united states direct comparison of general equilibrium and

/0^\ United States iiáJi "^^Partment of ^^SÍ4 Agriculture

Economic Research Service

Technical Bulletin Number 1799

Direct Comparison of General Equilibrium and Partial Equilibrium Models In Agriculture James V. Stout

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Direct Comparison of General Equilibriiim and Partial Equilibrixim Models in Agriculture. By James V. Stout III. Agriculture and Trade Analysis Division, Economic Research Service, U.S. Department of Agriculture. Technical Bulletin No. 1799.

Abstract

Partial equilibrium models detail agricultural markets and policies without considering inter-sectoral effects; general equilibrium models capture these effects but often lack specificity. The model described in this paper produces agricultural sector supply and demand response which is consistent with partial equilibrium elasticity estimates because it uses a generalized form of constant elasticity of substitution (CES) function called a "constant-difference elasticity" (CDE) function to represent producer and consumer behavior. It shows how changes in nonagricultural supply and demand occur after agricultural policy liberalization, and it allows welfare changes to be easily and unambiguously calculated in terms of either equivalent or compensating variation.

Keywords: Trade, computable general equilibrium model, constant- difference elasticity

Washington, DC 20005-4788 September 1991

111

Contents

Introduction 1

Deriving Elasticities for a SWOPSIM-Based CGE Model 3

Supply Elasticity Matrices 4

Demand Elasticity Matrices 4

Results: Comparison of the New Model to SWOPSIM 5

Conclusions 7

References 7

Appendix 1—The CDE Functional Form 9

Appendix 2—Development of the Two-Commodity SWOPSIM Model 12

Appendix 3—Aggregating Elasticities 19

Appendix 4—GAMS Input File 2 3

IV

Direct Comparison of General Equilibrium and Partial Equilibrium Models

in Agriculture James V. Stout

Introduction

Both partial equilibrium and general equilibrium models are used for the study of agricultural policy liberalization. Partial equilibrium models include detailed descriptions of agricultural markets and agricultural policies but are criticized for not considering inter-sectoral effects.^ General equilibrium models capture the inter-sectoral effects and offer better methods of calculating welfare changes, but they often lack the agricultural market detail of the partial equilibrium models. As a result of this dichotomy, the relationship between partial equilibrium and general equilibrium analyses of agricultural policy liberalization is not well understood. Discrepancies between the results of partial equilibrium and general equilibrium models often go unexplained.

The model of Horridge and Pearce (1988) represents one attempt to reconcile partial equilibrium and general equilibrium modeling techniques. This is a general equilibrium model based on the same agricultural sector information as in the partial-equilibrium Tyers and Anderson model. The model described below is, in the spirit of Horridge and Pearce, a general equilibrium model based on the same agricultural sector information as a partial equilibrium SWOPSIM model.^

Most CGE (computable general equilibrium) models use CES (constant elasticity of substitution) functions to describe production technology and consumer preferences. In models used for agricultural policy analysis, parameters in CES functions across inputs into production are designed to produce agricultural supply

^ Partial equilibrium models of agriculture include the model described in Tyers and Anderson (1986), USDA's SWOPSIM (Static World Policy Simulation model) (Roningen and Dixit, 1989), and the Organization for Economic Cooperation and Development (OECD) Ministerial Trade Mandate (MTM) model (OECD, 1987) .

^SWOPSIM (Static World Policy Simulation) models have been used in USDA analyses of agricultural policy liberalization since 1986.

response which can be justified based on partial equilibrium analysis of agricultural markets. The model described in this paper goes further in its efforts to model agricultural supply response that is consistent with partial equilibrium estimates. It uses a generalized form of the CES function called a "constant- difference elasticity" (CDE) function that allows the modeler, in an n-sector system, to choose n substitution parameters to represent producers' behavior toward production (output) decisions or consumers' behavior toward consumption decisions. The fact that the general equilibrium model is calibrated to the same set of own-price elasticities as the SWOPSIM model makes comparison of the results of the two models a test of the importance of general equilibrium considerations in the analysis of agricultural policy liberalization.^ The general applicability of the CDE approach was first pointed out by Hanoch (1975, 1978). Hertel and others (1990) describe preliminary work on a large CDE-based general equilibrium model which will also be based on data from SWOPSIM.

A complete explanation of the CDE functional form and its use in this model is presented in appendix 1. The GAMS (General Algebraic Modeling System) input file for this model is presented in appendix 4.

The CDE-CGE model described in this report can potentially be extended in several ways:

(1) Armington specifications could be introduced, especially in the nonagricultural sector. In the current model all three sectors are assumed to be trading homogeneous goods at perfectly competitive prices.

(2) Liberalization experiments could be performed that keep domestic price levels unchanged but allow trade balances to change (the current model uses the more standard assumption that prices adjust to maintain fixed external (trade) balances).

(3) Savings, investment, government spending, and government tax revenues could be made endogenous. In the current model these are not explicitly modeled. Only a region's net savings (dissavings) is modeled and this, as described in (2) above, is treated as an exogenous variable.

(4) Policies that distort nonagricultural sector prices or exchange rates could be introduced.

The objective of the prototype model described in this report is to provide a straightforward comparison of partial equilibrium and

^The general equilibrium model also has obvious advantages in the estimation of welfare changes.

general equilibrium results by translating a partial equilibrium SWOPSIM model into a general equilibrium framework in the simplest manner possible.

Deriving Elasticities for a SWOPSIH-Based C6E Model

The model developed for this paper is based on the 1986, 22- commodity, 11-region SWOPSIM model. It was first aggregated to a model consisting of four regions (United States, other developed- market economies (ODME)\ centrally planned economies (CP)^, and the rest-of-the-world (ROW)) and two agricultural commodities (livestock and dairy, and crops).^ Then, one aggregate nonagricultural commodity representing the rest of the economy was added to the model. As in most SWOPSIM models, U.S. and ODME exports are fully competitive in both domestic and export markets, but CP and ROW domestic prices are somewhat insulated from world price effects by the introduction of "price-transmission elasticities" that are less than perfect.^ All prices are denominated in a common currency, the U.S. dollar.

The primary focus of SWOPSIM models is analysis of the costs and benefits of agricultural trade liberalization. The objective of this study is to gain a better understanding of the costs and benefits of adjustments that must be made in other sectors when agricultural trade policies are eliminated. In the model used for this analysis, all nonagricultural production and consumption is described by one aggregate nonagricultural sector. Production decisions move an economy between points on its production possibilities frontier based on relative prices of products. Input types, quantities, and prices are not modeled, but are implicitly assumed to be fully employed.

