Technical

Bulletin

Number 1918

February 2008

United States 

Department

of Agriculture

Economic 

Research 

Service

David H. Harrington and Robert Dubman

Equilibrium Displacement

Mathematical Programming 

Models

Methodology and a Model 

of the U.S. Agricultural Sector
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Harrington, David H.

 Equilibrium displacement mathematical programming models : 

 methodology and a model of the U.S. agricultural sector.

 (Technical bulletin (United States. Dept. of Agriculture); no. 1918)

 1. Programming (Mathematics). 

 2. Agriculture—Economic aspects—United States—Mathematical 

 models.

 3. Agriculture—Economic aspects—United States—Computer

 programs.

 4. Agriculture and state—United States.

 I. Dubman, Robert.

 II. United States. Dept. of Agriculture. Economic Research Service.

 III. Title.

QA402.5

Photo credit: PhotoDisc.
United States

Department

of Agriculture

www.ers.usda.gov

A Report from the Economic Research Service

Abstract

The objective of this research is to extend and generalize the equilibrium displacement 

methodology by combining it with mathematical programming methods and existing 

knowledge of farm sector relationships to develop sectoral adjustment models that can 

operate in pure competition, monopoly/monopsony, or mixed-competition. A model of 

the U.S. agricultural sector at the national aggregate level is presented to illustrate the 

methods. An appendix contains a user’s manual describing the operation of the model. 

Further appendices contain documentation of the structure of the spreadsheets, the 

programming tableau, and the SAS solution program.

Keywords: Equilibrium displacement models, mathematical programming, positive mathematical programming, U.S. agricultural sector, U.S. farm programs, direct 

payments, counter-cyclical payments, loan deficiency payments, marketing loan gains, 

conservation reserve program, wetlands reserve program, crop insurance

David H. Harrington and Robert Dubman

Equilibrium Displacement 

Mathematical Programming 

Models

Methodology and a Model 

of the U.S. Agricultural Sector

Technical

Bulletin

Number 1918

February 2008
ii

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Economic Research Service/USDA

Contents

Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . iv

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

EDMP Methodology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2

Review of Literature . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2

Theoretical Development . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3

The EDMP Formulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5

Modeling the Supply Side . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8

Modeling the Demand Side . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10

Modeling Agricultural Policies and Programs . . . . . . . . . . . . . . . . . . . . 11

Payment Bases . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11

Decoupled Payments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11

Counter-Cyclical Payments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11

Loan Deficiency Payments and Marketing Loan Gains . . . . . . . . . . . . . 12

Conservation Reserve, Wetlands Reserve, and Grassland 

 Reserve Programs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13

Working Lands Conservation Programs . . . . . . . . . . . . . . . . . . . . . . . . 14

Crop Insurance Subsidies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14

Superseded Agricultural Programs . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15

Model Calibration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16

What Do Gradients Mean? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17

Structure of the Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18

Commodities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18

Specified Resources . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18

Specified Purchasable Inputs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19

Processes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19

Agricultural Policies and Programs . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20

Solving the Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22

Supply Parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23

Implicit Acreage- and Supply-Response Elasticities . . . . . . . . . . . . . . . 26

Demand Parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28

Government Program Parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30

Post-Optimal Calculations of Performance Variables . . . . . . . . . . . . . 32

Net Farm Income and Net Cash Flow . . . . . . . . . . . . . . . . . . . . . . . . . . 32

Government Budgetary Exposure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33

Consumer and Producer Surpluses . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33

Commodity Cash Incomes, Expenses, and Margins . . . . . . . . . . . . . . . 34
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References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36

Appendix I: User’s Manual . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39

Appendix II: The SAS Excel Link Program . . . . . . . . . . . . . . . . . . . . . . 45

Appendix III: Model Spreadsheets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53

Appendix III model spreadsheets are 

accessible by contacting 

David Harrington, 202-694-5571, 

davidh@ers.usda.gov
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Summary

Development of the Equilibrium Displacement Mathematical Programming 

Model (EDMP) started in response to the passage of the Federal 

Agricultural Improvement and Reform Act of 1996. The 1996 Farm Act 

fundamentally changed the traditional economic incentives in commodity 

policy by decoupling most Government commodity payments from the 

levels of individual farmers’ production of the commodities, by eliminating 

acreage reduction programs, and by no longer limiting production eligible 

for support to a producer’s historic production base. The effects of these 

changes in economic incentives were to render temporarily obsolete all 

econometric simulators estimated under the previous policy regime. The 

first published article using EDMP assessed the likely effects of the 1996 

Farm Act on production, prices, net farm incomes, and farm asset values 

in the Great Plains. Subsequent applications of the EDMP framework 

evaluated the effects of market resistance to genetically modified grains and 

the implications of demand and supply elasticities for the distribution of 

rents in supply chain industries. 

This bulletin documents the theory, structure, and operating characteristics 

of a U.S. aggregate agricultural sector EDMP model that is flexible and user 

friendly. This bulletin includes all activities and parameter values in tabular 

summary form, the actual quadratic programming tableau, the SAS code for 

solving the model, and a user’s manual. The authors have cast the discussion 

in simple, conceptual terms rather than detailed, technical terms, in order to 

demystify the methodology for researchers not specifically trained in mathematical programming. 

What Are the Issues?

Government policies, both agricultural and general economic, have pervasive influences on the structure and performance of the agricultural sector. 

Furthermore, policies and programs frequently interact to potentiate or mitigate their separate effects on sector structure and performance. The model 

documented in this bulletin focuses on the effects of agricultural policies and 

programs on the performance of the U.S. agricultural sector. The agricultural 

sector is treated as operating in perfect competition, subject to the provisions 

of agricultural and economic policies. Scenario analyses—”what if” questions—concerning alterations in policy, technology, demand, and/or supply 

are addressed by comparing the new equilibrium under the scenario with the 

base period equilibrium. Economic changes frequently occur in cascades of 

changes involving several policies, commodities, or technologies. The effects 

of such cascades of changes can be very different from the sum of the effects 

of the individual changes. This model specifically addresses such interactions. In addition to portraying a sector or industry in perfect competition, 

the EDMP model can be formulated to allow monopolistic/monopsonistic 

behavior in one or more sectors, while the remainder of the model operates in 

perfect competition.
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What Does the Model Do?

The U.S. agricultural sector EDMP model is a price-endogenous quadratic 

programming model providing sectorwide comparative static analyses of 

production and disposition of the 16 top crop commodities and 8 top livestock commodities, including disposition among farm sector use, domestic 

demands, exports and competing imports, and storage and dis-storage. 

The model is constructed from data compiled by U.S. Department of 

Agriculture’s Economic Research Service: cost-of-production estimates, farm 

income and production accounts, and Agricultural Resource Management 

Survey (ARMS). The sector performance effects of major agricultural policies—such as direct payments, counter-cyclical payments, loan deficiency 

payments, the Conservation Reserve Program, and crop insurance—are 

endogenously calculated in the model. 

How Does the Model Work?

In solving the model, the quadratic programming solution algorithm enforces 

the optimality conditions of perfectly competitive equilibrium across all 

products and factors. That is, marginal revenues from a one-standard-unit 

increase in production are equalized across all products while simultaneously 

equalizing the marginal values (shadow prices) of each limiting factor across 

all products using that factor. This procedure is conceptually equivalent to 

maximizing the combined producer plus consumer surplus. The base period 

model is calibrated to reproduce all base period prices and quantities to the 

desired degree of accuracy without the use of artificial constraints or limitations. Scenario analyses are performed by comparing the equilibrium solution 

under the scenario assumptions with the base period equilibrium. Change 

parameters allow the user to customize both the base period solution and the 

scenario solution by specifying acreages, yields, cost levels, and demand 

parameters for any combination of products in the model. A post-optimal 

calculations spreadsheet calculates the following performance indicators:

• Net farm income, short and long run

•	Net cash flow, short and long run

•	Crop acreages, by commodity

•	Livestock production levels, by commodity

•	Domestic nonfarm demands, by commodity

•	Market demand prices, by commodity

•	Storage and dis-storage levels, by commodity

•	Exports and competing import levels, by commodity

•	Direct payments, by base commodity

•		Counter-cyclical payments, by base commodity

•	Loan deficiency payments and marketing loan gains, by commodity

•	Crop insurance subsidies, by commodity

•	Domestic consumer surplus, by commodity
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•	Export consumer surplus, by commodity

•	Producer cash market income, by commodity

•	Producer cash expenses, by commodity

•	Producer net cash margin, by commodity

Other user-defined performance activities, constraints, and performance 

measures can be added to fit the model to the problem.
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Introduction

Equilibrium displacement (ED) models, or their forerunners, have been part 

of the agricultural economics literature since 1958 (Buse, 1958) and have had 

recent applications (Piggott et al., 1995, and Sumner, 2005). One reason for 

their popularity is ease of computation with today’s spreadsheet technology. 

Some researchers have noted their restrictive assumptions as limitations.

Mathematical programming (MP) models have been relatively neglected in 

the theoretical literature of agricultural economics in recent years, while still 

being used in applications such as computable general equilibrium models, 

the ERS Regional Environment and Agriculture Programming (REAP) 

Model (formerly the USMP Model) and Howitt’s positive MP method 

(Howitt, 1995). Both the equilibrium displacement and MP approaches, individually, have fallen short of adequately addressing some emerging issues. 

To address the types of adjustments to the agricultural sector currently being 

raised requires models that:

•	Assure feasibility and efficiency of solutions with respect to the underlying physical production and demand functions. 

•		Simultaneously and gradually adjust to changes in technology, organizational structure, and/or policy without imposing artificial constraints or 

mechanisms not supported by theory. 

•	Portray progressive investment in emerging technologies and disinvestment in superseded technologies. 

•	Allow analysis of large displacement scenarios, often without historical 

precedent. 

•	Allow portrayal of pure competition, monopoly/monopsony, or mixedcompetition, as the issues and markets may require. 

•	Can model the simultaneous interaction of detailed Government policies 

affecting the farm sector. 

•	Incorporate economic structures synthesized from known physical and 

economic relationships, such as process technology, production alternatives, demand substitutions, and market linkages.

•	Allow calibration to base situations, such as forecasts, baselines, and 

coordinated studies. 

•	Allow the user to control which activity levels are predetermined and 

which are endogenous to the analysis. 

This bulletin describes the methodology, structure, and supply-response characteristics of such a model for the U.S. agricultural sector. We have cast the 

discussion in simple, conceptual terms rather than detailed, technical terms in 

order to demystify the methodology for researchers not specifically trained in 

MP. Equilibrium Displacement Mathematical Programming Models (EDMP) 

combine the equilibrium displacement modeling approach with the positive MP technique, an asset-fixity conceptualization of supply response, and 

consistent specification of demand relationships for subaggregates such as 

regions or types of farms (see fig. 1 in box on page 7).
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EDMP Methodology

Review of Literature

There have been a number of contributors to the development of equilibrium 

displacement modeling. The literature is usually traced back to Muth (1964) 

who developed the reduced forms for proportional displacements from 

equilibrium for a system of equations of supply and demand for a product 

dependent on two factors of production and exogenous shifters for each of 

the functions. However, in a 1958 article in the Journal of Farm Economics, 

Buse (1958) demonstrated the development of what he called “total elasticities”—the reduced-form elasticities of a system of supply and demand 

equations for two commodities similar to that later devised by Muth—and 

contrasted his “total elasticities” with Marshallian ceteris paribus elasticities. 

Buse’s was the first article to use matrix algebra to state and solve his system 

of equations. Gardner (1975) employed a formulation identical to Muth’s 

to investigate the relationship of retail food prices to farm prices. Sumner 

and Wohlgenant (1985) first applied the term “equilibrium displacement 

modeling” to Muth’s formulation. Wohlgenant (1993) also extended Muth’s 

formulation to multistage industries. Piggott et al. (1995) employed the term 

“equilibrium displacement modeling” and formulated their model in matrix 

algebra. Davis and Espinoza (1998) extended the Gardner analysis to develop 

the full distribution of parameter values rather than only selected values. 

Most recently, Sumner (2005) used equilibrium displacement methods to 

assess the effects of U.S. commodity polices on world prices and trade.

Samuelson (1952) first demonstrated that the spatial equilibrium problem 

could be cast and solved as a linear programming (LP) problem. Takayama 

and Judge (1971) demonstrated how quadratic programming could be used 

to solve linear supply and demand equations, determining both prices and 

quantities endogenously. However, Plessner (1965) and Yaron et al. (1965) 

had earlier applied quadratic programming methods to price-endogenous 

modeling of the U.S. agricultural sector. Because of the scarcity and cost 

of quadratic programming solution algorithms, early MP literature of priceendogenous models in agricultural economics turned to LP methods. Martin 

(1972) incorporated stepped supply and demand functions in LP models. 

Martin’s method significantly increased the dimensionality of LP problems 

because it required a row and column for each step of the supply and demand 

schedules. However, Miller (1963) had earlier published a method of incorporating sloping demand and supply functions in LP models by selecting among 

activities representing the area (price times quantity) under each step of the 

functions. Miller’s method required a column for each step but required only a 

single convex combination constraint, thus reducing the model dimensionality 

significantly from that required by Martin’s formulation. 

With the advent of efficient and affordable quadratic programming algorithms in the early 1970s, price-endogenous MP modeling rapidly adopted 

quadratic programming methods. Harrington (1973) combined price-endogenous quadratic programming modeling and input/output analysis to develop 

a forerunner of today’s computable general equilibrium models.


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The literature of positive MP is replete with applications but only two methodological articles. Howitt (1995) explains a pragmatic method of using 

dual values of LP model solutions to introduce quadratic terms that assure 

that the model’s base period solution matches the base period primal variable levels of the system. An additional advantage of Howitt’s positive MP 

is that it eliminates most corner solutions; hence the model adjusts gradually 

and proportionally to changes in prices, rather than abruptly shifting from 

one corner solution to another. Preckel et al. (2002) extend the Howitt positive MP methods to calibrate both the primal and dual levels of the system. 

They apply their method to calibrating base period prices and quantities in a 

system of agricultural sector supply and demand relationships. 

The asset-fixity or investment-disinvestment literature—most closely associated with Johnson and Hardin (1955), Johnson and Quance (1972), and 

Schmid (1997)—is central to specifying the supply response of the model. 

