed, and Livestock Markets,” Staff Report 07-SR 101. 

This study was supported by the following organizations: National Grain and Feed Association, American Meat 

Institute, Grocery Manufacturers Association/Food Products Association, National Cattlemen’s Beef Association, 
30

 

National Chicken Council, National Pork Producers, Council, National Oilseed Processors Association, National 

Turkey Federation, and the North American Millers Association. 

xii F.O. Lichts. Online Database, Licht Interactive Data. http://www.agranet.com/portal/puboptions.jsp?Option=menu&pubId=ag072

xiii FAOSTAT. Database. http://faostat.fao.org/faostat/collections?subset=agriculture 

xiv United States Department of Agriculture. Foreign Agricultural Service Production, Supply, and Distribution 

database. http://www.fas.usda.gov/psdonline/psdHome.aspx 

xv United States Department of Agriculture. Foreign Agricultural Service Production, Supply, and Distribution 

database. http://www.fas.usda.gov/psdonline/psdHome.aspx 

xvi United States Department of Agriculture Foreign Agricultural Service. 

http://ffas.usda.gov/scriptsw/attacherep/default.asp

xvii The reference is "Annual Energy Outlook 2007 with Projections to 2030", Energy Information Administration, 

Report #:DOE/EIA-0383(2007), February 2007 available at 

http://www.eia.doe.gov/oiaf/archive/aeo07/pdf/0383(2007).pdf 

xviii Noll, S., V. Stangeland, G. Speers and J. Brannon, 2001. Distillers Grains in Poultry Diets. 62nd Minnesota 

Nutrition Conference and Minnesota Corn Growers Association Technical Symposium, Bloomington, MN. 

September 11-12, 2001. 

xix Shurson, J. n.d. “The Advantages of Using Corn Distillers Dried Grains with Solubles in Swine Diets.” Fact 

sheets, Dept. of Animal Science, University of Minnesota. http://www.ksgrains.com/ethanol/DDGSFacts.pdf

xx Thaler, B. 2002. “Use of Distillers Dried Grains With Solubles (DDGS) in Swine Diets.” Extension Extra 2035, 

August 2002, College of Agriculture & Biological Sciences, South Dakota State University, USDA Cooperative 

Extension Service, SDSU, http://agbiopubs.sdstate.edu/articles/ExEx2035.pdf

xxi Trenkle, A. n.d. “The Advantages of Using Corn Distillers Grains with Solubles in Finishing Beef Cattle Diets.” 

Fact sheets. http://www.ksgrains.com/ethanol/DDGSFacts.pdf

xxii Tjardes, K., and C. Wright. 2002. “Feeding Corn Distiller’s Co-Products to Beef Cattle.” Extension Extra 2036, 

August 2002, College of Agriculture & Biological Sciences, South Dakota State University, and USDA Cooperative 

Extension Service, SDSU 

xxiii Schingoethe, D.J., K.F. Kalscheur, and A.D. Garcia. 2006. “Distillers Grains for Dairy Cattle.” Extension Extra

4022, Dairy Science Department, College of Agriculture & Biological Sciences, South Dakota State University, 

USDA Cooperative Extension Service, SDSU. http://agbiopubs.sdstate.edu/articles/ExEx4022.pdf. 
31

 

Annex 1 – New yield specification 

 The new yield specification includes a trend, ratio of current revenue and cost, moving average of revenue 

and cost, and total area, 

[A1]   10

10

Re Re i y ave

i y ave

it it t it it t it

T v T v

y Trend a a TCost TCost       



                  

To illustratrate the methodology, we use yield and land data for the U.S. and Brazil (table A1.1) and elasticities from 

the U.S. model (table A1.2) to derive adjustment factors to calibrate the elasticities for Brazil. The derivation of the 

adjustment factors are given in table A1.3. 