^The EC-10 plus Australia, Austria, Canada, Finland, Iceland, Japan, Malta, New Zealand, Norway, Portugal, South Africa, Spain, Sweden, and Switzerland.

^Albania, Bulgaria, China, Czechoslovakia, East Germany, Poland, Hungary, Romania, Soviet Union, and Yugoslavia.

2. ^The commodity aggregation procedure is described in appendix

^A "price-transmission elasticity" is any factor that prevents the incentive price for consumers and producers in a particular region from fully reflecting world price changes. In this model, a coefficient of 0.5 for the ROW and 0.2 for the CP region multiplies any change in the world price level before it is translated into a change in the "trade price" level that will be experienced by agents in those regions.

Supply Elasticity Matrices

The U.S. supply matrix for the two-sector SWOPSIM model used in this study is shown below:

Livestock and dairy Crops Livestock and dairy 0.630 0.000 Crops 0.000 0.310

CDE substitution parameters were chosen (see appendix 1) to (a)reproduce the SWOPSIM own-price elasticities exactly, and (b)come as close as possible to the cross-price elasticities in SWOPSIM. The CDE parameters that were chosen produce the following elasticity matrix across all three sectors in the complete general equilibrium case:

Livestock and dairy Crops Nonaariculture Livestock and dairy 0.630 -0.002 -0.628 Crops -0.004 0.310 -0.306 Nonagriculture -0.005 -0.002 0.007

Substitution parameters chosen for all other regions were based on the supply matrices from SWOPSIM. Supply elasticity matrices for ODME, CP, and ROW regions are presented in appendix table 8 (app. 3).

Demand Elasticity Matrices

The U.S. demand elasticity matrix for the two-sector SWOPSIM model and the general equilibrium three-sector version of the same demand elasticity matrix are shown below:®

Livestock and dairy Crops Livestock and dairy -0.540 0.000 Crops 0.000 -0.210

Livestock and dairy Crops Nonaariculture Livesto^ck and dairy -0.540 -0.003 -0.051 Crops -0.004 -0.210 -0.017 Nonagriculture -0.012 -0.004 -0.999

The CDE-calibrated three-sector system again comes very close to reproducing the elasticity matrix elements from the two-sector SWOPSIM model.

®A set of income elasticities (see appendix 2) must also be known to calibrate a CDE-consistent set of demand elasticities. These were obtained after some adjustment from Seeley and others (1989) .

Results: Comparison of the New Model to SWOPSIM

Table 1 presents results from the analysis of multilateral agricultural policy liberalization by the United States and the other developed-market economies using both SWOPSIM and the new general equilibrium model. The liberalization experiment consists of complete removal of production and consumption price wedges (as measured by producer subsidy equivalents (FSE's) and consumer subsidy equivalents (CSE's)) in both the United States and the other developed-market economies. Set-aside programs cannot be considered in the liberalization since inputs are not modeled.

Column 1 results are from a two-sector model created by aggregating the 22-region SWOPSIM model but making no other changes.

The partial equilibrium column 2 results are from a model that removes the SWOPSIM terms describing the price responsiveness of livestock supply to feed prices (in the general equilibrium model that is being developed, input prices will not be a consideration in production decisions). Comparison of column 1 and column 2 results shows that the effects of this change to the model are not very large; agricultural price and quantity changes as seen in column 1 and column 2 results differ by less than 2 percent.

The partial equilibrium column 3 results use the slightly dif- ferent cross-price supply and demand elasticities that were described above as necessary to fit the CDE specifications. The similarity of the results in columns 2 and 3 demonstrates that the introduction of CDE-consistent elasticities does not significantly change the performance of the model.

Finally, the results in column 4 are from the complete, general equilibrium solution to the CGE model. The general equilibrium solution uses CDE specifications of production and consumption behavior and equilibrates all three sectors of the model. A general equilibrium model adds some important information about the performance of the nonagricultural sector of the economy to the analysis. Comparison of the results of column 1 and column 4 shows how production in the United States switches from nonagriculture to agriculture as a result of multilateral agricultural policy liberalization. Welfare benefits can be easily and unambiguously calculated in the general equilibrium model in terms of either equivalent or compensating variation.

In each of the other three regions of the model, the general equilibrium solution comes close to reproducing the agricultural sector results of SWOPSIM. Nonagricultural supply changes in the ODME, CP, and ROW regions are 0.50 percent, -0.44 percent, and -0.37 percent, respectively.

As explained above, the general equilibrium model lacks two elements that are included in SWOPSIM: it does not consider set- aside acreage under the U.S. crops programs, and it does not include the effect on livestock and dairy supply of the price of

Table 1--Effects of agricultural policy liberalization by the United States and other developed-market economies

Item

Partial Partial Partial equilibrium equilibrium equilibrium

solution using solution using solution using SWOPSIM SWOPSIM CDE-consistent

elasticities elasticities elasticities General Initial and the and new and new equilibrium values SWOPSIM model model structure model structure solution

Dollars/unit

2,091.0 2,784.4 2,770.3 2,769.2 2,728.3 115.0 161.5 159.9 160.1 158.7

1,000.0 NA NA

1.000 units

NA 980.2

36,981 39,724 39,597 39,607 39,729 398,260 372,232 371,041 371,045 372,272

4,109,863 NA NA

1.000 units

NA 4,108,262

37,888 35,605 35,663 35,669 35,556 116,581 116,827 116,904 116,836 116,605

4,237,609 NA NA NA 4,252,771

c\

World price: Livestock and dairy Crops Nonagriculture

U.S. supply quantity: Livestock and dairy Crops Nonagriculture

U.S. demand quantity :^ Livestock and dairy Crops Nonagr i culture

U.S. equivalent variation $8.05 billion

NA = not applicable

■^Final demand; not including use as an intermediate input. Note: All model results neglect the effect of U.S. (and other nations') set-asides.

the input "crops." Future development of this model will address both of these important issues. The current model simply represents a straightforward mapping of supply elasticities from SWOPSIM into production relationships among the three sectors that keeps the economy at what is assumed to be full employment and on the surface of a production possibilities frontier.

Comparison of the results of column 1 and column 2 provides a way of estimating the importance of the general equilibrium model's failure to consider "crops" input prices. As for set-asides, comparison of SWOPSIM results with and without set-aside "supply shifters" shows that set-aside removal reduces the world price of crops by $7.90/unit (4.9 percent), increases U.S. crops production by 26.9 million units (6.7 percent), and increases the value of U.S. agricultural production by $1.2 billion. The CGE model described in McDonald (1990) has been used to estimate that the additional U.S. welfare benefits of removing the set-asides amount to about $1 billion.