The asset-fixity paradigm is predicated upon there being a gap between the 

cost of investing in an additional unit of durable capital (its acquisition cost) 

and the return from disinvesting in it (its salvage value). When the marginal 

value product of a capital item is within this range, it is considered fixed 

but allocatable, while outside the range, it is considered variable. Not all 

capital is either fixed or variable in a problem; but, different items can be at 

their acquisition costs, at their salvage values, or in their fixed but allocatable range in between. Under the asset-fixity hypothesis, the length of run is 

endogenized separately for each different type of capital. In the 1980s, there 

was some controversy over whether the asset-fixity theory was a defensible 

viewpoint; but Chavas (1994) rigorously demonstrated Johnson’s underlying 

premises under sunk costs and temporal uncertainty. 

Theoretical Development 

In specifying the theoretical model, we first start with the equilibrium 

displacement method, recast it in the positive MP framework, discuss the 

modeling of the supply side with the asset-fixity paradigm, then complete 

the EDMP model with consistent aggregation/disaggregation of the demand 

side. We note certain limitations of each of these building blocks that may be 

strongly determinative of model performance.

The equilibrium displacement methodology starts with a standard set of 

economic structural equations of supply and demand.

Structural equations:

Dc = ec,pc Pc + ec,pL PL + ewW Crop demands 1 . . n

Sc = ec,pc Pc + ec,pL PL + exX Crop supplies 1 . . n

DL = eL,pc Pc + eL,pL PL + eyY Livestock demands 1 . . m (1)

SL = eL,pc Pc + eL,pL PL + ezZ Livestock supplies 1 . . m

Qc= Dc = Sc Crops market clearing 1 . . n

QL= DL= SL Livestock market clearing 1 . . m


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Where: 

Dc

 = Crop demands, DL = Livestock demands

Sc

 = Crop supplies, SL = Livestock supplies

Pc

 = Prices of crop commodities, 1 . . n

PL = Prices of livestock commodities, 1 . . m

Qc

 = Quantities of crop commodities, 1 . . n

QL = Quantities of livestock commodities, 1 . . m

W = Exogenous factors influencing crop demands

X = Exogenous factors influencing crop supplies

Y = Exogenous factors influencing livestock demands

Z = Exogenous factors influencing livestock supplies

e.,. = elasticities of demand w.r.t subscripted variables

	 e.,. = elasticities of supply w.r.t subscripted variables

Substitute displacements from equilibrium: D*, S*, P*, Q*, W*, X*, Y*, and 

Z* for respective variables. For example, D* = (Dscenario - Dequilibrium).

Substitute market clearing equations into S and D equations.

Rearrange so that Q*s and P*s are functions of exogenous variables: W*, X*, 

Y*, and Z*.

Q*c = ec,pc P*c + ec,pL P*L + ewW*

Q*c = ec,pc P*c + ec,pL P*L + exX* (2)

Q*L = eL,pc P*c + eL,pL P*L + eyY*

Q*L = eL,pc P*c + e,pL P*L + ezZ*

Arrange above equations in matrix form:

I

n 0m - ec,pc - ec,pL Q*c

 ew 0 0 0 W*

I

n 0m - eL,pc - eL,pL Q*L = 0 ex 0 0 X* (3)

0n Im - ec,p - ec,p P*c 0 0 ey 0 Y*

0n Im - eL,pc - eL,pL P*L 0 0 0 ez Z*

G * D = B * W

Then solve for D: D = G-1 B W = P W

P = G-1 B are generally termed reduced-form elasticities of endogenous 

response.


Equilibrium Displacement Mathematical Programming Models / TB-1918 

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Assumptions of Equilibrium Displacement Models

As noted by Piggott et al. (1995), equilibrium displacement models rest on 

four key assumptions:

1. Elasticities of endogenous supply and demand relationships are 

known and constant.

2. Elasticities of supplies and demands, with respect to exogenous 

variables, are known and constant.

3. Technology of production is known and constant.

4. Displacements are restricted to be in the neighborhood of equilibrium.

Limitations of Equilibrium Displacement Models

Those assumptions are also the Achilles heel of equilibrium displacement 

models:

1. Adjustment scenarios often entail changing any or all of the above 

assumptions, analyzing large displacement from the initial equilibrium, 

and/or determining base equilibrium values from indirect data, thus 

complicating their application. 

2. Expansionary displacements assume that no physical constraints to 

expansion exist, for example, no limitations on total cropland or limitations on existing production capacity.

3. Some contractionary displacements can exceed 100 percent of the base 

level of the activity. Such solutions are a priori infeasible because they 

imply the process in question is operating in reverse. 

4. Equilibrium displacement model supply functions are assumed to be 

downwardly continuous, whereas a correct specification requires that 

each supply function be truncated at the point where its supply price 

drops below its average variable cost. 

5. Neither expansionary nor contractionary displacements can be guaranteed to be on the efficient frontier of the underlying production/demand 

functions, but may be either interior points or infeasible points.

6. In the constant elasticity equilibrium displacement formulation, it is 

not conceptually possible to calculate a correct monopolistic/monopsonistic maximum quasi-rent solution. Quasi-rents change monotonically upward or downward, with successive restrictions in output, 

depending on whether demand is inelastic or elastic.

To overcome these limitations, we adopt an MP implementation of the equilibrium displacement model. 

The EDMP Formulation

We redefine the constant elasticity equilibrium displacement problem to one 

of comparing successive equilibria of a system of linear (constant slope) 

supply and demand functions with quadratic programming.


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Following Preckel et al. (2002):

Max: Z = F'x - 1/2 x' H x. (4)

Z is the objective function to be maximized. Z can be either the sum of 

consumer plus producer surpluses or the sum of residual quasi-rents, 

depending on whether the model is perfectly competitive or monopolistic.

Subject to:

A11x = Free Indicator accounts, (4a)

A21x ≤ b Technical constraints, (5)

I31x = c Calibration constraints, and (6)

x ≥ 0 Non-negativity constraint. (7)

Where:

A11, A21 = A matrix of Leontief technical requirements of 

 processes 

I31 = An identity matrix of calibration constraints, 

 suspended after calibration

 x = A vector of optimized variables (which assure 

 that all solutions are feasible and efficient) 

b = A vector of right hand sides of constraints

c = A vector of calibration targets to reproduce base 

 equilibrium, suspended after calibration

F = A vector of intercepts of supply and demand 

 processes

H = Hessian matrix of marginal adjustment costs and 

 demand slopes, assumed to be positive semidefi-

 nite for maximization.

Equation 4a is necessary because the value of the objective function, equation 4, is confounded by perturbations necessary to calibrate the model to 

the base period prices and quantities. Similarly, to model some agricultural 

policies, it may be necessary to define processes differently from observed 

supply and demand relationships. Any such changes need to be backed out of 

the model solutions to reflect true supply and demand prices and quantities.

Equation 6, which contains the quantity targets of the equilibrium solution, is 

enforced only in the initial calibration solutions. When the model is calibrated 

to the desired accuracy, its optimal solution will return exactly the quantities 

specified in equation 6, without any quantity constraints. After that, equation 

6 is suspended to allow the model to adjust all prices and quantities simultaneously in response to changes in the scenario. Thus, differences of scenario 

solutions from the base solution enforced in equation 6 are equilibrium 

displacements under the assumption of constant slope relationships rather 

than constant elasticity relationships. The constant slope formulation inherent 

in EDMP models has the advantage of being theoretically consistent with 

monopolistic maximization of quasi-rents, in contrast to constant elasticity 

equilibrium displacement models.


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Monopolistic Firm and Competitive 

Industry Cases

Let F(x) be a general multi-output multi-input profit 

function, with x containing both inputs (-) and outputs 

(+) and with prices related to quantities, subject to equations 5 and 7. 

A second order Taylor series expansion of F(x) in the 

neighborhood of its maximum (x*) is:

F(x) = F(x*) + F'(x*)(x-x*) + F''(x*)(x-x*)2 + R,	 (8)

1! 2!

where F' and F'' are the first and second derivatives of 

F(x*) and R represents the higher order nonlinearities 

of F(x).

By definition, F''(x*) is the Hessian, H(x*). 

Assuming the base situation to be in equilibrium (a 

maximum), then F'(x*) = 0. Rearranging terms to matrix 

notation, the Taylor series expansion becomes: 

F(x) = F(x*) + 1/2(x-x*)' H (x-x*), (9)

where the Hessian matrix is assumed to be negative 

semidefinite. Changing the sign in equation 9 allows 

the Hessian to be specified as positive semidefinite. 

From equation 9, it is clear that, in the monopolistic 

case, the equilibrium displacement maximand, Z, once 

calibrated, is identical to the monopolistic firm’s profit 

function.

The model can be solved either monopolistically (that 

is, for a firm with market power) by equating marginal 

factor costs to marginal revenues or perfectly competitively by maximizing the sum of producers’ plus 

consumers’ surpluses (that is, for a perfectly competitive firm or an industry). Both monopolistic and 

perfectly competitive behavior can be combined for 

different activities within a single model. (For applications of EDMP to mixed competitive and monopolistic 

problems, see Jefferson-Moore and Harrington (2006) 

and Harrington and Jefferson-Moore (2007).)

Figure 1 illustrates the EDMP perfectly competitive 

supply and demand equilibrium for a commodity. The 

gradient is the perfectly competitive market price, and 

residual rents are identically equal to zero. Figure 2 illustrates monopolistic/monopsonistic equilibrium, found 

by equating marginal revenue with marginal factor cost. 

Factor and product prices are found on the original factor 

supply and product demand functions. Residual rents, 

shown as the shaded area, are at a maximum. 

Equivalence of EDMP Formulation to a Profit Function Formulation

Figure 1

EDMP purely competitive supply and 

demand of commodity

Demandi

Demand Supplyi

intercepti

Hdi

- Hsi

0

Allocation to slack below average variable costs

P

Q

Gradient

Figure 2

Monopolistic/monopsonistic supply and demand

Demandi

Competitive

supplyi

Demand

intercepti

Product

pricei

Factor

pricei

Marginal

factor cost

Marginal

revenue 

P

0 Q

Residual

Rents
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Modeling the Supply Side

Supply response of each activity is endogenous in the EDMP model, 

reflecting the asset-fixity of capital paradigm of Johnson and Hardin (1955), 

Johnson and Quance (1972), and Schmid (1997). Supply response in the 

EDMP model is a multicommodity formulation composed of: (1) a Hessian 

matrix of marginal adjustment costs of changing levels of supply activities 

and (2) a vector of changes in levels of supply activities from the calibrated 

base solution. The marginal adjustment costs of changing levels of activities 

are diagonal elements of the supply side of the Hessian matrix. Increasing 

any activity that has a binding constraint requires simultaneously reducing 

one or more other activities limited by that constraint. Thus, the net income 

response for increasing an activity is analogous to the total derivative, that is, 

the sum of: (a) the product of its marginal adjustment costs times the increase 

in that activity, and (b) the marginal adjustment costs of all other activities 

times their respective changes. 

The supply-response mechanism in the Johnson asset-fixity paradigm is as 

follows. All enterprises are assumed to seek to cover variable costs. If an 

enterprise can cover capital replacement costs as well as variable costs, it 

will expand its capital stock at the acquisition cost of capital. If it is unable to 

cover variable costs, it will reduce its scale by reallocating some of its capital 

stock to another more profitable enterprise, or if lacking a more profitable 

enterprise, it will disinvest in the substitutable capital at its salvage value 

(that is, allocate some capital to slack). Under these assumptions, substitutable capital assets are fixed but allocatable among enterprises if their shadow 

values fall between their acquisition cost and their salvage value—or variable 

if their shadow values fall below their salvage values or above their acquisition costs. 

In the asset-fixity paradigm, it is important to distinguish between substitutable capital, such as tractors, combines, and wagons, which can be used in a 

variety of enterprises, and specialized capital, such as cotton pickers, sugar 

beet harvesters, and tobacco curing equipment, which can be used only in 

one specific enterprise. Enterprises with the highest proportions of substitutable capital are such crops as corn, soybeans, small grains, hay, and pasture. 

Specialty crops and most livestock enterprises have the lowest proportions of 

substitutable capital—sugar beets, sugar cane, tobacco, rice, peanuts, cotton, 

potatoes, dairy, cow-calf, fed beef, hogs, and poultry. 

Given that some of the capital stock can be allocated among enterprises, 

activities will typically have some maximum level of that enterprise possible 

with the existing stock of substitutable capital. The difference between that 

maximum capacity and the current level of that activity is its excess capacity. 

Enterprises with the highest proportions of excess capacity are such crops as 

corn, soybeans, small grains, hay, and pasture. Specialty crops and most livestock enterprises have the lowest proportions of excess capacity. 

If we assume there is a uniform distribution of excess capacity for each 

enterprise ranging from zero (the stock of substitutable capital is fully used 

at the current level of production) to some maximum (the level of production possible at the maximum allocation of currently owned capital to the 
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enterprise), we can identify two points in cost-production space: (1) current 

production and current variable costs and (2) maximum production and 

variable cost plus substitutable capital replacement cost. If there were only 

substitutable capital, the slope of the Hessian element would be the straight 

line connecting these two points, that is, a linear, continuous relationship. 

Correcting the Hessian element for the proportion of capital replacement costs 

that is attributable to substitutable capital defines the Hessian elements as:

Hii = [Capital Replacementi/(% Substitutable * % Excess Capacityi)]

*Base Quantityi

. (10)

One realistic implication of this formulation of adjustment costs is that 

capital replacement costs may be less than fully covered for some enterprises, 

causing these enterprises to exhibit the “overproduction trap” of Johnson and 

Quance (1972). A second realistic implication of this formulation is that both 

substitutable and specialized capital will be allocated to slack if their shadow 

values drop below their salvage values. Hence, in keeping with microeconomic production theory, supply functions are truncated below the average 

variable costs of each enterprise. Finally, a third implication of this formulation is that—in keeping with the asset-fixity paradigm—the length of run, 

that is, which factors are considered fixed or variable for each enterprise, is 

endogenous to the model. Not all enterprises are in either shortrun or longrun 

decision mode with respect to capital in any solution. Solutions to the EDMP 

model are akin to linear combinations of shortrun allocation decisions and 

longrun investment/disinvestment decisions. 
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Modeling the Demand Side

The demand side elements of the Hessian matrix are linear demand slopes. 

Further, the demand functions represent only nonfarm demands for the 

commodity. Commodity use by the farm sector is modeled within the 

constraint matrix. Demand slopes in a comprehensive (farm sectorwide) 

model are derived as follows.

By definition, elasticity of demand for a commodity is:

Ed = dQ/dP *P/Q.

Similarly, by definition: 

Slope = dP/dQ.