Table A1.1. U.S. and Brazil yield and land data 

 

Yield specification US Brazil 

 Corn Yield 8.55 2.91 

 Arable Land 175,379 58,048 

Forest area, permanent meadow, 

 Pasture 538,557 689,327 

 Ratio 0.75 0.92 

Source: USDA PSD Database and FAO Agriculture Database 

Table A1.2. Elasticity of corn yield in the U.S. corn belt region 

Variable Short-run Long-run 

 Price-Cost ratio 0.013 0.074 

 10-year moving average of price-cost ratio 0.061 

 Area planted to all crops -0.023 

Source: FAPRI-CARD U.S. Crops Model 

Table A1.3 Adjustment factor for elasticity calibration methodology 

Yield specification US Elasticity Adjustment Factor Brazil Elasticity 

Technology Adjustment 0.061 2.95(a) 0.181 

Marginal area adjustment -0.023 0.81(b) -0.018 

(a) ratio of U.S. – Brazil yield to represent differential yield gap. 

(b) ratio of U.S.-BR proportion of forest plus permanent meadows plus pasture relative to total area (0.92 in 

Brazil and 0.75 in U.S.) 
32

 

Annex 2 – New land allocation approach in the Brazil model 

 Two additional features in the new Brazil model warrant more detailed description. This includes the twostage land allocation approach where land supply constraints are imposed, and the other one is the simultaneous 

modeling of animal numbers and pasture area to account for stocking rate. 

 

The first stage in the land allocation approach determines the total amount of land to be used for all 

agricultural enterprises covered in the model based on expected returns and the potential availability of land using 

the following equation; 

  ag T A Am r jt j j jt  , 

where ag Ajt is the land that will be used for agriculture (including pastures) in region j, and year t, T Aj is the 

potential amount of land for agricultural activities in region j, and m r j jt   is the share of that potential land that 

will be actually used depending on aggregate expected returns in the region and year jt r . In the Control Case, this 

share ranged from 49% for the North Amazon region to 93% for the Northeast Coast region by 2022 . These 

agriculture-wide expected returns evolve with time base on the following formula, 

1

1 1

*

I

ijt ijt

jt jt ag

i jt ijt

A r

r r

A r 

 

    

   

, 

which indicates that it evolves based on a weighted average of the change in returns of the activities considered. The 

variable Aijt

 is defined in the next paragraph. 

The second stage of this approach (which follows closely the method published by Holt (1999)xxiii) consist 

of sharing that area out to the different activities, based on own returns, and returns of competing activities with the 

restriction that the sum of the shares needs to add to one. Hence, for these activities we have * ag A Av 

ijt jt ijt  , where 

ijt v is the share (just mentioned) for activity i in region j and year t, with

1

1

I

ijt

i

v



  for all j and t. 

For each crop in each region and year production is thus projected as 

ˆ * ˆ Y Ay ijt ijt ijt   , 

and the country level area and production of a crop i are obtained by summing across regions, that is, 

6

1 it ijt j

A A

    and 

6

1

ˆ ˆ

it ijt j

Y Y   . Total supply available for that crop would then be estimated as 

ˆ ˆ ˆ it it it S Y BS  

Another new feature of the Brazil model is an explicit modeling of pasture area as an integrated decision in 

the overall area allocation. A link between pasture availability and the size of the cattle herd is introduced by 

modeling the stocking rate (number of cows per hectare of pasture) directly. We model “stocking rate” of cows to 

directly link the cattle inventory and pasture area needed. Let t s be the stocking rate in period t, b E t S , d E t S , 

ot ESt denote ending stocks of beef cows, dairy cows, and other cattle respectively, and 1p At is pasture area. Thus 

b d ot

b d ot ttt

t ttt p

t

BS BS BS

s sss

A

 

 
33

 

For each region we model 

   1 2 0

1

*

b

b bb t

t tt p

t

ES

s at s r

A

     

Where tr denotes returns. In log form 

ln( ) ' ln( ) ln( ) ln( ) ln ln 1 10 1 12     b pp b b ES a A A t ES r t tt t t          

If pasture area is reduced say because of competition from crops, the cattle herd will get a signal to contract (fewer 

cows will result in fewer calves and less “other cattle” in the next periods). Pasture expansion will let the herd grow 

quicker.