Conclusions

The model described in this paper is designed to provide a link between partial equilibrium and general equilibrium model results. The general equilibrium model uses much of the same agricultural sector supply, demand, price, and quantity information as in the partial equilibrium SWOPSIM model and produces practically the same agricultural sector results as SWOPSIM. Comparison of the partial equilibrium and general equilibrium results shows how production in each region switches out of or into nonagriculture as a result of agricultural policy liberalization. An important advantage of the general equilibrium approach is that it allows economywide welfare benefits to be easily and unambiguously calculated in terms of either equivalent or compensating variation. In the multilateral liberalization simulated here, the U.S. equivalent variation is $8.05 billion and the compensating variation is $7.91 billion. Because this model fails to consider set-asides, it underestimates the potential U.S. welfare benefits of full agricultural policy liberalization by perhaps as much as $1.2 billion.

References

Hanoch, G. "Production and Demand Models with Direct or Indirect Implicit Additivity," Econometrica, 43(1975): 395-419.

Hanoch, G. "Polar Functions with Constant Two Factors-One Price Elasticities," Chapter II.3 in Fuss and McFadden (eds.). Production Economics; A Dual Approach to Theory and Applications. Amsterdam: North Holland Press, 1978.

Hertel, T.W., E.B. Peterson, P.V. Preckel, Y. Surry, and M.E. Tsigas. Notes on the Constant Difference Elasticity fCDE) Functional Form and Its Implementation in Applied General Equilibrium Models. Staff Paper #90-10, Dept. Agr. Econ., Purdue Univ., 1990.

Horridge, M., and D. Pearce. Modelling the Effects on Australia of Interventions in World Agricultural Trade. IMPACT Preliminary Working Paper No. OP-65, Univ. of Melbourne, 1988.

McDonald, Bradley J. "Agricultural Negotiations in the Uruguay Round," The World Economy. Vol. 13, No. 3, Sept. 1990.

Organization for Economic Cooperation and Development (OECD). National Policies and Agricultural Trade. Paris, 1987.

Roningen, V.O., and P.M. Dixit. Economic Implications of Agricultural Policy Reform in Industrial Market Economies. Staff Report AGES 89-36. U.S. Dept. Agr., Econ. Res. Serv., Aug. 1989.

Seeley, R., S. Magiera, V.O. Roningen, and J. Sullivan. "Projection Parameters: Income Elasticities and Growth Rates." Unpublished paper, U.S. Dept. Agr., Econ. Res. Serv., 1989.

Tyers, R., and K. Anderson. "Distortions in World Food Markets: A Quantitative Assessment," background paper for the World Development Report, Washington, DC: The World Bank, 1986.

Appendix 1—The CDS Functional Form

The constant-difference elasticity (CDE) functional form (Hanoch, 1975, 1978) specifies the expenditure (or revenue) function, normalized by minimum cost in consumption or maximum revenue in production, as:

G(z,,t7)=¿S,C7^^^^z^ = 1; (1) 1=1

where: I = number of goods

b. = "substitution parameter" for good i

ei = "expansion parameter" for good i (all e^ are equal to one in the case of constant returns to scale in production)

Bi = "shift parameter" for good i

U = utility for consumption; the level of input use for production

Zi = Pi/E

E = minimum expenditure to obtain utility U in consumptions- maximum revenue from production using input level U

Pi = price of good i

with Bi>0, ei>0 for all i, and all bi<l in consumption^, but all bi>l in production.

The constant returns to scale CES, a special case of the CDE which is commonly used in CGE analysis, is obtained if ei = e = 1 and bi = b (Hertel and others, 1990). Equation 1 becomes:

j

G{Z^,U)=Y^B^U''Z^^1 (2) i=l

=Y,B¿U^{p^/E)^=l (3) i=l

^In consumption, all bi must be either between 0 and 1 or less than 0.

Solving for E yields the general form of the CES expenditure or revenue function:

£; = t/[¿o^(p^)^]^/^ (4) 2=1

The CDE-relative compensated supply or demand functions are derived from equation 1 by applying Shepherd's lemma and the implicit function theorem:

for all i, with i f 1,

where Xi = the level of supply in production or demand in consumption

Thus, n independent equations define the CDE system in an n-sector system.

Own-price demand (and supply) elasticities can be shown (Hanoch, 1975) to be:

N

Y^ Sjê^(l-jb^)

e,,= s,[ (1-b,) - -^l.^ - Azl_ ]-{l-h,) (6)

/ V ^k^k Z^ ^k^k k=l Jc=l

where s, are initial shares,

Income elasticities are

ni = E (î.^).)"' [eA-Êsj,ej,(l-¿j,) ] ^ ii-b,) -J2s„{l-b^) (7) k=l k=l k=l

In the CGE model created for this study, each region contains three sectors: livestock and dairy, crops, and nonagriculture. Again following Hertel and others (1990), the nine CDE parameters (b^, e^,

10

and Bi, i=l,2,3) for the demand side of each region in this model were chosen to fit nine equations: three that define the CDE class of functions, three that describe the own-price elasticities of demand at the calibration point (two of these price elasticities were taken from SWOPSIM and the other was chosen by the modeler) ^°, and three that describe the income elasticities at the calibration point. Similarly, the six CDE parameters for the supply side of each region in this model (all ei=l assuming constant returns to scale) were chosen to fit the three CDE-defining equations and to yield the own-price elasticities of supply (from SWOPSIM) at the calibration point.

In production, the CDE specifications simply map out a production possibilities frontier for each region. In consumption, each region's CDE specifications define a system of community indifference curves from which a consumption point is chosen.

^°The modeler must specify nonagricultural sector own-price elasticities of supply and demand that complete the model without violating the CDE parameter restrictions described on page 9. Since the nonagricultural sector in this model is so large, the feasible range of choices for the nonagricultural elasticities was very small. Within this feasible range, nonagricultural own-price elasticities^ of supply and demand were chosen which, upon calibration of the complete (nine equation) demand or (six equation) supply system, produced cross-price elasticities which came close to SWOPSIM cross-price elasticities.

11

Appendix 2—Development of the Two-Commodity SWOPSIM Model

The SWOPSIM coitimodities beef and veal, pork, mutton and lamb, poultry- meat, poultry-eggs, dairy-milk, dairy-butter, dairy-cheese, and dairy- milk powder were aggregated into the commodity "livestock and dairy." Wheat, corn, coarse grains, soybeans, soymeal, soyoil, other oilseeds, other meals, other oils, cotton, sugar, and tobacco were aggregated into the commodity "crops." Aggregation of the commodities in each region followed the procedures described below.