Hence, for sectorwide models, how ever they may be disaggregated on the 

supply side: 

Hii = dP/dQ = (1/Ed )P/Q. (11)

If the model is disaggregated to represent single region or group of farms 

(not marketwide), the demand slopes must be adjusted to remain consistent 

with a marketwide model. 

The demand slope adjustment for own market share (q/Q) in partial models 

is:

dP/dq = [(q/Q)/Ed ] P/Q, (12)

where uppercase letters represent the aggregate level and lowercase letters 

represent the disaggregate level.

Next, the slope must be adjusted for competitors’ market shares and supply 

responses:

DdP/dq = - [(1-q/Q)Esx] P/Q, (13)

where Esx is the elasticity of supply of the excluded subsectors or regions 

(competitors).

Combining equations 12 and 13 completes the required adjustment to 

demand slopes for partial models:

dP/dq = (q/Q)/Ed [1- (1- q/Q)Esx] P/Q. (14)

The elasticity of equation 14 varies from zero to Ed, as own market share 

expands from zero to 1.
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Modeling Agricultural Policies 

and Programs

Major agricultural policies and programs, as currently in effect in the Farm 

Security and Rural Investment Act (the 2002 Farm Act), are modeled as 

below.

Payment Bases

Producers’ payment bases establish the producer’s eligibility for direct 

payments and counter-cyclical payments but do not limit production of these 

crops. Payment bases apply to the following commodities: corn, soybeans, 

grain sorghum, wheat, rice, barley, oats, and cotton. They are based on the 

producer’s crop and yield history for each crop. However, the producer need 

not produce the crop (or any crop) to be eligible for the decoupled payments.

Decoupled Payments

Production flexibility contract, market loss assistance payments, and post2002 direct payments apply to the same list of commodities and are modeled 

as lump sum additions to gross income that are decoupled from current 

production levels and prices. They are limited by payment bases and affect 

only net farm income. Direct payments associated with the payment bases of 

particular commodities are calculated post-optimally according to the provisions and parameters of the farm legislation and proportionally adjusted 

to equal the aggregate direct payments reported in the ERS farm income 

accounts.

Counter-Cyclical Payments

Counter-cyclical payments can be termed partially decoupled payments, 

because though they depend on the average market prices of the commodity, 

they do not depend on the quantity of production by any individual. They 

are disbursed in the same manner and on the same payment bases as decoupled payments. Counter-cyclical payments are treated the same as direct 

payments in this model because they do not change the market prices for 

the commodity that the producer faces. Rational producers would not alter 

their market-determined optimal production levels unless they believed 

that their actual production history would someday be used to update their 

payment bases.1 Counter-cyclical payments for supported commodities are 

calculated post-optimally as the payment base acreage times the program 

yield times the difference between: (1) the higher of the average market 

price or the loan rate and (2) the target price minus the direct payment rate. 

The result is then multiplied by an adjustment factor to scale the aggregate 

counter-cyclical payment level to that reported in the ERS farm income 

accounts. This amount is paid as a lump sum, and, as with the decoupled 

payments, the owner of the payment base need not produce the commodity 

or any commodity to be eligible to receive them. Note that counter-cyclical 

payments will be at their maximum whenever loan deficiency payments or 

marketing loan gains are active.

1This ignores any changes in risk or 

wealth that may affect the producer’s 

decisions.
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Loan Deficiency Payments and 

Marketing Loan Gains

Loan deficiency payments and marketing loan gains are two different 

support mechanisms that have identical results—they allow the effective 

price to producers to be above the market price of supported commodities. 

The programs have remained the same under the 1996 Farm Act and the 

2002 Farm Act. Marketing loan gains operate in the following manner. The 

producer can obtain a loan equal to the value of the crop at the loan rate and 

later repay it at the value of the crop at a lower posted county price (market 

price), which may be changed daily or weekly. The marketing loan gain 

rate, the difference between the average market price and the loan rate, is 

paid to the producer on all production of the supported commodity, whether 

marketed, stored, or used on the farm. In the EDMP model, marketing loan 

gains are endogenously calculated by successively introducing perfectly 

elastic nonrecourse loan demands at the loan rate, then introducing activities that sell from the nonrecourse loans into the market (fig. 3). At levels of 

production at which the nonrecourse loans are active, the effective price to 

the producer for the commodity is the loan rate. Market prices, in contrast, 

seek market-determined levels below the loan rate determined by the 

sales from the nonrecourse loan activities. Loan deficiency payments and 

marketing loan gains are thus coupled payments; producers know that the 

lowest effective price they will receive for the commodity is the loan rate 

and will take this into consideration in making production and asset value 

decisions.2 2 Two versions of this EDMP model 

were constructed on an experimental 

basis. The first version modeled the 

loan deficiency payment mechanism by 

inserting loan deficiency payment activities that activated at the loan rate and 

its corresponding demand quantity and 

offset the decline in market prices. This 

kept the effective prices to the producer 

constant when market prices fell below 

the loan rate. Some problems arose 

with this formulation in that it allowed 

multiple optimal solutions to the model. 

The alternative formulation of the marketing loan gain mechanism, adopted 

and discussed in this version, does not 

allow multiple optimal solutions.

Figure 3

Marketing loan gains

Non-recourse loan

Market price

Marketing loan gain

Original demand function

S

P

Q 0 Total sales

Market sales

D

Sales from non-recourse 

loan stocks
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Conservation Reserve, Wetlands Reserve, and 

Grassland Reserve Programs

Under the Conservation Reserve Program (CRP) and Wetlands Reserve 

Program (WRP), landowners can voluntarily retire environmentally sensitive cropland or grant easements or restore wetlands in return for long-term 

rental contracts that pay them cost-share benefits and an annual rental fee for 

retiring the land and maintaining it in conservation uses. Landowners submit 

bids for the amount they are willing to accept as annual payments. Bids are 

accepted based on an environmental benefit index. The CRP and WRP are 

modeled by activities through which the Government rents cropland up to an 

authorized limit for a rental rate that can be either constant or endogenously 

determined by equating marginal returns from the CRP or WRP with the 

marginal returns from using the land in production. The CRP and WRP thus 

reduce the amount of cropland available for planting and shift all supply 

functions to the left. 

The CRP and WRP interact with the loan deficiency payment program, as 

shown in figure 4, to greatly reduce Government budgetary cost exposure. 

Under normal circumstances, shifting supply functions to the left would 

result in higher prices and lower quantities of commodities. However, with 

the loan deficiency payment or marketing loan plan in place, if prices and 

quantities are in the range where loan deficiency payments or marketing 

loan gains are made, effective prices to producers remain at the loan rate, but 

quantities produced are reduced by the shift in the supply function, market 

prices are increased, and the loan deficiency payment rate or marketing loan 

gain is reduced. 

The Grassland Reserve Program uses similar long-term leases for maintenance of native grasslands and prevents their conversion or development. 

Figure 4

Conservation reserve program

Market demand 

(national)

Loan rate

Marketing loan 

gains

Supply

P

Supply

w/CRP 

Acres
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The program is modeled by altering the endowment of rangeland and cropland pasture resources and/or hay production activities to reflect relevant 

provisions of the program.

Working Lands Conservation Programs

Working lands conservation programs include the Environmental Quality 

Incentives Program, the Wildlife Habitat Incentive Program, and the 

Conservation Security Program. Each of these programs provides technical 

and cost-sharing incentives which are modeled as alterations to the cost and/

or yield components of crop production activities. 

Crop Insurance Subsidies 

Crop insurance subsidies are paid in an effort to foster greater producer 

participation in risk management programs. This EDMP model focuses 

only on the static, deterministic, supply-increasing effects of the subsidies, 

considered as a normal production input for each commodity for which they 

are available. The model abstracts from any supply-inducing effects of reductions in risk, wealth effects of insurance, or issues of adverse selection or 

moral hazard, which are typically central issues addressed in crop insurance 

studies. In keeping with the theoretical specification of the EDMP model, it 

addresses only the deterministic allocative effects of the subsidies that result 

from changes in producers’ marginal costs or marginal revenues. As shown 

in figure 5, crop insurance is modeled as having a factor demand elasticity of 

-0.6, a quantity equal to the observed insured acreage of that commodity, and 

a premium equal to the average unsubsidized premium for that commodity. 

The subsidy is applied as 57 percent of the unsubsidized premium. Increasing 

the subsidy decreases the net premium and increases the acres insured. 

Decreasing or eliminating the subsidy does the opposite. In order to focus 

Figure 5

Crop insurance subsidies

$

0 Acreage

Crop insurance demand

Premium

Net premium

Subsidy

Acres insured, 

unsubsidized

Acres insured, 

subsidized 
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only on the subsidy, we assume that the crop insurance aggregate loss ratio is 

1.0, that is, that indemnities paid out exactly equal net premiums collected. 

Crop insurance programs interact with the loan deficiency payment and 

marketing loan programs in a manner opposite to the interaction of the CRP 

and WRP with the loan deficiency payment program shown in figure 4. Crop 

insurance subsidies lower production costs, which shifts the supply function to the right. Under normal circumstances this would result in higher 

quantities of commodities and lower effective prices to producers. However, 

with the loan deficiency payment plan in place, if prices and quantities are 

in the range where payments are made, effective producer prices remain at 

the loan rate, quantities produced are increased by the rightward shift in the 

supply function, market prices are reduced, and the loan deficiency payment 

rate is increased.

Superseded Agricultural Programs

Acreage bases were in effect prior to the 1996 Farm Act for corn, soybeans, 

grain sorghum, wheat, rice, barley, oats, and cotton. Acreage bases (if they 

are ever re-instituted) are modeled as limiting constraints on the production 

of the base commodity. 

Acreage reduction programs (ARPs) or set-asides were periodically authorized for several commodities prior to the 1996 Farm Act. These required 

producers to reduce the acreages they planted to the crops with ARPs by 

some proportion of their production base in order to be eligible to receive 

commodity payments. The 1996 Farm Act eliminated the authority for 

acreage bases and ARPs, but we have retained the capability to analyze them. 

ARPs are modeled by simply reducing acreage bases by the amount of the 

ARP requirement.

Nonrecourse loans, wherein the Commodity Credit Corporation would take 

ownership and store supported commodities whenever the market price 

fell below the loan rate, were used prior to the introduction of marketing 

loans and loan deficiency payments beginning with the1985 Farm Act. 

Nonrecourse loans supported market prices at the loan rates for supported 

commodities but also led to the accumulation of CCC-owned stocks that 

were said to “overhang the market” tending to keep market prices from 

rising above the loan rates. They were also alleged to encourage imports 

from foreign countries, thereby supporting prices in those countries. While 

no longer used, the model retains the capability to analyze nonrecourse loans 

through its mechanism for analyzing marketing loan gains.
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Model Calibration

Calibration of the EDMP model is an iterative process of adjusting the 

Hessian elements of activities through which the model is calibrated to 

match the equilibrium prices and quantities to the desired degree of accuracy. 

As illustrated in figure 6, initial values of intercepts of supply and demand 

processes are set as the product of the Hessian element times the target quantity of that activity plus the target price of the commodity for demand activities, and plus the residual net cash income of the activity for supply activities. 

The optimal solution for these initial intercept estimates will generally only 

approximately match the target prices and quantities. One or more intercepts 

are then perturbed by a positive or negative additive adjustment based on the 

deviation of the current optimal solution for that activity from its target price 

or quantity. If a higher price or quantity is needed, the adjustor should be 

positive for demand activities or negative for supply activities. A good first 

approximation for the adjustor is the product of the Hessian element times 

the deviation of the current activity level from its target level. The model 

is then re-solved with the adjusted intercept values, and the new optimal 

solution should show several activities converging toward the target values. 

This process is repeated iteratively for all activities until the desired level 

of accuracy for all prices and quantities is attained. Once the desired level 

of accuracy has been attained by adjusting intercepts, all Hessian elements 

are divided by the ratios of adjusted intercepts to initial intercepts, and the 

intercepts are returned to their initial values. The optimal solution to this 

final model will match the optimal solution of the next-to-final model. This 

last calibration step accomplishes two necessary conditions of a calibrated 

model: (1) it restores all demand elasticities to their original values (all linear 

demand functions with a common intercept have identical elasticities at a 

given price) and (2) it restores all intercept values to estimates based solely 

on model data (no artifacts of calibration are left in the intercept values).

Figure 6

Calibration of EDMP models

Final element of Hessian (3)

(1)

(2)

(3)

Original intercept of (1) P

0 Q

Original element of Hessian (1&2)

Shifted intercept (2)
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What Do Gradients Mean?

Calibrated intercepts have specific economic meanings in EDMP models. 

Solution gradients are the implicit changes in the value of the objective function for a one-unit increase in the activity at equilibrium. For demand activities in perfect competition, the intercepts are the prices satisfying a priori

targets for that activity’s base period prices, quantities, and elasticity of 

demand. Hence, for demand activities, the gradients are the perfectly competitive equilibrium market prices of the commodities, as shown in figure 1. 

However, if the activity is monopolistic or monopsonistic, the gradients are 

intercepts of marginal revenue or marginal factor cost functions satisfying the 

same a priori targets, as shown in figure 2. Note that gradients are not prices 

for monopolistic or monopsonistic activities. They are the intersections of 

marginal revenues and/or marginal factor costs for these activities. For activities exhibiting monopoly power, prices and quantities are on the demand 

curve, but not on the supply curve. For monopsony power situations, the 

opposite is true. Market prices for monopolistic/monopsonistic demand and 

factor supply activities must be post-optimally calculated with respect to the 

original demand functions and factor supply functions, that is, the calibrated 

intercept minus respective Hessian element times the respective activity level. 

Production activities are the crop, intermediate product, and livestock 

production activities that use factors supplied in factor acquisition activities 

and produce products sold or products used in further processing activities 

within the model. In perfect competition, the gradients of production activities are the negative of the gross margin of that activity above the costs specified in the model.
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Structure of the Model

In this section of this bulletin, we list the commodities, inputs, processes, 

and agricultural programs included in the model and the data sources from 

which we obtained the estimates. In subsequent sections of this bulletin, 

we will present specific parameter values in tabular form and discuss postoptimal economic indicator calculations and supply-response characteristics 

of the model.