Step 1:

For each commodity group, the aggregate value of the following were calculated:

The trade balance at world prices

The value of production at producer prices

The value of domestic producer support wedges (DPSW) (production quantities multiplied by wedges)

The value of consumption at consumer prices

The value of consumer price support wedges (CSW) (consumption quantities multiplied by wedges)

The value of "marketing margins" (consumption quantities multiplied by wedges)

The value of import support wedges (MSW) (the average of consumption and production quantities multiplied by wedges^^)

The value of export support wedges (ESW) (the average of consumption and production quantities multiplied by wedges)

^^Import and export support wedges were evaluated using the average of the quantity produced and the quantity consumed of each commodity, because, in the SWOPSIM framework, export and import support wedges affect both producer and consumer prices.

12

step 2:

Next, price relationships from SWOPSIM were applied. In SWOPSIM, the relationships among prices are as follows:

Producer price = TP + DPSW - MSW + ESW (8)

Consumer price = TP - CSW - MSW + ESW + "marketing margin" (9)

Where TP = trade price

DPSW = domestic producer support wedge

CSW = consumer support wedge

MSW = import support wedge

ESW = export support wedge

"marketing margin" = remaining cost differences attributed to marketing costs by SWOPSIM

Now, letting QS = aggregate production quantity QD = aggregate consumption quantity.

and

Trade balance = (QS - QD) * world price, (10)

the objective of the aggregation procedure was to choose a set of aggregate prices and quantities that would

(a) keep the relationships among prices in equations 8 and 9 unchanged, and

(b) keep the aggregate values of trade balance, production, domestic producer price support wedges, consumption, etc. (from step 1), unchanged.

Defining production value/QS as the aggregate producer price, DPSW value/QS as the aggregate DPSW, etc., and rewriting equations 8 and 9 in terms of aggregate prices (and substituting) yielded equations 11 and 12 below:

Production value/QS = trade price + DPSW value/QS - MSW value/((QS+QD)/2) + ESW value/((QS+QD)/2) (11)

Consumption value/QD = trade price - CSW value/QD - MSW value/((QS+QD)/2) + ESW value/((QS+QD)/2) + marketing margin value/((QS+QD)/2) (12)

13

The world price (index) for each aggregate commodity was chosen to equal the price of a representative good in each aggregate: specifically, beef = $2,091/metric ton for "livestock and dairy" and wheat = $115/metric ton for "crops." Equations 10, 11, and 12 were then solved simultaneously for trade price, QS, and QD.

The results of each aggregation are presented in appendix tables 1-4 together with the raw, disaggregated data from which they were created.

14

Appendix table 1--U.S. commodity aggregation results

Producer Consumer Trade Final Marketing Commodity price price price 'Supply demand DPSW csw MSW ESW margin

—Dollars/metric ton— —Metric tons— —Doll, ars/metric ton

Beef, veal 2,049 3,414 1,833 11,292 12,031 171 0 -44 0 1,536 Pork 1,612 2,988 1,494 6,379 6,849 117 0 0 0 1,494 Mutton, lamb 3,336 5,803 2,889 153 171 435 0 -12 0 2,902 Poultry meat 1,131 1,907 952 8,263 7,987 82 0 0 97 858 Poultry eggs 1,160 1,668 1,073 4,058 3,994 68 0 0 19 576 Dairy - milk 246 514 222 65,354 27,449 24 0 0 0 292 Dairy - butter 2,549 3,187 1,024 545 522 0 0 0 1,525 637 Dairy - cheese 2,358 3,188 1,372 2,363 2,470 986 -966 0 0 851 Dairy - powder 1,659 2,014 992 582 282 0 0 0 667 355

Livestock and dairy aggregate 1.720 2.868 1.447 36.981 37.888 206 -63 -14 53 1,291

Wheat 168 122 68 56,925 23,535 82 0 0 17 37 Corn 101 66 53 209,632 33,939 42 0 0 6 7 Other coarse grain 102 78 53 43,316 4,841 32 0 0 17 8 Rice 348 244 113 4,280 1,644 226 0 0 9 122 Soybeans 189 180 171 52,801 1,655 18 0 0 0 9 Soymeal 184 230 184 25,163 0 0 0 0 0 46 Soyoil 342 684 342 5,803 5,304 0 0 0 0 342 Other oilseeds 298 266 240 6,634 1,817 58 0 0 0 27 Other meals 166 207 166 1,611 0 0 0 0 0 41 Other oils 569 1 ,138 569 697 1,456 0 0 0 0 569 Cotton 2,040 2 ,304 1,150 2,119 664 889 0 0 2 1,152 Sugar 324 885 67 5,461 7,158 257 -415 0 0 404 Tobacco 3,946 7 ,212 3,606 475 465 340 0 0 0 3,606

Crops aggregate 145 199 83 398,260 116,581 52 -25 10 81

Note: Supply total value in livestock and dairy was adjusted to eliminate double—counting of dairy milk and its processed products; supply total value in crops was adjusted to eliminate double-counting of beans (soybeans and other oilseeds) and their products—meal and oil.

15

Appendix table 2--Other developed-market economies commodity aggregation results

Producer Consumer Trade Final Marketing Commodity price price price Supply demand DPSW csw MSW ESW margin

r^/-k1 T o-»"o /m£i+->•-1 i-» ^r\f\ —Metr:

12,199

ic tons—

10,506

—Doll,

-466

o ■*-<-• /m i-^-t--^-? #-» +-^

Beef, veal 3,504 6,095 2,091 560 -7 846 2,684 Pork 4,492 8,821 2,341 15,452 15,319 130 -98 -401 1,619 4,361 Mutton, lamb 2,765 4,708 2,030 2,093 1,717 415 -7 -320 0 2,350 Poultry meat 1,977 3,514 1,083 8,043 8,008 57 -24 -19 818 1,571 Poultry eggs 2,426 3,929 2,145 7,815 7,939 69 0 -140 73 1,572 Dairy - milk 319 635 275 166,149 99,689 43 0 0 0 360 Dairy - butter 5,141 5,998 2,048 3,020 2.527 775 -461 0 2,318 1,172 Dairy - cheese 5,475 7,146 2,744 5,068 4,699 646 -207 -3 2,082 2,110 Dairy - powder 5,718 6,886 1,984 3,180 2,568 508 -321 0 3,227 1,354

Livestock and dairy aggregate 4,073 6.895 2,385 61,115 57.470 412 -166 -137 1.139 3,068

Wheat 147 188 115 124,864 77,335 32 -23 0 0 49 Corn 106 112 87 33,305 41,659 9 -4 -10 0 11 Other coarse grain 131 132 82 93,811 62,967 20 -8 -2 27 12 Rice 1 ,914 1,771 210 12,268 12,450 1 ,702 -1,347 -2 0 212 Soybeans 486 219 208 2,243 2,761 278 0 0 0 11 Soymeal 184 230 184 14,989 4,796 0 0 0 0 46 Soyoil 342 684 342 3,320 2,417 0 0 0 0 342 Other oilseei ds 533 360 324 13,630 643 209 0 0 0 36 Other meals 166 207 166 7,145 3,516 0 0 0 0 41 Other oils 614 1,109 569 5,909 7,399 45 29 0 0 569 Cotton 2 ,113 2,112 1,056 497 2,364 1 ,057 0 0 0 1,056 Sugar 219 541 133 19,862 17,795 23 -91 -3 60 254 Tobacco 4 .975 7,210 3,606 527 929 1, ,370 0 0 -1 3,605

Crops aggregate 195 233 98 382,219 357,140 85 -58 -2 10 65

Note: Supply total value in livestock and dairy was adjusted to eliminate double-counting of dairy milk and its processed products; supply total value in crops was adjusted to eliminate double-counting of beans (soybeans and other oilseeds) and their products—meal and oil.

16

Appendix table 3--Centrally planned economies commodity aggregation results

Producer Consximer Trade Final Marketing Coimnodity price price price Supply demand DPSW csw MSW ESW margin

—Dollars/metric ton— —Metric tons— —Dollars/metric ton

Beef, veal 3,791 3,305 2,091 10,797 10,858 1,700 497 0 0 1,711 Pork 2,259 4,376 2,341 30,661 30,110 -82 306 0 0 2,341 Mutton, lamb 2,468 3,408 2,030 1,803 1,751 438 652 0 0 2,030 Poultry meat 1,164 1,891 1,083 6,566 6,405 81 78 0 0 886 Poultry eggs 2,263 3,575 2,145 7,085 7,024 118 0 0 0 1,430 Dairy - milk 251 453 275 149,249 89,549 -24 0 0 0 178 Dairy - butter 4,530 1,499 2,048 2,454 2,598 2,482 1,061 0 0 512 Dairy - cheese 3,022 3,186 2,744 1,549 1,504 278 734 0 0 1,176 Dairy - powder 1,984 2,480 1,984 2,217 2,095 0 0 0 0 496

Livestock and dairy aggregate 2,367 3.533 2.091 75.860 75,074 276 268 0 0 1.710

Wheat 99 127 115 221,925 192,698 -16 37 0 0 49 Corn 87 97 87 120,300 33,686 0 0 0 0 10 Other coarse grain 93 74 82 145,840 53,344 11 17 0 0 9 Rice 210 415 210 121,714 121,499 0 5 0 0 210 Soybeans 210 207 208 13,163 5,223 2 12 0 0 11 Soymeal 184 230 184 3,919 104 0 0 0 0 46 Soyoil 342 684 342 697 1,658 0 0 0 0 342 Other oilseeds 338 360 324 3,4847 5,814 -14 0 0 0 36 Other meals 166 207 166 13,114 336 0 0 0 0 41 Other oils 569 1 ,138 569 7,597 7,885 0 0 0 0 569 Cotton 1,065 1 ,640 1,056 6,193 5,759 9 472 0 0 1,056 Sugar 228 291 133 19,677 25,650 95 -25 0 0 133 Tobacco 3,606 7 ,212 3,606 2,247 2,350 0 0 0 0 3,606

Crops aggregate 116 184 115 880,913 704,746 15 84


17

Appendix table 4--Rest of the world commodity aggregation results

Producer Consumer Trade Final Marketing Commodity price price price Supply demand DPSW CSW MSW ESW margin

—Dollars/metric ton— —Metric tons— —Dollars/metric ton

Beef, veal 2,138 3,940 2,091 9,890 10,783 71 -181 0 -24 1,691 Pork 2,314 4,773 2,341 4,254 4,468 -27 -60 0 0 2,372 Mutton, lamb 1,919 3,964 2,030 1,535 1,945 -111 96 0 0 2,030 Poultry meat 1,157 2,052 1,083 7,043 7,515 74 -81 0 1 887 Poultry eggs 2,148 3,591 2,145 5,241 5,242 3 -16 0 0 1,430 Dairy - milk 257 526 275 81,494 48,896 -18 0 0 0 251 Dairy - butter 2,343 2,928 2,048 1,035 1,407 294 -294 -1 0 586 Dairy - cheese 2,746 3,923 2,744 1,319 1,626 2 -2 0 0 1,177 Dairy - powder 2,017 2,521 1,984 367 1,401 33 -33 0 0 504

Livestock and dairy aggregate 2,080 3,809 2,092 34,678 38,202 -5 -84 -7 1,640

Wheat 101 145 115 125,155 168,121 -14 19 0 0 49 Corn 117 93 87 111,899 103,316 29 5 -1 0 10 Other coarse grain 87 92 82 77,132 67,987 5 0 0 0 9 Rice 241 469 210 177,434 180,103 31 -48 0 0 210 Soybeans 222 212 208 30,089 4,184 45 -25 -2 -33 9 Soymeal 184 230 184 21,596 2,549 0 0 0 0 46 Soyoil 356 713 342 4,858 5,299 0 0 -14 0 356 Other oilseeds 329 364 324 38,692 1,705 7 -6 3 0 36 Other meals 164 205 166 15,447 3,307 0 0 0 -2 41 Other oils 576 1 ,153 569 19,042 16,505 9 -11 -17 -20 576 Cotton 1,043 2 ,036 1,056 6,560 6,582 -10 53 0 -3 1,036 Sugar 165 318 133 53,802 48,199 29 -45 0 4 137 Tobacco 3,620 7 ,212 3,606 2,094 1,599 14 0 0 0 3,606

Crops aggregate 124 206 114 967,103 923,298 11 85


18

Appendix 3—Aggregating Elasticities

Deinand elasticities in SWOPSIM are in many cases themselves entered as aggregates—aggregates of food and feed demand elasticities or aggregates of food demand elasticities and elasticities of demand for some other type of input use such as the use of milk to produce cheese, butter, and milk powder. The general equilibrium approach taken here required that such final and intermediate demand elasticities be disaggregated and handled separately. SWOPSIM spreadsheets contain the information necessary to do this. Goods such as dairy milk and feed grains which have both final and intermediate uses have elasticities expressed as weighted averages of the elasticities for the various components of total demand. Demand elasticities for the aggregate goods "livestock and dairy" and "crops" were then calculated as value-weighted averages.