Commodities 

Production quantities in the EDMP model are average acreages and production by commodity, summarized nationally and by region and type of farm, 

from the Agricultural Resource Management Survey (ARMS) for 1996-2000 

and updated to 2001-05. ARMS is an annual survey of farm economic information that underpins most of the Commodity Costs and Returns (USDA, 

ERS, 2006) accounts and Farm Income and Costs (USDA, ERS, 2006) 

accounts published by ERS. Model national estimates are matched to quantities in USDA Agricultural Projections to 2016. Farm prices for the respective 

commodities are also calculated from USDA Agricultural Projections to 2016.

The EDMP model includes the following commodities: 

•	16 Top crop commodities: corn, soy, wheat, rice, barley, oats, sorghum, 

cotton, sugar beets, sugar cane, potatoes, dry beans, sunflowers, peanuts, 

tobacco, and hay and crops not elsewhere classified;

•	8 Top livestock commodities: cow-calf, fed beef, hogs, dairy, sheep lamb 

and wool, broilers, eggs, turkeys, and livestock not elsewhere classified; 

•	3 Nontradable forages: crop pasture, range, and corn silage;

•	4 Balanced grain rations, produced in region: corn, barley, oats, and 

sorghum rations, protein balanced with soy meal; 

•	4 Joint products: straw, cottonseed, excess calves, and cull cows; 

•	Import hay to region; 

•	Import balanced grain ration to region;

•	Farm-related income; and

•	Off-farm income.

Specified Resources 

The model requires specification of total availabilities of resources, nationally and by type and region. These are summarized from ARMS data for 

1996-2000 and the 1997 Census of Agriculture (USDA, ERS, 2006), the 

most recent data available when the model was last updated: 

•	Total cropland (ARMS, 1996-2000);

•	Total crop pasture (1997 Census of Agriculture); 

•	Total permanent pasture/range (1997 Census of Agriculture);
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•	Facilities by livestock commodity (estimated from ARMS 1996-2000);

•	Dollar-equivalent of operator and family labor (Commodity Costs and 

Returns (USDA, ERS, 2006)); and 

•	Land rent (Farm Income and Costs (USDA, ERS, 2006)).

Specified Purchasable Inputs 

Commodity yields and specified purchasable inputs are calculated from 

Commodity Costs and Returns datasets. The ERS commodity costs and 

returns accounts are annual estimates of the average dollar value of input 

requirements for producing crops and livestock, assuming they are produced 

with Leontief (constant proportion) production technology. Supplies of 

purchasable inputs are assumed to be perfectly elastic. The dollar values of 

the following categories of inputs from the ERS commodity costs and returns 

accounts are incorporated in the EDMP model:

•	Hired labor at regional wage rates. 

•	Miscellaneous variable inputs at rates and prices that may vary by region 

or farm grouping.

•	Fuel, lube, and electricity-related inputs at rates and prices variable by 

region or farm grouping.

•	Seed and specialized genetic inputs at rates and prices variable by region 

or farm grouping.

•	Specialized technology inputs at rates and prices variable by region or 

farm grouping.

•	Fertilizer and lime inputs at rates and prices variable by region or farm 

grouping.

•	Chemical inputs at rates and prices variable by region or farm grouping.

•	Fixed cash costs, by commodity. These costs do not vary with acreage or 

production and are incurred whether or not the commodity is produced.

•	Capital replacement costs, by commodity. These costs are financial allowances for replacement of depreciable machinery and equipment when it 

wears out. They are not cash costs in the shortrun but must be covered in 

the longrun if the farm or sector is to maintain its productive capacity.

•	Residual overhead costs, by commodity. These costs are endogenously 

determined to calibrate the model to sector accounts.

Processes

Processes or activities are specified for each model commodity from costof-production budgets in the ERS commodity costs and returns accounts. 

Each process assumes a Leontief (fixed proportion) technology. Thus, they 

are essentially recipes for producing one unit of the product, using all the 

required inputs in their specified proportions:

•	Produce crops and livestock (national, regional, or farm grouping levels).
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•	Fallowing required in arid western regions.

•	Use forages, feed grains, and oilseeds in livestock production (national, 

regional, or farm grouping levels).

•	Sell commodities into domestic nonfarm market (price differentials by 

region or farm grouping).

•	Purchase any deficit of mixed grain ration and/or hay in regional or type 

of farm grouping from domestic markets.

•	Sell commodities into domestic nonfarm demands, nationally. (Demand 

functions are estimated by removing farm sector use for feed, seed, 

and residual from domestic use estimates from the USDA Agricultural 

Projections to 2016):

Corn, soy, wheat, rice, barley, oats, sorghum, cotton, dry beans, 

sunflower, peanuts, tobacco, fed beef, hogs, dairy, and poultry.

•	Sell commodities into export demands, nationally. (Demand functions are 

estimated from USDA Agricultural Projections to 2016):

Corn, soy, wheat, rice, barley, oats, sorghum, cotton, dry beans, 

sunflower, peanuts, tobacco, fed beef, hogs, dairy, and poultry. 

Poultry proportions are fixed in the same proportions as in base year. 

•	Competing import supplies, nationally. (Calculated from USDA 

Agricultural Projections to 2016):

Corn, soy, wheat, rice, barley, oats, sorghum, cotton, fed beef, and 

hogs.

•	Storage demands/dis-storage supplies, nationally. (Calculated from 

USDA Agricultural Projections to 2016):

Corn, soy, wheat, rice, barley, oats, sorghum, dry beans, and 

sunflower.

•	Farm-related income, by region or farm grouping. (Calculated from ERS 

farm income accounts.)

•	Work off-farm, by region or farm grouping. (Calculated from ERS farm 

income accounts.) 

Agricultural Policies and Programs

Provisions and economic parameters for agricultural programs in the 1996 

and 2002 Farm Acts are taken from the briefing room, Farm and Commodity 

Policy (2007). Major agricultural programs included in the model are:

•	Production flexibility contract payments, market loss assistance 

payments, and post-2002 direct payments (decoupled from current 

production levels and prices). These are lump sum payments that are 

post-optimally calculated and affect only net farm income.

•	Post 2002 counter-cyclical payments (decoupled from current production levels by individual producers, but coupled to current market prices). 

These payments are post-optimally calculated for individual crops but 

paid as lump sum payments. They affect net farm income but do not 
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affect producer choices of crops to raise because they do not alter the 

market-determined marginal revenues of producers.

•	Loan deficiency payments and marketing loan gains (fully coupled to 

current production levels and prices). These programs put a floor under 

producer incentive prices for commodities whenever commodity prices 

are below the loan rate. They do affect production choices because they 

alter the marginal revenues the producer faces. 

•	Conservation reserve and wetlands reserve payments (long-term rental of 

eligible cropland). These programs reduce aggregate supply of cropland 

and, as a result, restrict production of commodities, thus raising their 

market prices.

•	Crop insurance subsidies. These indirect subsidies stimulate increased 

production of insured commodities by underwriting some of the cost of 

managing production risks. In addition, they may encourage expansion of 

commodity production to more risky production areas.
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Solving the Model

In solving the model, all commodity prices and quantities are simultaneously 

determined as a competitive equilibrium subject to agricultural program 

provisions, that is, the marginal revenues from expanding the production of 

each commodity by one standard unit are equalized across all commodities 

while simultaneously equalizing marginal values (shadow prices) of limiting 

factors across all activities using that factor. Each solution to this model 

represents the equilibrium adjustment by the farm sector to the economic 

situation portrayed in that scenario under the assumption that producers 

think the change is a permanent, once-and-for-all change. Scenarios from 

the base period equilibrium assume that producers have had time to adjust to 

a new equilibrium under the changed policy. For all but very large displacements, this is approximately the second year after enactment of the change 

in the scenario.
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Supply Parameters

Table 1 lists the base solution parameters of supply activities based on 

average values for 2002-05. For each activity, its model acronym, base 

period acreage or quantity, percent excess capacity, and percent substitutable 

capital are listed. The base period acreages or quantities are endogenous to 

the model, but the user can re-calibrate them to customize the base situation 

to reflect his/her problem. The percent excess capacity and percent substitutable capital contribute to determining the responsiveness of the activity to 

endogenous changes in either quantity or price. 

Unfortunately, we are not aware of any research that estimates the excess 

capacities and percent substitutable capital by commodity. In the absence 

of such producer data, we have assigned these parameters based on our 

own estimates. These parameters can be adjusted by the model user. These 

data could be collected from respondents to the ARMS surveys if carefully 

phrased. For example, an excess capacity question might ask: “How many 

acres of commodity x could you produce with your current complement of 

machinery and equipment without experiencing yield reductions, taking into 

consideration weather conditions and timeliness of planting and harvesting?” 

Questions related to proportion of substitutable capital might be phrased: 

Table 1

Supply activity parameters: Base solution: U.S. aggregate EDMP model, 2002-2005 average

Activity name Corn Soybeans Wheat Rice Barley Oats Sorghum

Symbol CORNUS SOYUS WHEUS RICUS BARUS OATUS SRGUS

Acreage (mil. acres) 77.575 76.930 68.515 3.607 6.016 2.570 9.555

% Excess capacity 40 120 120 20 120 120 120

% Substitutable capital 100 100 100 50 100 100 100

Cotton Sugar beets Sugar cane Potatoes Dry beans Sunflower Peanuts

Symbol COTUS SGBUS SGCUS POTUS BENUS SNFUS PNTUS

Acreage (mil. acres) 14.788 1.477 0.575 1.320 1.741 2.059 1.380

% Excess capacity 20 20 20 20 120 120 20

% Substitutable capital 50 25 25 25 100 100 25

Tobacco Hay Crops NEC Fallow Corn silage Crop pasture Range/ past.

Symbol TBCUS HAYUS CNCUS FALUS CSILUS CPASUS RNGUS

Acreage (mil. acres) 0.660 55.159 23.360 34.081 6.730 66.800 481.000

% Excess capacity 20 120 40 120 32 120 120

% Substitutable capital 25 100 50 100 32 100 100

Cow-calf Fed beef Ind. hog Contract hog Dairy Sheep/lamb/wool Broilers

Symbol CCFUS FBFUS IHOGUS CHOGUS DAIRUS SHPUS CBRLUS

Quantity (mil. units) 33.930 381.642 146.703 96.669 1683.421 9.622 305.478

% Excess capacity 40 40 40 20 20 40 40

% Substitutable capital 50 50 50 50 50 50 50

Ind. egg Contract egg Ind. turkey Cont. turkey Livestock NEC

Symbol IEGGUS CEGGUS ITRKUS CTRKUS LNCUS

Quantity (mil. units) 390.403 331.612 13.235 37.569 3158.100

% Excess capacity 40 40 40 20 40

% Substitutable capital 50 50 50 50 50

Source: Calculated from USDA Agricultural Projections to 2016.
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“What is the total value of machinery and equipment you use in production 

of commodity x?” and “What is the value of machinery and equipment that is 

specialized to only the production of commodity x?” 

Table 2 lists the process budgets for each activity including yields and dollar 

values of operator labor, hired labor, seeds/genetics, specialized technologies, fertilizer/lime, chemicals, fuel/lube/electricity, and other variable costs. 

These cost components make up the shortrun variable cost of the activities. 

Fixed cash costs and capital replacement costs are included in longrun variable costs. The values are the average ERS cost-of-production accounts at the 

national level for 1996-2000 and 2001-05.

Table 2

Supply activities: Yields, costs and supply responses: Base solution: U.S. aggregate 

EDMP model, 2002-2005 average

Activity name Corn Soybeans Wheat Rice Barley Oats Sorghum

Yield per acre 143.685 bu 40.872 bu 44.3848 bu 65.02 cwt 62.54 bu 48.19 bu 38.46 bu

Operator labor $ 29.69 16.01 14.75 31.29 8.59 17.16 17.75

Hired labor $ 3.10 1.76 2.11 39.88 6.41 2.06 3.10

Seed/genetics $ 29.10 18.09 7.48 26.68 8.41 7.62 3.87

Specialized tech $ 3.63 3.31 0.00 0.00 0.00 0.00 0.00

Fert/lime/etc $ 40.17 7.87 18.30 48.79 18.96 15.09 9.45

Chemicals $ 26.52 23.57 7.24 72.48 10.09 1.77 7.16

Fuel/lube/elect. $ 22.25 5.28 6.04 61.79 12.10 9.38 11.73

Other variable $ 27.94 13.69 16.09 121.22 25.31 15.78 28.14

Fixed cash $ 17.95 17.53 10.12 73.80 18.94 19.37 10.43

Capital repl. $ 64.42 44.80 42.29 63.73 31.17 18.82 37.34

Implicit acreage response 0.333% 0.539 0.344 0.199 0.013 0.361 0.000

Implicit supply response 1.246% 1.402 1.265 1.222 2.345 1.508 3.100

Implicit price response 0.273% 0.224 0.347 0.334 0.014 0.137 0.003

Cotton Sugar beets Sugar cane Potatoes Dry beans Sunflower Peanuts

Yield per acre 580.0 lb 21.1 ton 33.1 ton 337.9 cwt 14.6 cwt 16.8 cwt 2644 lb

Operator labor $ 30.99 51.96 15.50 57.22 12.00 7.28 89.52

Hired labor $ 36.56 112.66 330.75 58.03 6.48 2.12 37.63

Seed/genetics $ 19.83 43.71 50.36 9.83 24.94 7.82 75.48

Specialized tech $ 5.00 0.00 0.00 0.00 0.00 0.00 0.00

Fert/lime/etc $ 35.25 61.00 103.90 52.71 13.73 2.84 39.52

Chemicals $ 64.97 71.68 89.13 48.66 26.56 8.75 97.96

Fuel/lube/elect. $ 29.18 36.52 60.23 17.03 6.47 3.58 34.60

Other variable $ 101.01 105.98 312.16 60.82 18.00 7.88 144.04

Fixed cash $ 31.53 78.97 106.99 40.55 20.87 15.48 37.48

Capital repl. $ 103.41 55.86 54.68 83.38 53.19 24.35 120.89

Implicit acreage response 0.042 0.761 1.279 1.032 0.985 1.241 0.477

Implicit supply response 1.063 0.957 0.957 1.032 1.481 1.946 0.866

Implicit price response 0.381 1.086 1.086 0.934 0.175 0.182 1.939

 —continued
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Table 2

Supply activities: Yields, costs and supply responses: Base solution: U.S. aggregate 

EDMP model, 2002-2005 average—Continued

Activity name Tobacco Hay Crops NEC Fallow Corn silage Crop pasture Range/pasture