Income elasticities for the disaggregate set of SWOPSIM commodities and regions (22 commodities and 3 6 regions) from Seeley and others (1989) provided a starting point for the calculation of income elasticities for the four-region, two- commodity model. In some cases, however, the income elasticities from Seeley and others were inconsistent with the demand elasticities from SWOPSIM. For the United States, for example, the (uncompensated) demand elasticities from SWOPSIM and the income elasticities from Seeley and others are shown below:

Livestock and Nonagri- Income

dairy Crops culture elasticities Livestock and dairy -.54 .00 ??? .46 Crops .00 -.21 ??? .05 Nonagriculture ??? ??? ??? by Engel aggregation

The matrix elements marked with question marks were to be filled in during the process of creating the general equilibrium model for this study. The objective was to complete the demand elasticity matrix in a theoretically consistent manner without changing the livestock-dairy and crops own-price elasticities.

The own-price elasticities of demand from SWOPSIM were significantly larger in (absolute) size than the income elasticities from Seeley and others, though, which made the development of a consistent system unachievable. To understand why, consider that all three sectors have inelastic own-price demand, which means that an increase in the price of any good results in an increase in spending on that good. Other goods, taken as a group, therefore tend to behave as complements to the first, that is, to have negative cross-price elasticities of demand. If cross-price terms are (mostly) negative, the homogeneity conditions,

N

E^ij ^ili = 0 for all i (13)

19

where e^^ are uncompensated elasticities of demand and rj^ are income elasticities, cannot be met unless the income elasticity is very close to or greater than the (absolute value of) the own- price demand elasticity in each sector.

To keep the SWOPSIM elasticity data unchanged, it was therefore necessary to make arbitrary changes in income elasticity values. The U.S. livestock-dairy and crops income elasticities were increased to 1.1 times the (absolute value of the) own-price demand elasticity from SWOPSIM. In the data for the other developed-market economies, a similar inconsistency between the SWOPSIM own-price elasticity for crops (-.32) and the income elasticity from Seeley and others (.06) existed, and it too was eliminated by arbitrarily increasing the income elasticity to 1.1 times the SWOPSIM own-price elasticity. No other sectors or regions of the model had income elasticities that required adjustment. Sensitivity analysis was performed to test the importance of the income elasticities chosen. Substantial increases in the arbitrarily assigned income elasticities for the United States and the other developed-market economies (up to 1.5 times the SWOPSIM own-price elasticity) had very little impact on liberalization results of the general equilibrium model.

The tables below provide comparison of complete demand and supply elasticities for the original, two-sector SWOPSIM model, and for the three-sector general equilibrium model created for this study.

20

Appendix table 5—SWOPSIM model demand elasticities

Region and Livestock commodity and dairy Crops

United States: Livestock and dairy -0.5400 0.0000 Crops 0.0000 -0.2100

Other developed-market economies: Livestock and dairy -0.4300 0.0000 Crops 0.0000 -0.3200

Centrally planned economies: Livestock and dairy -0.2800 0.0000 Crops 0.0000 -0.1600

Rest of the world: Livestock and dairy -0.3800 -0.0500 Crops -0.0300 -0.3800

Appendix table 6—General equilibrium model demand and income elasticities

Region and Livestock Nonagri- Income commodity and dairy Crops culture elasticities

United States: Livestock and dairy -0.5400 -0.0027 -0.0513 0.59 Crops -0.0037 -0.2100 -0.0173 0.23 Nonagriculture -0.0118 -0.0043 -0.9986 1.015

Other developed-market economies: Livestock and dairy -0.4300 -0.0064 -0.1936 0.63 Crops -0.0101 -0.3200 -0.0219 0.35 Nonagriculture -0.0456 -0.0109 -0.9841 1.041

Centrally planned economies: Livestock and dairy -0.2800 -0.0901 -0.3399 0.71 Crops -0.0765 -0.1600 -0.0535 0.29 Nonagriculture -0.2834 -0.1331 -0.8480 1.265

Rest of the world: Livestock and dairy -0.3800 -0.0005 -0.2495 0.63 Crops 0.0032 -0.3800 -0.1832 0.56 Nonagriculture -0.0357 -0.0464 -0.9720 1.054

21

Appendix table 7—SWOPSIM model supply elasticities

Region and Livestock commodity and dairy Crops

United States: Livestock and dairy 0.6300 0.0000 Crops 0.0000 0.3100

Other developed-market economies: Livestock and dairy 0.6000 0.0000 Crops 0.0000 0.3500

Centrally planned economies: Livestock and dairy 0.3500 0.0000 Crops 0.0000 0.1400

Rest of the world: Livestock and dairy 0.4900 0.0000 Crops 0.0000 0.2900

Appendix table 8—General equilibrium model supply elasticities

Region and Livestock Nonagri- commodity and dairy Crops culture

United States: Livestock and dairy 0.6300 -0.0022 -0.6278 Crops -0.0039 0.3100 -0.3061 Nonagriculture -0.0054 -0.0015 0.0068

Other developed-market economies: Livestock and dairy 0.6000 -0.0016 -0.5984 Crops -0.0153 0.3500 -0.3347 Nonagriculture -0.0223 -0.0013 0.0236

Centrally planned economies: Livestock and dairy 0.3500 -0.0048 -0.3452 Crops -0.0077 0.1400 -0.1323 Nonagriculture -0.0567 -0.0135 0.0702

Rest of the world: Livestock and dairy 0.4900 -0.0090 -0.4810 Crops -0.0064 0.2900 -0.2836 Nonagriculture -0.0114 -0.0093 0.0207

22

Appendix 4—GAMS Input File

This appendix reproduces the GAMS input file for the constant-difference elasticity (CDE) computable general equilibrium model created for this study:

$OFFUPPER OPTIONS LIMROW =50; OPTIONS DECIMALS = 7;

SETS

N regions / US ODME CP

ROW

I sectors / A B C

United States Other developed-market economies Centrally planned economies Rest of the world /

Livestock and Dairy Crops Non-agriculture /

M(N) /ODME, CP, ROW/ T(I) /A,B/ ALIAS (I,J);

PARAMETERS

WP(I) world prices /A 2.091 B .115 C 1.000/;

A 1.447 2.385 2.091 2.092

B 083 098 115 114

TABLE TP(N,I) "trade prices"

US ODME

CP ROW

PARAMETERS FF(N,I);

FF(N,I) = TP(N,I)/WP(I);

TABLE RSW(N,I) supply wedges to be removed

TABLE PSW(N,I)

C 1.000 1.000 1.000 1.000;

A B C US .206 .052 0

ODME .412 .085 0 CP 0 0 0

ROW 0 0 0;

permanent supply wedges A B C

US 0 0 0 ODME 0 0 0

CP .276 .001 0 ROW -.005 .011 0;

23

TABLE RCW(N,I) consumption wedges to be removed

TABLE RTW(N,I)

TABLE PTW(N,I)