Yield per acre 2120 lb 2.5 ton 1721.4 $ 0.0 15.81 ton 35.4 cwt HE 7.50 cwt HE

Operator labor $ 215.09 3.83 188.81 1.35 25.23 2.05 0.45

Hired labor $ 530.11 3.83 125.87 1.50 16.06 1.35 0.45

Seed/genetics $ 61.27 2.97 36.71 0.00 22.51 3.40 0.85

Specialized tech $ 0.00 0.00 25.17 0.00 2.81 0.00 0.00

Fert/lime/etc $ 345.59 2.55 62.94 1.80 31.08 2.91 0.73

Chemicals $ 228.28 0.42 62.94 0.30 20.52 0.49 0.11

Fuel/lube/elect. $ 61.75 6.36 62.94 4.50 17.22 7.28 1.82

Other variable $ 432.15 7.64 330.41 5.00 21.23 8.74 2.18

Fixed cash $ 334.22 9.76 125.87 6.90 13.89 11.17 2.79

Capital repl. $ 294.14 5.35 368.17 3.84 51.91 3.67 0.92

Implicit acreage response 0.453 0.896 1.034 N/A N/A N/A N/A

Implicit supply response 1.087 1.432 1.034 N/A N/A N/A N/A

Implicit price response 0.645 0.202 1.132 N/A N/A N/A N/A

Cow-calf Fed beef Ind. hog Cont. hog Dairy Sheep/lamb/wool Broilers

Yield & units 5.5 +2.0 cwt 1.0 cwt 1.0 cwt 1.0 cwt 1.0 cwt 82.57 $ 1.0 cwt

Operator labor $ 229.58 0.58 3.52 1.54 1.73 6.81 3.00

Hired labor $ 3.12 0.83 0.45 3.86 0.59 7.20 0.90

Fuel/lube/elect. $ 19.14 2.00 1.33 0.94 0.53 1.91 1.00

Other variable $ 84.63 5.08 2.08 3.64 2.95 8.46 4.35

Fixed cash $ 87.95 1.25 1.98 2.21 0.92 8.79 8.40

Capital repl. $ 122.54 1.21 15.15 8.11 2.15 12.25 8.40

Implicit production 

 response 0.982 0.960 0.661 0.618 0.863 0.000 0.937

Implicit supply response 1.069 1.069 0.785 0.785 0.886 0.000 1.148

Implicit price response 0.887 0.887 1.511 1.511 1.376 2.708 0.758

Ind. egg Cont. egg Ind. turkey Cont. turkey Livestock NEC

Yield & units 1.0 doz 1.0 doz 1.0 cwt 1.0 cwt 1.0 $

Operator labor $ 0.06 0.06 2.50 2.00 0.09

Hired labor $ 0.06 0.06 2.00 2.50 0.09

Fuel/lube/elect. $ 0.03 0.03 1.00 1.00 0.12

Other variable $ 0.12 0.12 8.00 8.00 0.31

Fixed cash $ 0.1425 0.1425 13.00 13.00 0.05

Capital repl. $ 0.1525 0.1625 13.00 13.50 0.10

Implicit production response 1.035 1.055 1.173 0.599 0.000

Implicit supply response 1.044 1.044 0.974 0.974 0.000

Implicit price response 0.788 0.788 1.033 1.033 2.138

Source: Calculated from USDA Agricultural Projections to 2016.
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Implicit Acreage- and Supply-Response 

Elasticities

Table 2 presents the implicit acreage-response and the implicit supplyresponse elasticities of all commodities. These were calculated by repeatedly 

solving the model while perturbing the intercept of each domestic demand 

function by 10 percent and scaling the new equilibrium solution down to a 

1-percent change. Acreage and supply responses are determined by simultaneous adjustments of all quantities and prices to the new equilibrium. 

The acreage and supply responses are complex and not easily traced. But 

some factors that influence them are the proportions of total acreage of the 

commodity under consideration relative to other competing commodities, 

the slope of the production function of the commodity under consideration 

relative to the slopes of competing commodities, and the slope of the owndemand function relative to the demand functions of other commodities. 

For example, the acreage response for corn is 0.333 percent, that is, a 1-

percent increase in the domestic nonfarm demand for corn causes a 0.333-

percent increase in corn acreage. Because yield per acre is constant in the 

EDMP model, corn production also increases by 0.333 percent from a total 

production level of 11,143 billion bushels. In order to expand the production 

of corn, it is necessary to reduce the production of the competing commodities in the model, giving rise to cross-elasticities of acreage response. Soybean 

acreage declines 0.099 percent, wheat acreage declines 0.179 percent, oats 

declines 0.042 percent, and several other commodities decline by less than 

0.04 percent. However, barley, sorghum, and corn silage, which can substitute 

for corn in livestock feed rations, increase by 0.518, 0.047, and 0.034 percent, 

respectively. The most responsive commodities—sugar cane, sunflowers, and 

potatoes—have own-acreage responses above 1 percent. At the other extreme, 

own-acreage responses for cotton, barley, rice, and sorghum are less than 0.20 

percent. Major field crops—soybeans, corn, and wheat—have own-acreage 

responses of 0.539, 0.333, and 0.334 percent, respectively.

The quantity reconciliation of the implicit supply response for corn begins 

with the absolute value of the 37.11-million-bushel increase in corn production, then adds 5.24 million bushels from consigning less corn to storage plus 

2.87 million bushels from drawing down existing stocks of stored corn, plus 

11.07 million bushels from decreased exports, plus 0.77 million bushels from 

increased imports, plus 5.61 million bushels from decreased onfarm livestock 

feeding, for a total of 62.67 million bushels, or 1.246 percent of the 5.033-

billion-bushel domestic nonfarm demand. Finally, the price of corn increases 

by 0.273 percent in response to the new equilibrium supply and demand 

changes. After all adjustments in production, farm sector use, imports and 

exports, net storage, and own price, the final supply-response elasticity for 

corn becomes 1.246 percent—quadruple the acreage-response elasticity. A 

large proportion of the increase in corn supply response over corn acreage 

response is due to the fact that the divisor of the ratio, domestic nonfarm corn 

demand, is less than half of total corn production. 

Common assumptions from other studies are that supply-response elasticities are 1.0 or less for crop commodities.3 From our results, these common 

assumptions appear to be not bad; but they bear further examination. Our 

3 For example, Sumner (2006) 

assumed values of supply-response 

elasticities of 1.0 for corn, wheat, rice, 

and soybeans in the United States and 

elasticities of 0.5 to 0.2 for corresponding commodities in the rest of the world 

in his analysis of potential conflicts of 

U.S. agricultural support policies and 

obligations under the WTO. See table 5 

of Sumner (2005).
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results for acreage responses are grouped around 0.3, but the corresponding 

supply-response elasticities consistently are as much as three to four times 

higher, except for commodities that are neither internationally traded, nor 

storable, nor used on farms. Own-acreage response elasticities ranged from 

1.279 for sugar cane to 0.042 for cotton and 0.013 for barley and sorghum. 

But, because more elastic supply sources (adjustments in exports, imports, 

storage/dis-storage, and onfarm use) contribute to the magnitudes of implicit 

domestic supply-responses, supply elasticities for soybeans, wheat, corn, 

and rice cluster near 1.25. Cotton supply-response is near 1.0, and livestock 

commodities have supply-response elasticities between 0.78 and 1.15—the 

smallest for hogs and the largest for broilers. 
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Demand Parameters

Table 3 lists the base quantities, base prices, and elasticities in all markets—

domestic nonfarm, export, competing imports, and storage/dis-storage. 

Elasticities in the model can be altered as specified by the user. All quantities 

and prices are endogenous but can be re-calibrated by the user. Model prices 

obey the law of one net price. Prices for commodities in different markets 

may differ slightly because there may be different physical costs such as 

storage, transportation, and handling required to access different markets.

Table 3

Disposition activity parameters: Base solution: U.S. aggregate EDMP model, 2002-05 average

Domestic nonfarm demands

Activity name Corn Soybeans Wheat Rice Barley Oats Sorghum

Symbol SELCRNUS SELSOYUS SELWHEUS SELRICUS SELBARUS SELOATUS SELSRGUS

Base quantity (mil. units) 5033.11 1931.14 1878.65 153.85 177.22 85.71 27.93

Base price ($/unit) 1.786 4.501 2.602 6.001 2.427 1.266 2.181

Price elasticity -0.7 -0.99 -0.85 -0.75 -0.67 -0.47 -0.92

Cotton Sugar Potatoes Dry beans Sunflower Peanuts Tobacco

Symbol SELCOTUS SELSGRUS SELPOTUS SELBENUS SELSNFUS SELPNTUS SELTOBUS

Base quantity (mil. units) 5124.59 50.20 446.13 20.45 26.15 3193.88 885.21

Base price ($/unit) 0.490 38.772 5.457 24.261 13.113 0.218 2.021

Price elasticity -0.27 -0.50 -0.50 -0.50 -1.00 -0.50 -0.25

Hay Crops NEC Straw Cottonseed Beef Hogs Dairy

Symbol SELHAYUS SELNCCUS SELSTRUS SELCTSUS SELFDBUS SELHOGUS SELMLKUS

Base quantity (mil. units) 94.92 40212.11 10.02 794.26 457.00 236.95 1654.35

Base price ($/unit) 45.979 0.977 52.528 1.086 69.789 33.520 13.988

Price elasticity -0.75 -0.50 -1.00 -0.27 -0.52 -0.43 -0.31

Sheep/lamb/wool Broiler Eggs Turkey Livestock NEC

Symbol SELSHPUS SELBRLUS SELEGGUS SELTRKUS SELNCLUS

Base quantity (mil. units) 794.50 264.13 722.01 40.47 3158.10

Base price ($/unit) 1.041 39.168 0.672 37.523 0.999

Price elasticity -0.50 -0.63 -0.23 -0.80 -0.75

Export demands

Activity name Corn Soybeans Wheat Rice Barley Oats Sorghum

Symbol EXPCRNUS EXPSOYUS EXPWHEUS EXPRICUS EXPBARUS EXPOATUS EXPSRGUS

Base quantity (mil. units) 1885.95 822.09 978.30 72.15 26.62 18.61 36.86

Base price ($/unit) 1.936 4.961 2.752 6.501 2.427 1.346 2.181

Price elasticity -1.20 -2.50 -0.85 -2.62 -0.67 -3.93 -1.86

Cotton Dry beans Sunflower Peanuts Tobacco Beef Hogs

Symbol EXPCOTUS EXPBENUS EXPSNFUS EXPPNTUS EXPTOBUS EXPBEFUS EXPHOGUS

Base quantity (mil. units) 3603.22 2.22 2.62 454.58 514.80 21.76 12.40

Base price ($/unit) 0.525 24.261 13.113 0.218 2.021 69.789 33.520

Price elasticity -1.34 -1.00 -1.75 -1.75 -1.00 -0.61 -0.6

 —continued
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Table 3

Disposition activity parameters: Base solution: U.S. aggregate EDMP model, 2002-05 average—Continued

Export demands—continued

Activity name Dairy Poultry

Symbol EXPDRYUS EXPPOUUS

Base quantity (mil. units) 29.07 51.68

Base price ($/unit) 13.988 38.839

Price elasticity -0.31 -0.67

Competing import supplies

Activity name Corn Soybeans Wheat Rice Barley Oats Sorghum

Symbol IMPCRNUS IMPSOYUS IMPWHEUS IMPRICUS IMPBARUS IMPOATUS IMPSRGUS

Base quantity (mil. units) 13.32 1.85 38.03 9.20 15.25 1.15 0.64

Base price ($/unit) 1.936 4.961 2.752 6.501 2.427 1.346 2.181

Price elasticity 2.00 2.00 2.00 2.00 2.00 2.00 2.00

Cotton Beef Hogs

Symbol IMPCOTUS IMPBEFUS IMPHOGUS

Base quantity (mil. units) 150.79 25.52 5.97

Base price ($/unit) 0.525 69.789 33.520

Price elasticity 2.00 2.00 2.00

Storage demands/dis-storage supplies

Activity name Corn Soybeans Wheat Rice Barley Oats Sorghum

Symbol STORCRN STORSOY STORWHE STORRIC STORBAR STOROAT STORSRG

Base quantity (mil. units) 1502.45 294.74 781.99 27.08 116.29 55.01 27.20

Base price ($/unit) 1.963 4.988 2.793 6.541 2.453 1.373 2.208

Price elasticity -1.20 -1.20 -1.20 -1.20 -1.20 -1.20 -1.20

Symbol DSTORCRN DSTORSOY DSTORWHE DSTORRIC DSTORBAR DSTOROAT DSTORSRG

Base quantity (mil. units) 930.41 157.23 559.91 9.34 81.96 49.04 64.22

Base price ($/unit) 1.920 4.945 2.730 6.479 2.410 1.330 2.165

Price elasticity 0.80 0.80 0.80 0.80 0.80 0.80 0.80

Activity name Dry beans Sunflowers

Symbol STORBEN STORSNF

Base quantity (mil. units) 10.33 15.70

Base price ($/unit) 24.302 13.154

Price elasticity -1.20 -1.20

Symbol DSTORBEN DSTORSNF

Base quantity (mil. units) 7.58 9.88

Base price ($/unit) 24.302 13.091

Price elasticity 0.80 0.80

Source: Calculated from USDA Agricultural Projections to 2016.
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Government Program Parameters

Table 4 lists the Government program parameters—for decoupled programs: 

the direct payment rate, maximum counter-cyclical payment rate, program 

yield, payment per base acre, and total payment. An implicit scale factor—

subsuming payout proportions, coverage rates, and participation rates—is 

calculated to equate the endogenously calculated program payments to 

reported aggregate program payments. For loan deficiency payments, the 

loan rate, weighted average loan deficiency payment rate, total production, and total loan deficiency payments are listed. Maximum CRP acreage, 

average CRP payment per acre, and maximum aggregate CRP payout can 

be set by the user. For crop insurance, the acreage insured, elasticity of crop 

insurance demand, premium per acre, and subsidy per acre are consensus 

estimates based on data from the Risk Management Agency, published by 

the USDA’s Office of the Chief Economist (2006). Each of these parameters 

can be set by the user. 

Table 4

Government program parameters: Base solution: U.S. aggregate EDMP model, 2002-05 average

Direct payments

Activity name Corn Soybeans Wheat Rice Barley Oats Sorghum Cotton

Direct payment rate 0.28 0.44 0.52 2.35 0.24 0.24 0.35 0.0667

* Program yield 131.82 36.119 40.72 55.18 54.38 48.192 33.44 522.00

= Payment/acre 31.373 13.509 17.998 110.222 11.093 9.831 9.948 29.595

Total direct payment 2116.30 903.64 1072.88 345.74 58.04 21.97 82.66 380.56

Implicit scale factor 0.8696 0.8695 0.8700 0.8696 0.8696 0.8696 0.8696 0.8696

Counter-cyclical payments

Activity name Corn Soybeans Wheat Rice Barley Oats Sorghum Cotton

(Target price 2.63 5.80 3.92 10.50 2.24 1.44 2.57 0.724

-Direct payment 0.28 0.44 0.52 2.35 0.24 0.024 0.35 0.0667

-Loan rate) 1.95 5.00 2.75 6.50 1.85 1.33 1.95 0.52

* Program yield 131.82 36.119 40.72 55.18 54.38 48.192 33.44 522.00

= CC payment/ acre 52.728 13.003 26.468 408.994 8.157 4.145 9.029 71.671

Total CC payment 2390.32 584.55 1059.73 191.93 28.68 6.22 50.42 619.36

Implicit scale factor 0.5844 0.5844 0.5844 0.5844 0.5844 0.5844 0.5844 0.5844

Marketing loan gains and loan deficiency payments

Activity name Corn Soybeans Wheat Rice Barley Oats Sorghum Cotton

Loan rate 1.95 5.00 2.75 6.50 1.85 1.33 1.95 0.52

Wtd. ave. LDP rate 0.164 0.499 0.148 0.499 0.000 0.064 0.000 0.030

*Total sales & Use 11116.80 2910.88 3100.59 245.46 238.14 111.06 27.76 8788.9

=Total LDP payment 1821.03 1451.14 455.36 122.52 0.00 7.07 0.00 260.28

Conservation reserve program

Enrolled CRP acres (mil) 36.90

*CRP payment/acre ($/acre) 58.392

=Maximum CRP payout ($ mil) 2191.56

 —continued
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Table 4

Government program parameters: Base solution: U.S. aggregate EDMP model, 2002-05 average—Continued

Crop insurance subsidies

Activity name Corn Soybeans Wheat Rice Barley Oats Sorghum Cotton

Acres insured 71.369 61.544 56.182 2.092 3.790 2.184 9.460 14.640

Percent insured 92% 80% 82% 58% 63% 85% 99% 99%

Ins. dem. elasticity -0.6 -0.6 -0.6 -0.6 -0.6 -0.6 -0.6 -0.6

Premium/acre 22.415 17.185 9.765 33.812 9.255 4.519 5.999 24.128

Subsidy/acre 12.776 9.795 5.566 19.273 5.276 2.576 3.419 13.753

Sugar beets Sugar cane Dry beans Sunflower Peanuts Tobacco All insured crops

Acres insured 1.256 0.532 1.480 1.750 1.076 0.480 227.72

Percent insured 90% 71% 85% 85% 78% 73% 85%

Ins. dem. elasticity -0.6 -0.6 -0.6 -0.6 -0.6 -0.6 -0.6

Premium/acre 65.764 65.764 26.663 17.781 46.323 345.984 4660.75 total

Subsidy/acre 37.486 37.486 16.338 10.135 26.404 197.211 2636.63 total

Source: Calculated from USDA Agricultural Projections to 2016.
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Post-Optimal Calculations of 

Performance Variables

Because the value of the model’s objective function is confounded by the 

presence of calibration constraint values, it is necessary to post-optimally 

calculate several model performance measures. These post-optimal calculations are in a page labeled INCOMES of the Excel spreadsheet model. This 

section of this bulletin describes the calculation of farm income measures, 

Government budgetary expenditures, consumer and producer surpluses, and 

commodity cash incomes, expenses, and margins.

Net Farm Income and Net Cash Flow 

Shortrun net farm income is calculated as the sum of:

+	Commodity cash receipts from domestic and export markets;

+ Government payments (direct and counter-cyclical payments, loan 

deficiency payments, conservation reserve and wetlands reserve 

payments, and crop insurance indemnities);

+ Farm-related income;

- Variable input purchases (hired labor, seed and genetics, specialized 

technologies, fertilizer, chemicals, and fuel, lube, and electricity, and 

miscellaneous variable inputs); 

- Rent paid; 

- Crop insurance premiums; 

- Interest paid; 

- Cash overhead expenditures; 

- Other fixed cash expenditures; and 

- Storage-related costs (hired labor, variable inputs, technology, capital 

costs, and fixed cash expenditures).

Note:

•	The dollar value of operator and family labor is not an expense in net 

farm income but is a resource endowment that can be allocated among 

activities.

•	Longrun net farm income includes all of the above items and adds in the 

value of perquisites and subtracts out capital replacement costs.

•	Shortrun net cash flow includes all of shortrun net farm income plus offfarm income and subtracts principal paid and family living expenses. 

•	Longrun net cash flow adds in the value of perquisites and subtracts out 

capital replacement costs.
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Government Budgetary Exposure 

Government budgetary exposure is also calculated in the INCOMES page 

of the Excel spreadsheet. The parameter values of Government programs 

are shown in table 4 but may be changed if policy provisions or parameters 

change. The INCOMES spreadsheet shows the calculated values of major 

Government programs—direct payments, counter-cyclical payments, loan 

deficiency payments, conservation reserve payments, and crop insurance 

subsidies.

Direct payments and counter-cyclical payments are decoupled from current 

production by individual farmers. Counter-cyclical payments depend on 

average market prices, which in turn depend on aggregate production of the 

covered commodities; thus they are semicoupled. Since both are disbursed 

irrespective of whether the recipient grows the covered crop, they do not alter 

the effective market prices perceived by producers and have the same effect 

as lump-sum payments to producers and/or nonoperator landlords. 

Loan deficiency payments and marketing loan gains, on the other hand, are 

paid on all production of actual producers of the covered commodity. They 

are fully coupled to individual production and stimulate additional supply 

because they raise the effective prices perceived by the producers. 

Conservation reserve and wetlands reserve payments essentially rent the land 

in question on a long-term basis, and remove it from production. Thus, these 

programs have a supply control component that enhances their effects on 

farm income by restricting supply. 

Crop insurance subsidies act in the opposite way—they stimulate additional 

production by underwriting some of the costs of production and possibly 

paying out indemnities in excess of premiums collected.

Consumer and Producer Surpluses 

Changes in consumer surplus, also calculated in the INCOMES spreadsheet, 

correctly measure the consumer welfare implications of changes in supply or 

demand because they vary directly with consumer preferences—increasing 

with either increases in quantity or decreases in price. Consumer expenditures, in contrast, are not a reliable measure of consumer welfare, because 

consumer expenditures may or may not reflect changes in welfare, depending 

on whether consumer demand is elastic or inelastic. With an inelastic 

demand, a change in quantity results in a larger change in prices in the opposite direction, thereby causing the change in expenditures to be opposite 

in direction to the change in consumer welfare. With an elastic demand, a 

change in quantity has only a small opposite effect on price; thus consumer 

expenditures have the same sign as consumer welfare changes but are smaller 

by the price effect. In the INCOMES page, the model separately calculates 

and sums consumer surplus for each commodity in domestic markets and in 

export markets using the formula:

CS = 1⁄2 (Intercept – Price) *Quantity. (15)
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This model does not calculate changes in producer surplus by commodity 

to correspond with the consumer surplus. The reason for this is that changes 

in producer surplus for a single commodity do not conceptually represent 

the producer welfare implications of a change in production if Government 

transfer payments coupled to production or price levels are present. In the 

EDMP model, the loan deficiency payment program, the CRP, and crop 

insurance subsidies are all coupled to production levels, and the countercyclical payments are coupled to price levels. For more defensible and informative measures of changes in producer welfare by commodity, we suggest 

commodity cash incomes, expenses, and margins, as calculated below.

Commodity Cash Incomes, Expenses, 

and Margins 

Cash incomes, expenses, and margins by commodity are included in the 

INCOMES spreadsheet. These measures accurately track the shortrun 

net farm income implications of changes in the model solutions. For crop 

commodities, the formulas are:

Accrued cash market income = Acreage * Yield * Domestic 

market price, (16)

Commodity cash expenses = Acreage * Variable cash costs 

per acre, and (17)

Net cash market income = Accrued cash market income – 

Commodity cash expenses. (18)

For livestock commodities, “production” is substituted for “acreage times 

yield.” 

These measures reveal important producer welfare information for each 

commodity. For example, rice, oats, and cotton all have negative net cash 

market incomes, indicating that their variable production costs exceed their 

market revenues, with Government transfer payments making up all of their 

net cash margins. There is an incentive for production of these commodities to decline if decoupled payments are used to effect the Government 

transfer payments because producers can avoid the cash income losses from 

production and still receive the decoupled payments. However, if coupled 

payments, such as the loan deficiency payment program, are used to effect 

the Government transfer payments, then there is no incentive for farmers 

to reduce production. Additional commodities that have very high ratios of 

cash expenses to cash incomes include barley, grain sorghum, sugar (beets 

and cane), and peanuts, all of which have high levels of Government income 

supports, which distort their cost structures relative to their market prices. 

Livestock commodities have uniformly high costs and low margins because 

the internal transfer prices of the farm-produced grains and forages they 

consume are calculated at their opportunity costs (market prices) instead 

of their variable production costs. Using opportunity costs as the internal 

transfer prices is conceptually correct, but it causes the production costs 

of farm-produced feeds to be over-estimated and livestock margins to be 

correspondingly under-estimated. Both independent and contract turkeys 
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display negative net cash incomes. That result is probably not true in actual 

production, however, because these industries are highly industrialized and 

exercise strict cost control at all stages. These activities and results should 

be re-examined in later improvements to the EDMP model. The results may 

be due to errors in specification of the production budgets for these activities or errors in the distribution of market receipts between independent and 

contract producers.
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References

Buse, R.C. (1958) “Total Elasticities: A Predictive Device,” Journal of 

Farm Economics. Vol. 40, pp. 881-891.

Chavas, J-P. (1994) “Production and Investment Decisions Under Sunk 

Costs and Temporal Uncertainty,” American Journal of Agricultural 

Economics. Vol. 76, (February), pp. 114-127.

Davis, G.C., and M.C. Espinoza. (1998) “A Unified Approach to Sensitivity 

Analysis in Equilibrium Displacement Models,” American Journal of 

Agricultural Economics. Vol. 80, (November), pp. 868-879.

Gardner, B.L. (1975) “The Farm-Retail Price Spread in a Competitive Food 

Industry,” American Journal of Agricultural Economics. Vol. 57, (August), 

pp. 399-409.

Harrington, D.H. (1973) “Quadratic Input/Output Analysis: Methodology for 

Empirical General Equilibrium Models.” Ph.D. thesis, Purdue University, 

West Lafayette, Indiana, (August). 

Harrington, D.H., and R. Dubman. (1998) “Agriculture and New Agricultural 

Policies in the Great Plains,” Rural Development Perspectives. (February).

Harrington, D.H., and R. Reinsel. (1995) “A Synthesis of Forces Driving 

Structural Change,” Canadian Journal of Agricultural Economics, Special 

Issue, Farms, Farm Families, and Farm Communities, Harrington, D.H., R. 

Bollman, P. Ehrensaft, D. Freshwater, and L. Whitener (Eds.), (December), 

pp. 3-14. 

Howitt, R.E. (1995) “Positive Mathematical Programming,” American 

Journal of Agricultural Economics. Vol. 77, No. 2, (May), pp. 329-342.

Jefferson-Moore, K.Y., and D.H. Harrington. (2006) “The Distribution of 

Rents in Supply Chain Industries: The Case of High Oil Corn.” Paper delivered at the 2006 Conference of the International Association of Agricultural 

Economists, Brisbane, Australia, (August). 

Johnson, G.L., and L. Hardin. (1955) The Economics of Forage Evaluation. 

Purdue Agricultural Experiment Station Bulletin No. 623, Purdue University, 

West Lafayette, Indiana.

Johnson, G.L., and C.L. Quance. (1972) The Overproduction Trap in U.S. 

Agriculture. Johns Hopkins Press, Baltimore, Maryland.

Martin, N.R. (1972) “Stepped Product Demand and Factor Supply Functions 

in Linear Programming Analyses,” American Journal of Agricultural 

Economics. Vol. 54, (February), pp. 116-120.

Miller, C.E. (1963) “The Simplex Method for Local Separable 

Programming,” Recent Advances in Mathematical Programming. P. Wolfe 

and R.L. Graves (Eds.), McGraw-Hill, New York.
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Muth, R.F. (1964) “The Derived Demand Curve for a Productive Factor and 

the Industry Supply Curve,” Oxford Economic Papers. New Series, Vol. 16, 

No. 2, (July), pp. 221-234.

Piggott, R.R., N.E Piggott, and V.E Wright. (1995) “Approximating 

Farm-Level Returns to Incremental Advertising Expenditure: Methods 

and an Application to the Australian Meat Industry,” American Journal of 

Agricultural Economics. Vol. 77, No. 3, pp. 497-511.

Plessner, Y. (1965) “Quadratic Programming Competitive Equilibrium 

Models for the U.S. Agricultural Sector.” Ph.D. thesis, Iowa State 

University, Ames.

Preckel, P.V., D.H. Harrington, and R. Dubman. (2002) “Primal/Dual 

Positive Math Programming: Illustrated Through an Evaluation of the 

Impacts of Market Resistance to Genetically Modified Grains,” American 

Journal of Agricultural Economics. Vol. 84, No. 3, pp. 679-690.

Samuelson, P.A. (1952) “Spatial Equilibrium and Linear Programming,” 

American Economic Review. Vol. 42, No. 3, pp. 282-303.

Schertz, L.P., and O.C. Doering, III. (1999) The Making of the 1996 Farm 

Act. Iowa State University Press, Ames.

Schmid, A.A. (Ed.). (1997) Beyond Agriculture and Economics: 

Management, Investment, Policy, and Methodology. Michigan State 

University Press, East Lansing, Michigan.

Sumner, D.A. (2005) Boxed In: Conflicts Between U.S. Farm Policies 

and WTO Obligations. Trade Policy Analysis No. 32, CATO Institute, 

Wasington, DC, December 5.

Sumner, D.A., and M.K. Wohlgenant. (1985) “Effects of an Increase in 

the Federal Excise Tax on Cigarettes,” American Journal of Agricultural 

Economics. Vol. 67, (May), pp. 235-242.

Takayama, T., and G.G. Judge. (1971) Spatial and Temporal Price and 

Allocation Models. North-Holland Publishing Co., Amsterdam, Netherlands.

USDA. (2007) 2007 Farm Bill Proposals, (hard copy) (January). 