A B c US -.063 -.025 0

ODME -.166 -.058 0 CP 0 0 0

ROW 0 0 0;

permanent consumption wedges A B c

US 0 0 0 ODME 0 0 0

CP .268 .015 0 ROW -.084 - .008 0;

trade wedges to be removed A B C

US .067 .010 0 ODME 1.276 .012 0

CP 0 0 0 ROW 0 0 0;

permanent trade wedgei 5 A B c

US 0 0 0 ODME 0 0 0

CP 0 0 0 ROW -.007 - .001 Oi r

original consumption prices A B c

US 2.868 .199 1. .000 ODME 6.895 .233 1. .000

CP 3.533 .184 1. .000 ROW 3.809 .206 1. .000;

PARAMETERS ASUPP(N,I), SUPP(N,I), DEMP(N,I), AFCPDW(N,I), FCPDW(N,I);

ASUPP(N,I) = TP(N,I)+RTW(N,I)+PTW(N,I)+RSW(N,I)+PSW(N,I);

SUPP(N,I) = ASUPP(lf,I)/FF(N,I) ;

DEMP(N,I) = ADEMP(N,I)/FF(N,I);

AFCPDW(N,I) = ADEMP(N,I)-TP(N,I)-RTW(N,I)-PTW(N,I) +RCW(N,I)+PCW(N,I);

FCPDW(N,I) = AFCPDW(N,I)/FF(N,I);

24

TABLE QS(N,I) supply quantities A B

US .036981 .398260 4.109863 ODME .061115 .382219 5.108137

CP .075860 .880913 .696918 ROW .034678 .967103 2.588855;

TABLE VARATIO(N,I) value added ratios

A B C US .5521 .3430 1.0

ODME .7651 .2638 1.0 CP .6379 .6940 1.0

ROW .8479 .7108 1.0;

PARAMETERS QSVA(N,I) supply quantities adjusted to represent value added only;

QSVA(N,I) = QS(N,I) * VARATIO(N,I);

TABLE QC(N,I) demand quantities A B C

US .037888 .116581 4.237609 ODME .057470 .357140 4.939694

CP .075074 .704746 .638739 ROW .038202 .923298 2.540666;

PARAMETERS PRTR(N) price transmission elasticities;

PRTR ("US") = 1.0; PRTR("ODME") = 1.0; PRTR ("CP") = 0.2; PRTR ("ROW") = 0.5;

25

*** ***

Note: Calibration of the CDE parameters takes place outside of this GAMS program.

TABLE ALPHA(N,I) *** cde substitution parameters in demand (alpha

ABC US .5354540 .2074740 .6653719

ODME .4061232 .3165024 .5202577 CP .0845422 .1280465 .2962110

ROW .3793511 .3844555 .1097235;

= 1-b)

TABLE F(N,I) cde expansion parameters in demand A B C

US .1147590 .0230792 1.028048 ODME .3629641 .0397614 1.067278

CP .6422361 .1427092 1.322604 ROW .4362081 .3178123 1.083360;

TABLE B(N,I) cde shift parameters in demand A B C

US .0220040 .0261945 1.604620 ODME .0521677 .0943522 2.089457

CP .0698714 .4976034 0.6901531 ROW .0579732 .4609023 2.151772;

TABLE BETA(N,I) *** cde substitution parameters in supply (beta = 1-b)

ABC US -0.6366093 -0.3106272 -0.4889858

ODME -0.6251134 -0.3505626 -0.5468750 CP -0.3927131 -0.1231088 -0.5007622

ROW -0.5011069 -0.2924769 -0.5125900;

PARAMETERS S F(N,I); *** Note: cde expansion parameters in supply are set equal to 1;

SF(N,I) = 1;

TABLE SB(N,I) cde shift parameters in supply A B

US .032620468 .440438950 8.25750270 ODME .0526478999 .3684325070 12.75507491

CP .0341273 1.011222 0.6311728 ROW .0338014 1.977474 4.312565;

26

PARAMETERS CINL(N NINL(N NINC(N

RCINL(N RNINL(N RNINC(N

CINL ("US") = CINL("ODME") = CINL ("CP") = CINL ("ROW") =

NINL ("US") = NINL("ODME") = NINL ("CP") = NINL ("ROW") =

NINC ("US") = NINC("ODME") = NINC ("CP") = NINC ("ROW") =

RCINL(N) = CINL(N RNINL(N) = NINL(N RNINC(N) = NINC(N

quantity of crops used in Livestock-Crops quantity of non-ag used as inputs in L-C quantity of non-ag used as inputs in crops calculated quantity relationship calculated quantity relationship calculated quantity relationship;

156121; 076743; 227337; 066529;

006357; 024889; 017953; 003606;

017278; 022331; 030575; 024076;

/QS(N, "A"); /QS(N, "A"); /QS(N, "B");

POSITIVE VARIABLES FWP(I) FQS(N,I) FQSVA(N,I) FQC(N,I) FDEMP(N,I) AFDEMP(N,I) FSUPP(N,I) AFSUPP(N,I) FZD(N,I) FZS(N,I) FCINL(N) FNINL(N) FNINC(N)

final world price, final quantity supplied, value added portion of final quantity supplied, final quantity consumed (final consumption only), final demand price, adjusted final demand price, final supply price, adjusted final supply price, final (normalized) demand price, final (normalized) supply price, final crops used in livestock production, final non-ag used in crops production, final non-ag used in crops production;

FWP.L(I) = WP(I)

FQS.L(N,I) = FQSVA.L(N,I) =

FQC.L(N,I) =

QS(N,I); QSVA(N,I) QC(N,I);

FDEMP.L(N,I)=DEMP(N,I)-(RTW(N,I)/FF(N,I))-(-RCW(N,I)/FF(N,I)); FSUPP.L(N,I)=SUPP(N,I)-(RTW(N,I)/FF(N,I))-( RSW(N,I)/FF(N,I));

27

AFDEMP.L(N,I) = FDEMP.L(N,I) * FF(N,I); AFSUPP.L(N,I) = FSUPP.L(N,I) * FF(N,I);

FZD.L(N,I) FZS.L(N,I)

AFDEMP.L(N,I)/SUM(J, FQC.L(N,J)*AFDEMP.L(N,J)); AFSUPP.L(N,I)/SUM(J, FQSV^.L(N,J)*AFSUPP.L(N,J));

FCINL.L(N) = CINL(N); FNINL.L(N) = NINL(N); FNINC.L(N) = NINC(N);

POSITIVE VARIABLES MULTU(N) one thousand times utility level;

MULTU.L(N) = 1000;

VARIABLES OBJ makes Gams believe it is optimizing something;

OBJ.L = 0;