USDA, ERS. (2006) Commodity Costs and Returns, website: http://www.

ers.usda.gov/Data/CostsAndReturns/.

USDA, ERS. (2006) 2002 Farm Bill, http://www.ers.usda.

gov/Features/FarmBill/.

USDA, ERS. (2007) 1996 Farm Bill, “Farm and Commodity Policy,” http://

www.ers.usda.gov/Briefing/Farm Policy/historyOfFarm.htm/.

USDA, ERS. (2006) Farm Income and Costs, http://www.ers.usda.

gov/briefing/farmincome/data/va_t1.htm.
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USDA, NASS. (2006) 1997 Census of Agriculture, website: http://www.nass.

usda.gov/census/census97/highlights/ag-state.htm.

USDA, Office of the Chief Economist. (2006) 2007 Farm Bill Theme Papers, 

http://www.usda.oce/, (December).

USDA, Office of the Chief Economist. (2007) USDA Agricultural 

Projections to 2016. Long-Term Projections Report OCE-1, www.usda.gov/

oce/commodity/ag_baseline.htm, (February). 

Wohlgenant, M.K. (1993) “Distribution of Gains from Research and 

Promotion in Multi-Stage Production Systems: The Case of U.S. Beef and 

Pork Industries,” American Journal of Agricultural Economics. Vol. 67, 

(August), pp. 642-651.

Yaron, D., Y. Plessner, and E.O. Heady. (1965) “Competitive Equilibrium 

Applications of Mathematical Programming,” Canadian Journal of 

Agricultural Economics. Vol. 13.
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Appendix I: User’s Manual

The Excel Workbook, U S Aggregate Marketing Loan Model.xls, contains 

six spreadsheet pages labeled: A, B, Log, OUTPUT, INCOMES, and 

MODEL. Spreadsheet A contains the supply side of the U.S. Aggregate 

EDMP Model; Spreadsheet B contains the demand side of the model. Sheets 

Log, OUTPUT, and MODEL are generated by the SAS program to track 

the status of the SAS program and written back into Excel for possible use in 

diagnosing any problems.

We will first concentrate on Sheets A and B, which define the model 

tableaux, containing parameters under control of the model user, and 

receiving the raw optimal solutions written back by SAS. 

Spreadsheet A, The Supply Side

• Rows 1 through 10: Scenario-base comparison post-optimal calculations. Scenario quantities and gradients (perfectly competitive prices) 

and base quantities and gradients and absolute and percentage differences of scenario from base. Each column is identified by its name within 

the EDMP model. Values in Rows 2 and 7 for the scenario solution 

and Rows 3 and 8 for the base solution must be copied and pasted as 

values from Rows 16 and 17. 

•	Rows 12 through 15: Parameters defining process supply slopes 

(Hessian elements) and base quantities: Capital requirements per unit 

(Row 12), decimal of excess capacity (Row 13) (which is the product of 

the percent excess capacity times the percent substitutable capital for that 

commodity and can be changed by the user). Row 14 shows the target 

base quantities. For supply processes, there is no target base price. The 

base prices of supply processes are initially defined as the product of the 

Hessian element times the base quantity. In the process of calibration, 

these initial estimates may increase or decrease as necessary to calibrate 

to the base quantities.

•	Rows 16 through 24: (Rows 16 through 19) are optimal solutions as 

written back into Excel by the SAS program. Row 23 is the calculated 

value of the Hessian element, defined as the negative of Row 12 divided 

by Row 13 times Row 14. The Intercepts (Row 24) are determined as the 

negative of Row 14 times Row 32 plus Row 21. Row 21 is the implicit 

gradient check for the uncalibrated intercept.

•	Rows 26 through 225 and Columns F through CX: This block constitutes the supply side quadratic programming tableau of the EDMP model. 

Column CX contains the values for the right hand side (RHS) of the 

supply side of the model. Column CY labels the constraint rows and 

how the values were derived for the base solution. The SAS program 

automatically identifies the block Rows 26 through 225 and Columns F 

through CX as the quadratic programming tableau.

•	Rows 32 and 30 are the diagonal of the Hessian (Row 32) and its corresponding calibrated intercept (Row 30) for the base solution. The diagonal of the Hessian values are calculated in Row 23 and must be pasted 

Appendix III model spreadsheets are 

accessible by contacting 

David Harrington, 202-694-5571, 

davidh@ers.usda.gov
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as values in Row 32. The uncalibrated intercept values are calculated 

in Row 24. The uncalibrated intercept values are modified upward or 

downward until the base period prices and quantities are achieved to the 

desired level of accuracy, then transferred to Row 32 by dividing Row 32

by the ratio of the original intercept to the calibrated intercept, and Row 

30 is returned to its original value (Row 24).

•	Customizing the Supply Functions. Rows 31 and 29 are the diagonal 

of the Hessian (Row 31) and the corresponding calibrated intercept 

(Row 29) for the scenario solution. These rows allow customization of 

the model for any additive (parallel shift) or multiplicative (rotational) 

change that the user specifies to the base values of either the diagonal of 

the Hessian or the calibrated intercepts.

•	Rows 33 through 36 contain the elements that will be used to calculate 

the net income measures in the INCOMES page of the spreadsheet. They 

are free rows that do not constrain the solution to the model in any way.

•	Rows 37 through 227 and Columns F through CX define the Aij 

constraint matrix and right hand side.

Columns C and D: Customizing the model supplies and demands to a 

specific problem. 

•	Column C labels the parameters the user can specify to modify the 

production processes (Aij entries), either the base solution or the scenario 

solution that will be compared with the base, and Column D contains 

the default values of the parameters. All model processes that are not 

specified by the user in Column D and remain at their default values are 

endogenously calculated as perfectly competitive adjustments within the 

program environment of the 1996 Farm Act, as modified by the 2002 

Farm Act.

•	In general, crop commodity processes allow the user to specify any of 

the following actions: (1) Change the commodity yields per acre, (2) 

Change the commodity variable costs per acre, (3) Change commodity 

acreage, (4) Fix the commodity acreage, (5) Change commodity 

exports, (6) Fix commodity exports, (7) Change commodity competing 

imports, and (8) Fix commodity competing imports. 

•	Livestock commodity processes allow the user to specify: (1) Change 

the variable costs per unit, (2) Change livestock production, (3) Fix 

livestock commodity production, (4) Change livestock commodity 

exports, (5) Fix livestock commodity exports, (6) Change livestock 

commodity competing imports, and (7) Fix livestock commodity 

competing imports.

•	Columns AX, AY, and AZ are Government program activities: CRP 

payments, the lump sum direct payments, and ARP (set-aside) requirements, if they are required.

•	Columns BA through BZ are crop insurance activities and crop insurance indemnities by crop commodity.

•	Columns CA through CQ are: (1) purchases of variable inputs (hired 

labor, miscellaneous variable inputs, seed/genetics, specialized tech-
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nology, fertilizers, chemicals, fuels, lubes, and electricity), (2) payments 

of overhead costs (fixed costs, capital replacement, interest, rent, and 

other residual overhead costs), and (3) cash flow items that are not part 

of farm income (family living costs, principal paid, farm-related income, 

off-farm income, and value of perquisites). The user can change the 

dollar prices of these inputs proportionally by modifying the entries in 

Row 30 up or down from -1.0.

•	Columns CR through CU are artifacts from an earlier version of the 

model and can be safely ignored.

•	Column CV specifies the type of constraint (EQ, LE, GE, or FREE) and 

specifies which Hessian row and intercept row (base or scenario) are to 

be maximized in that particular solution. The Hessian row will be labeled 

“QUAD” in column CV, and the intercept row will be labeled “MAX.” 

The other Hessian and intercept rows will be labeled “FREE.”

These must be consistent on Spreadsheets A and B.

Spreadsheet B, The Demand Side

Spreadsheet B contains the demand and disposition activities of the model. 

These include domestic demands by commodity, storage and dis-storage of 

storable commodities, exports and competing imports of tradable commodities, and program activities that depend on national rather than farm-specific 

variables (including storage costs and marketing loan gain mechanisms).

•	Rows 1 through 10: Scenario-base comparison post-optimal calculations. Scenario quantities and gradients (perfectly competitive prices) 

and base quantities and gradients and absolute and percentage differences 

of scenario from base. Each column is identified by its name within the 

EDMP model. Values in Rows 2 and 7 and 3 and 8 must be copied and 

pasted as values from Rows 16 and 17. Rows 3 and 8 are for the base 

solution, and Rows 2 and 7 are for the scenario solution. 

•	Rows 12 through 14: Parameters defining process supply slopes 

(Hessian elements) and base quantities: base quantity, target base price, 

and elasticity of demand. The base prices of demand processes are 

initially defined as the product of the Hessian element times the base 

quantity. In the process of calibration these initial estimates are increased 

or decreased as necessary to calibrate to the base quantities. Then they 

are transferred to Row 32 by dividing Row 32 by the ratio of the original 

intercept to the calibrated intercept. Finally, Row 30 is returned to its 

original value (Row 24).

•	In the final calibrated model, Row 30 should be equal to the demand 

intercept (Row 24).

•	Rows 16 through 24: Optimal solution as written back into Excel by 

SAS (Rows 16 through 19), calculated values of Hessian elements and 

intercepts (Rows 23 and 24), and calculated implicit gradients (Row 21).

•	Rows 26 through 160 and Columns F through DK: This block constitutes the demand/disposition side quadratic programming tableau of the 

EDMP model. Column DK contains the values for the right hand side 
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(RHS) of the demand side of the model. The SAS program automatically 

identifies Rows 26 through 160 and Columns F through DK as the 

quadratic programming tableau. Column DL labels the constraint rows 

and documents how the values were derived for the base solution. 

•	Columns C and D: Columns C and D are not used in Spreadsheet B

because all parameters under user control were specified in Spreadsheet A. 

•	Rows 32 and 30: As in Spreadsheet A, Rows 32 and 30 are the diagonal of the Hessian (Row 32) and the corresponding calibrated intercept 

(Row 30) for the Base Solution. In Spreadsheet B the values of the 

Hessian elements have been altered by calibration factors. The diagonal 

of the Hessian values are calculated in Row 22 and pasted as values in 

Row 32. The uncalibrated intercept values are calculated in Row 24 and 

pasted as values into Row 30. 

•	Customizing the demand functions. Rows 31 and 29 are the diagonal of 

the Hessian (Row 31) and the corresponding calibrated intercept (Row 

29) for the Scenario Solution. Any additive or multiplicative change 

to the base values of either the diagonal of the Hessian or the calibrated 

intercepts can be specified by the user in these rows. This feature allows 

the user to specify any desired parallel or rotational shifts to any demand 

function.

•	Rows 33 through 36 contain the elements that will be used to calculate 

the net income measures in the INCOMES page of the spreadsheet. They 

are free rows that do not constrain the solution to the model in any way.

•	Columns F through AE are domestic nonfarm demands by commodity.

•	Columns AF through AW are storage and dis-storage of storable 

commodities. 

•	Columns AX through BW are exports and competing imports of tradable commodities.

•	Columns BX through CB are inputs for national storage activities.

•	Columns CC through DH are program activities that depend on national 

rather than farm-specific variables (marketing loan gains and loan deficiency payments).

•	Column DI specifies the type of constraint (EQ, LE, GE, or FREE) 

and specifies the Hessian row and intercept row (base or scenario) to be 

maximized in that particular solution. The Hessian row will be labeled 

“QUAD” in column DI, and the intercept row will be labeled “MAX.” 

The other Hessian and intercept rows will be labeled “FREE.”

These must be consistent on Spreadsheets A and B.

Post-Optimal Calculations Spreadsheet

In the next section, we explain the use of the INCOMES spreadsheet, which 

can be custom configured to do post-optimal calculations as needed by the 

user. The INCOMES spreadsheet is automatically calculated from Rows 2 

and 7, Rows 3 and 8, and Rows 33 through 36 of Spreadsheets A and B. 
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We have not printed the row and column indices on the INCOMES spreadsheet to make it easier to read and facilitate associating the data with their 

variable names.

Four measures of farm well-being are calculated in Rows 8 through 34: 

(1) shortrun net cash farm income, (2) longrun net farm income, (3) 

shortrun net cash flow, and (4) longrun net cash flow. 

•	Shortrun net cash farm income does not include capital replacement, 

principal paid, family living expenses, off-farm income, or value of 

perquisites. 

•	Longrun net farm income includes all shortrun net cash farm income, 

subtracts capital replacement, and adds value of perquisites. 

•	Shortrun net cash flow excludes capital replacement and value of perquisites, but subtracts principal paid and family living costs, and adds offfarm income. 

•	Longrun net cash flow includes all shortrun net cash flow, subtracts 

capital replacement, and adds value of perquisites.

The following rows summarize levels of activities and derived calculations 

from the model:

•	Rows 38 through 42 summarize crop production activities, and Rows 44 

through 48 summarize livestock production activities. 

•	Domestic demand activities are summarized in Rows 50 through 60. 

Rows 50 through 54 summarize quantities, and Rows 56 through 60

summarize prices. 

•	Storage and dis-storage are shown in Rows 63 through 67.

•	Exports and competing imports are shown in Rows 69 through 73. 

•	Loan deficiency payments and marketing loan gains are summarized in 

Rows 75 through 85. Sums of marketing loan gains by commodity are 

automatically transferred to the marketing loan gains section (Rows 9 

and 10 of Columns DV through EC). 

•	Counter-cyclical payments are calculated by commodity in Rows 88 

through 92, and their sums are automatically transferred to Row 8 and 

9 of Column F. Although determined on an individual commodity basis, 

counter-cyclical payments are disbursed as lump sum payments that 

affect only net farm income.

•	Direct payments associated with supported commodities are calculated 

in Rows 94 through 98, and their sums are automatically transferred to 

Row 8 and 9 of Column E. These are disbursed as lump sum payments 

in the Government programs columns of the net incomes section. 

•	Crop insurance subsidies are calculated in Rows 100 through 104.
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•	Domestic consumer surpluses and export consumer surpluses are shown 

in Rows 107 through 117. These are shown separately because different 

groups of consumers receive them.

•	Producer gross commodity receipts, commodity cash expenses, and net 

cash income by commodity are calculated in Rows 119 through 139. 

•	Finally, the user can specify and print his/her own custom calculations in 

any unused area of the INCOMES Spreadsheet.

Solving the Model: The SAS Link Program

Appendix II contains the SAS code to optimize EDMP models with quadratic 

programming in Proc NLP. This code hotlinks SAS to an EDMP tableau in 

an Excel spreadsheet. It is executed in the background while running Excel. 

Upon reading a change in a trigger cell (cell A 17), SAS reads the tableau, 

optimizes the model, and prints results back to the spreadsheet, including an 

optimal solution, a complete tableau, and an iteration history. Five solutions 

may be run by incrementing cell A 17. After five solutions have been run, hit 

F8 to restore the program for another five solutions.
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Appendix II: The SAS Excel Link Program

/*

ExcelLinkNov2006.SAS.

*/

%macro ExcelSolve;

%macro ReadData;

option errors=0 nocenter;%global acts n sheet;%let acts=;%let n=;

%Do p=1 %to 2; 

 %let sheet=%sysfunc(byte(&p+64));%put sheet=&sheet;%global actsall&sheet;

 filename model1 dde “excel|&sheet.!r1c6:r1c220”;

 data _null_;infile model1 dlm=’09’x notab dsd missover lrecl=4000;

 array va{200} $ ;input va{*};length actsall $3000.;

 do ii=1 to dim(va);

 if upcase(va{ii})=’_TYPE_’ then do;N1=ii-1;leave;end;

 else actsall=trim(left(actsall))||’ ‘||trim(left(va{ii}));end;

 call symputx(“actsall&sheet”,actsall);call symputx(“N&sheet”,N1);run;

%put actsall&sheet=&&actsall&sheet;%put n&sheet=&&n&sheet;

%Let StartRow=;

filename model1a dde “excel|&sheet.!r1c1:r200c1”;

data _null_;infile model1a dlm=’09’x notab dsd missover lrecl=4000;

 informat startrow $char13.;input startrow;

 if UPCASE(startrow)=”CONSTRAINT” then call 

symputx(‘StartRow’,put(_n_+1,f2.0));run;

%put startrow=&startrow;

filename model1b dde “excel|&sheet.!r&StartRow.c1:r500c250”;

data &sheet free&sheet;infile model1b dlm=’09’x notab dsd missover lrecl=7000;

 informat name $char23. units $char20. slabel $char20. Default $char20. 

activity $34. _type_ $char4. _type_&sheet $char4.;

 input name $ units $ slabel $ default $ activity $ &&actsall&sheet 

 %if &p=1 %then _type_ nada _rhs_;

 %if &p>1 %then _type_&sheet nada _rhs_&sheet;;

 _error_=0;

 name=trim(left(upcase(name)));Order1=_n_;
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if upcase(lag(name))=’GROWER NON-SEED COSTS’ then stop;

if (upcase(name)=”SNFYUS”|upcase(name)=”SNCFUS”|upcase(name)=”LNFYUS”|upcase(n

ame)=”LNCFUS”)

 then do;output Free&sheet;f+1;end;

else output &sheet;

 run;

%put actsall&sheet;

%let Acts=&Acts &&actsall&sheet;%let N=%eval(&N+&&n&sheet);

proc sort data=&sheet;by name;run;

%if&p>1%then%do;

proc sort data=A;by name;run;

data A;length _type_ $8.; merge A(IN=A) &sheet(IN=&sheet);by name;

 if &Sheet then do;

 _rhs_=max(put(_rhs_,f30.10),put(_rhs_&sheet,f30.10));

 _type_=trim(left(_type_&sheet));

 end;

 _type_=trim(left(_type_));

 if ~index(upcase(_type_),”FR”);*Eliminate free constraints;

 if index(upcase(_type_),”LE”) then _type_=”LE”;

 if index(upcase(_type_),”PA”) then _type_=”PARMS”;*new;

 if index(upcase(_type_),”EQ”) then _type_=”EQ”;

 if index(upcase(_type_),”GE”) then _type_=”GE”;

 if index(upcase(_type_),”QU”) then _type_=”QUAD”;

 if index(upcase(_type_),”MA”) then _type_=”MAX”;

 if index(upcase(_type_),”MI”) then _type_=”MIN”;

 if index(upcase(_type_),”FI”) then _type_=”FIXED”;

 drop _rhs_&sheet _type_&sheet; 

 sheets=” “;s=0;

 if B then sheets=”B”||trim(left(sheets));

 if A then sheets=”A”||trim(left(sheets));

 sheets=trim(left(sheets));

if sheets=”AB” then s=1;

if sheets=”A” then s=2;

if sheets=”B” then s=3;

Output A;

 run;

%end;%end;

proc sort data=a out=a2;by s order1;run;

*This section writes out the entire tableau in Model sheet;

filename qpout dde “excel|model!r1c1:r6002c250” lrecl=4000;

data _null_;set A2;

 file qpout;
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Name_=trim(left(translate(trim(left(name)),”_”,” “)));

 format _type_ $4. _rhs_ d9.;

 if _n_=1 then put “Name sheets &acts _type_ _rhs_ Name”;

 format _type_ $char8.;

 put Name_ sheets &acts _type_ _rhs_ Name_;

 run;

%mend ReadData;

%ReadData;

%put acts=&acts n=&n;

%let BaseOrScen=Base;

data a;set a(drop=s sheets) end=end ;LENGTH _NAME_ $8 ;

if ~index(upcase(_type_),”FR”);

ARRAY ACTS(*) &ACTS;ARRAY ACTS2{&N} _TEMPORARY_;

************************************************;

*Set up Hession matrix;

 IF upcase(_type_)=’QUAD’ then do;

 DO I=1 TO DIM(ACTS);ACTS2{I}=ACTS{I};ACTS{I}=0;END;

 DO I=1 TO DIM(ACTS);

 ACTS{I}=ACTS2{I};

 CALL VNAME(ACTS{I},_NAME_);

 _RHS_=.;OUTPUT;ACTS{I}=0;

 END;END;

************************************************;

*Create separate constraints for fixed coefficients;

Else IF upcase(_type_)=’FIXED’ then do;

 DO I=1 TO DIM(ACTS);ACTS2{I}=ACTS{I};ACTS{I}=.;END;

 DO I=1 TO DIM(ACTS);

 IF ACTS2{I}~=. THEN DO;ACTS{I}=1;_RHS_=ACTS2{I};_TYPE_=”EQ”;*CALL 

SOUND(8500,1);

 *PUT ‘FIXED ‘ I= acts{i}= _rhs_=;

 OUTPUT;ACTS{I}=.;_RHS_=.;

 END;END;END;

************************************************;

ELSE if upcase(_type_)=’MAX’ then do;_type_=’LINEAR’;output;*Required for NLP;

 if index(upcase(name),”SCE”) then call symputx(“BaseOrScen”,”Scenario”);

 end;

************************************************;

ELSE output;

************************************************;

IF END THEN DO;

 do i=1 TO DIM(ACTS);ACTS{i}=0;_TYPE_=’LOWERBD’;_RHS_=.;name=’LOWERBD’;END;

 output;*Restrict to nonnegative quadrant;
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 /*_type_=”PARMS”;OUTPUT;*/*Starting solution of null vector;

 end;

run;

option ps=max ls=max;

filename nlplog dde “excel|LOG!r1c1:r500c25” notab lrecl=4000;

data _null_;file nlplog; do r=1 to 500;put “ “;end;run;

filename nlpout dde “excel|OUTPUT!r1c1:r500c25” notab lrecl=4000;

data _null_;file nlpout; do r=1 to 500;put “ “;end;run;

option notes;

proc printto print=nlpout log=nlplog;run;*allows log to be read;

***********************************************************;

*This is the quadratic optimization section. Parameters have

been set to Proc NLP (nonlinear programming) standards with

iteration restrictions and convergence criteria;

PROC NLP INQUAD=A OUTEST=QPOUT short maxiter=2000 absgconv=1e-10 20;

*maxtime=60 noeignum;* out=out1 outder=2;* nomiss;*PALL;*options;

MAX;

PARMS &ACTS;*list of activity names (parameters);

RUN;

************************************************************;

%put SYSERR=&syserr -A nonzero syserr code indicates NLP execution problems;

proc printto;run;

option nonotes;

%let crit=;

data log_;

 infile nlplog dlm=’09’x notab dsd missover lrecl=4000;

 informat row $char125.;input row;

 if index(row,”convergence criterion satisfied.”)then do;

 call symputx(‘crit’,”Convergence criterion satisfied.”);

 call sound(3000,5);put ‘It worked. ‘ row;*stop;

 end;

 if ~index(row,’randomly’)& ~index(row,’printto’)& ~index(row,’put s’);run;

data _null_;set log_;file nlplog;put row;

run;

%put crit=&crit;

filename Esystem dde “Excel|system”;

%if &crit=%then%do;

 data _null; file Esystem;
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 put ‘[ALERT(“Convergence criteria may not be satisfied for this NLP optimization.”, 3)]’;

 run;

 %let crit=Problem with convergence;

%end;

filename nlplog2 dde “excel|LOG!r1c1:r3c25” notab lrecl=4000;

data _null_;file nlplog2;

 d=date();t=time();

 put “U.S. Structural Change Model. &BaseOrScen intercepts”;

 put “Optimized “ d date8. “ “ t timeampm10.;

 put “&crit”;

 run;

filename nlpout2 dde “excel|OUTPUT!r1c1:r2c25” notab lrecl=4000;

data _null_;file nlpout2;

 d=date();t=time();

 put “U.S. Structural Change Model. &BaseOrScen intercepts” d date8. “ “ t 

timeampm10.;

 put “&crit”;

 run;

%macro WriteOut;

%Do p=1 %to 2;

%let sheet=%sysfunc(byte(&p+64));

filename Solution dde “excel|&sheet.!r16c6:r19c220”;

data qpout;set qpout(WHERE=((UPCASE(_TYPE_)=’PARMS’| UPCASE(_TYPE_)=’GRAD’|

 UPCASE(_TYPE_)=’UPPERBD’| UPCASE(_TYPE_)=’LOWERBD’) & _iter_~=0));

file solution lrecl=4000;

put &&actsall&sheet _type_ “09”x _rhs_;

run;

***************************************;

%if &BaseOrScen=Base %then filename Sol1 dde “excel|&sheet.!r3c6:r3c200”;;

%if &BaseOrScen=Scenario %then filename Sol1 dde “excel|&sheet.!r2c6:r2c200”;;

data _null_;set qpout(WHERE=(UPCASE(_TYPE_)=’PARMS’ & _iter_~=0));

file sol1 lrecl=4000;

put &&actsall&sheet _type_ “09”x _rhs_;

run;

%if &BaseOrScen=Base %then filename Grad1 dde “excel|&sheet.!r8c6:r8c200”;;
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%if &BaseOrScen=Scenario %then filename Grad1 dde “excel|&sheet.!r7c6:r7c200”;;

data _null_;set qpout(WHERE=(UPCASE(_TYPE_)=’GRAD’ & _iter_~=0));

file grad1 lrecl=4000;

put &&actsall&sheet _type_ “09”x _rhs_;

run;

***************************************;

%end;

%mend writeout;

%writeout;

DATA QPOUT1;LENGTH NAMES $14; SET QPOUT(WHERE=(UPCASE(_TYPE_)=’PARMS’));

 ARRAY ABC{*} _NUMERIC_;

 DO I = 1 TO DIM(ABC);

 CALL VNAME(ABC{I},NAMES);ESTIMATE=ABC{I};

 OUTPUT;

 END;

FORMAT ESTIMATE F13.4;

KEEP ESTIMATE NAMES;

call sound(3000,10);

RUN;

PROC PRINT;RUN;

**************;

data free;merge freeb freea;by f;

run;

proc iml;

use qpout(WHERE=( UPCASE(_TYPE_)=’PARMS’ ));

read all var{&acts} into parms;

use qpout(WHERE=(UPCASE(_TYPE_)=’GRAD’ & _iter_~=0));

read all var{&acts} into grads;

use free;

read all var{&acts} into free;

read all var{name} into name;*print name;

do x=1 to nrow(free);

do y=1 to ncol(free);

if free(|x,y|) then free(|x,y|)=1;

if ^free(|x,y|) then free(|x,y|)=0;

end;

end;

*print free;

Freegrads=free#grads;

cnames={&acts};

*print freegrads(|c=cnames|);* parms;

_rhs_=freegrads*t(parms); 
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print _rhs_(|r=name f=comma20.2|);

create freeOut var {_rhs_ name};

append var {_rhs_ name};

quit;run;

*proc print data=FreeOut;run;

%if &BaseOrScen=Base %then filename Frees dde “excel|INCOMES!r3c2:r6c3”;;

%if &BaseOrScen=Scenario %then filename Frees dde “excel|INCOMES!r3c4:r6c5”;;

data _null_;set FreeOut;

file Frees;Put name _rhs_ ;

run;

DATA _NULL_;

M=TIME()-&_H;

PUT “The combined SAS execution time is “ M TIME10.0;

RUN;

%mend ExcelSolve;

%macro loop;*Hotlinks with Excel spreadsheet;

option noquotelenmax nonotes;dm output ‘autopop off’ ;

filename cmds dde ‘excel|system’;

data _null_;

 file cmds;

put ‘[app.activate]’;

put ‘[app.maximize]’;

put ‘[window.maximize]’;

run;

%global flaga _H;

%do tt=1 %to 5; *This determines the number of solutions with each SAS run;

%let stop=;

filename start1 dde ‘excel|A!r17c1’;

data start;*This gives value of entry in cell A!r17c1;

 infile start1; input a $ @;call symputx(‘flaga’,a);stop;run;

%put flaga=&flaga;

filename start dde ‘excel|A!r17c1’ hotlink;

data start;*This indicates when to start the optimization;

 infile start;input b $ @;

 if upcase(b) eq “STOP” then do;call symputx(‘Stop’,’STOP’);call 

sound(2500,2);stop;end;

 if b ne “&flaga” then do;call sound(2500,2);stop;end;run;

%LET _H=%SYSFUNC(TIME());

%if &stop~=STOP%then%ExcelSolve;%else%let tt=100; 

data _null_;call sound(300,150);run;

%end;
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data _null_;file start1;put “STOPPED”;run; 

data _null; file Esystem;

 put ‘[ALERT(“SAS program stopped. Press F8 in SAS program window to resume 

Proc NLP.”, 2)]’;

 run;

option notes;

%mend loop;%loop;
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Appendix III model spreadsheets are 

accessible by contacting 

David Harrington, 202-694-5571, 

davidh@ers.usda.gov

Appendix III: Model Spreadsheets

Sheet A: Supply Side

Sheet B: Demand Side

Sheet INCOMES: Post-Optimal Calculations