VARIABLES CHECK to check Walras' law;

CHECK.L = 0;

EQUATIONS

FZDEQOl FBEQOl FBSUMOl DEMDOl CPCONVOl FZSEQOl FQSVAEQOl FSBEQOl FSBSUMOl SUPPOl SPCONVOl CINLEQOl NINLEQOl NINCEQOl MATBALAOl MATBALBOl MATBALCOl TRBALOl USTRBALOl INDEXOl OBJOl

(final) normalized demand prices equation, (final) relative demand relationship (Eg 5 of app. 1), (final) minimize expenditure equation (Eq 1 of app. 1), (final) domestic price after policy and WP change, adjusted (final) domestic demand price, (final) normalized supply prices equation, (final) value added portion of final quantity supplied, (final) relative supply relationship (Eq 5 of app. 1), (final) maximize revenue equation (Eq 1 of app. l), (final) domestic price after policy and WP change, adjusted (final) domestic supply price, crops used in livestock relationship, non-ag used in livestock relationship, non-ag used in crops relationship, material balance: supply equals demand in good a, material balance: supply equals demand in good b, material balance: supply equals demand in good c, trade balance unchanged for odme, cp, row regions, check to see that u.s. trade balance in unchanged, world price level (at world production) unchanged, gams must think it is doing an optimization problem;

28

FZDEQ01(N,I)..FZD(N,I) =E= AFDEMP(N,I) /SUM(J, FQC(N,J)*AFDEMP(N,J));

FBEQ01(N,T)

FBSUMOl(N)..

FQC(N,T) * (1-ALPHA(N,"C")) * B(N,"C") * MULTU(N)**((1-ALPHA(N,"C"))*F(N,"C")) * FZD(N,T)**(ALPHA(N,T)) * 1.0E+03**((1-ALPHA(N,T))*F(N,T))

=E= FQC(N,"C") * (1-ALPHA(N,T)) * B(N,T) * MÜLTU(N)**((1-ALPHA(N,T))*F(N,T)) * FZD(N,"C")**(ALPHA(N,"C")) * 1.0E+03**((1-ALPHA(N,"C"))*F(N,"C"));

1 =E= SUM(I, B(N,I) * MULTU(N)**( (1-ALPHA(N,I))*F(N,I) ) * FZD(N,I)**(1-ALPHA(N,I)) / 1.0E+03**( (1-ALPHA(N,I))*F(N,I) ) );

DEMD01(N,I)..FDEMP(N,I) =E= DEMP(N,I)-PRTR(N)*(WP(I)- FWP(I)) -(RTW(N,I)/FF(N,I)) -(-RCW(N,I)/FF(N,I));

CPCONV01(N,I)..AFDEMP(N,I) =E= FDEMP(N,I)*FF(N,I);

******************

FZSEQ01(N,I)..FZS(N,I) =E= AFSUPP(N,I) /SUM(J, FQSVA(N,J)*AFSUPP(N,J));

FQSVAEQ01(N,I).. FQS(N,I) =E= FQSVA(N,I) / VARATIO(N,I);

FSBEQ01(N,T).. FQSVA(N,T) * (1-BETA(N,"C")) * SB(N,"C") * FZS(N,T)**(BETA(N,T))

=E= FQSVA(N,"C") * (1-BETA(N,T)) * SB(N,T) * FZS(N,"C")**(BETA(N,"C"));

FSBSUMOl(N).. 1 =E= SUM(I, SB(N,I) * FZS(N,I)**(1-BETA(N,I)) );

SUPP01(N,I).. FSUPP(N,I) =E= SUPP(N,I) - PRTR(N)*(WP(I)-FWP(I)) - RTW(N,I)/FF(N,I) - RSW(N,I)/FF(N,I);

SPCONV01(N,I)..AFSUPP(N,I) =E= FSUPP(N,I)*FF(N,I);

CINLEQOl(N)..RCINL(N)*FQS(N,"A") =E= FCINL(N);

NINLEQOl(N)..RNINL(N)*FQS(N,"A") =E= FNINL(N);

NINCEQOl(N)..RNINC(N)*FQS(N,"B") =E= FNINC(N);

29

******************

MATBALAOl..SUM(N, FQS(N,"A")) =E=SUM(N, FQC(N,"A") );

MATBALBOl..SUM(N, FQS(N,"B")) =E= SUM(N, FQC(N,"B") + FCINL(N) );

MATBALCOl. .StrM(N, FQS(N,"C")) =E=SUM(N, FQC(N,"C") + FNINL(N) + FNINC(N) );

******************

TRBALOl(M)..FWP("A") * ( FQS(M,"A") - FQC(M,"A") ) + FWP("B") * ( FQS(M,"B") - FQC(M,"B") - FCINL(M) )

+ FWP("C") * ( FQS(M,"C") - FQC(M,"C") - FNINL(M) - FNINC(M) ) =E=

WP("A") * ( QS(M,"A") - QC(M,"A") ) + WP("B") * ( QS(M,"B") - QC(M,"B") - CINL(M) )

+ WP("C") * ( QS(M,"C") - QC(M,"C") - NINL(M) - NINC(M) );

USTRBALOl.. CHECK =E=

FWP("A") * (FQS("US","A") - FQC("US","A") ) + FWP("B") * (FQS("US","B") - FQC("US","B") - FCINL("US") )

+ FWP("C") * (FQS("US","C")-FQC("US","C")-FNINL("US")-FNINC("US")) -(+ WP("A") * ( QS("US","A") - QC("US","A") )

+ WP("B") * ( QS("US","B") - QC("US","B") - CINL("US") ) + WP("C") * ( QS("US","C")- QC("US","C")- NINL("US")-NINC("US")));

INDEXOl.. SUM(N, SUM(I, QS(N,I) * FWP(I))) =E=

SUM(N, SUM(I, QS(N,I) * WP(I)));

OBJOl.. obj =E= 0;

MODEL LIBMOD / FBEQOl, FZDEQOl, FBSUMOl, DEMDOl, CPCONVOl, FSBEQOl, FZSEQOl, FQSVAEQOl, FSBSUMOl, SUPPOl, SPCONVOl, CINLEQOl, NINLEQOl, NINCEQOl, MATBALAOl, MATBALBOl, MATBALCOl, TRBALOl, USTRBALOl, INDEXOl, OBJOl /;

Solve LIBMOD Using NLP minimizing OBJ; Solve LIBMOD Using NLP minimizing OBJ;

DISPLAY FSUPP.L, FDEMP.L;

DISPLAY FWP.L, FQS.L, FQC.L, AFSUPP.L, AFDEMP.L FCINL.L, FNINL.L, FNINC.L;

30

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