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An examination of the impacts of eliminating government payments on the Canadian beef sector Yang, Hae Young 1989

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A N EXAMINATION OF T H E IMPACTS OF ELIMINATING GOVERNMENT PAYMENTS ON T H E CANADIAN BEEF SECTOR by HAE YOUNG YANG B.Sc. Korea University, 1981 A THESIS SUBMITTED IN PARTIAL FULFILMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF SCIENCE in THE FACULTY OF GRADUATE STUDIES Department of Agricultural Economics We accept this thesis as conforming to the required standard THE UNIVERSITY OF BRITISH COLUMBIA March, 1989 © HAE YOUNG YANG, 1989 In presenting this thesis in partial fulfilment of the requirements for an advanced degree at the University of British Columbia, I agree that the Library shall make it freely available for reference and study. I further agree that permission for extensive copying of this thesis for scholarly purposes may be granted by the head of my department or by his or her representatives. It is understood that copying or publication of this thesis for financial gain shall not be allowed without my written permission. Department The University of British Columbia Vancouver, Canada DE-6 (2/88) ABSTRACT The objective of this research is to examine the impact of elimination of government subsidies on the supply response in the Canadian beef sector. The recent trend towards l iberalization of agricul tural trade ( G A T T and F T A ) suggests that government payments to the agr icul tural sectors be reduced and/ or eliminated over some planning horizon. Ass i s t an t programs by governments to the beef sector have been operative at the both federal and provincial levels. They have been paid directly and/ or indirectly to the beef producers through many different programs over many years. A s a result of these varied programs payments to beef producers differ by province. The p r ima ry hypothesis of this thesis is that when these payments are eliminated, the impacts w i l l va ry by province. This research considers the economic behaviour of cattle producers in terms of the investment and disinvestment rules and it assumes that the relationship between an increase in expected price of beef and the number of cattle retained by each producer is positive in the long run . Earn ings to producers consist of returns from the market plus government assistance payments. When government payments approach zero, the herd size is expected to decrease as a result of decreased government payments. A reduction of herd size leads to changes in the production, trade and income levels. Given the theoretical and empir ical considerations of the model, a simulated beef industry is analyzed assuming various elasticities of the long-run supply curve. In the "base" case the simulated result represents the current structure of the beef industry and represents a si tuation where the cattle producers have received government payments. In order to analyze the l iberalizing effect of trade on the beef i i sector three scenarios are considered. The three scenarios assume different own price elasticities. The base year for this analysis is 1986. Opening stock numbers of cows, replacements and stackers are estimated at approximately 7.7 million heads for the national level. In terms of herd size Alberta share is largest with 37% of total herd, Saskatchewan has 21% and Manitoba and Ontario fall relatively further down with approximately 19% and 10% of the total herd. Total government payments to the beef sector in the base case are estimated at $243 million. The beef sector in the Prairie provinces and Ontario receives generally less than the relative herd size of their cow-calf herds in terms of government payments while Quebec with only 5.9% of the national cow herd receives 23.8% of the total amount of payments. Changes between the base case and each of the scenarios are analyzed in terms of aggregated measures. At the national level the change in the breeding herd size is downwards with a range between 2% for scenario #1 and 12% for scenario #3. Comparing the base case with scenario #1, herd size in Quebec is reduced by approximately 10% whereas the adjustment for most other provinces is about 2%. Quebec producers in the finishing sector received payments amounting to $161.60 per head while Ontario producers have received amounts of $20.45 per head. Ontario has supported this sector at a lower level than other provinces and therefore is at a competitive advantage when subsidies are removed. In this sense, if the base case and scenario #1 are compared at the provincial levels, high quality beef yield in Quebec is down significantly by 19.4% while that in Ontario is up by approximately 3.5% in spite of a herd size reduction of 1.6%. Therefore, when payments to this sector are eliminated the observed impacts will vary by province. iii Canada i n the base case is a net exporter of feedlot yearlings and calves. In the base case, net exports in the western region are 258 thousand head and net imports in the eastern region are 230 thousand head. A s a result of the elimination of government payments and the decrease in farmer's returns and herd sizes, there is a decrease i n net exports of live animals. Under scenario #1 the eastern Canada increases imports by 75,000 head from the base of 230 thousand head and western Canada decreases their exports by 36,000 head from 258 thousand. In the base case net sector earnings to beef producers amount to $1.4 billion. Government payments amounted $243 mil l ion and therefore net sector earning in the absence of government payments amount to $1.2 bill ion. In the three scenarios which represent no payment situation earnings are $1.17 billion, $1.14 bil l ion and $1.04 bill ion respectively. When government payments are eliminated the corresponding reduction in the beef sector earnings is more than $243 mil l ion. iv T A B L E OF CONTENTS A B S T R A C T i i L I S T O F T A B L E S v i i L I S T O F F I G U R E S v i i i A C K N O W L E D G E M E N T S -. ix Chapter 1 Introduction ; 1 1.1 Background 2 1.2 Problem Statement 6 1.3 Objectives 8 1.4 Research Procedures .-. 9 1.5 Thesis Outl ine 10 Chapter 2 Theoretical Considerations 11 2.1 Government Programs in Canada 11 2.2 Beef Trade 15 2.3 Investment and Dis investment Behaviour of Beef Producers . 18 2.4 Demand Considerations 30 2.5 S u m m a r y 32 Chapter 3 A n Empi r i c a l Model of The Beef Sector 33 3.1 The Genera l Structure of C R A M .:. 33 3.2 A n Overv iew of Major Changes 37 3.3 The Beef Sector of C R A M , 40 . 3.3.1 Beef Production Activi t ies 40 3.3.2 The Trade Block 45 3.3.3 The Beef Demand Block 50 3.4 Incorporation of Retention Funct ion into Models 51 3.5 The Equat ions of the Beef Model 55 3.6 The E m p i r i c a l Model 60 3.6.1 Beef D a t a Fi les 61 3.6.2 Beef Coefficient Files 63 3.6.3 Beef Retention Funct ion Fi les 64 3.6.4 Government Payments 66 3.6.5 Transporta t ion Cost D a t a 66 3.6.6 Demand D a t a 68 3.7 S u m m a r y 70 Chapter 4 Results 71 4.1 Mode l Va l ida t ion 71 4.2 The Scenarios To Be Evaluated 77 4.3 Ana lys i s of the Base Case 82 4.4 Ana lys i s of E a c h Scenario 85 4.4.1 Changes in H e r d Sizes 86 4.4.2 Changes in Supplies to M a r k e t 88 4.4.3 Interprovincial Trade and Expor t 91 v 4.4.4 Analysis of Production Cash Costs and Feed Grain Use Levels 96 4.4.5 Beef Sector Earnings 99 4.5 Summary 102 Chapter 5 Summary and Conclusions 103 5.1 Summary and Conclusion '. ; 103 5.2 Recommendations for Further Study 107 BIBILOGRAPHY 110 vi List of Tables 1.1: A Pa r t i a l L i s t i ng of Direct Payments to Livestock Producers over the Period 1980-1986 5 2.1: Direct F inanc ia l Transfers from Provincia l and Federal Government 14 3.1: Input Requirements and Y i e l d by A n i m a l Categorj ' in Alber ta 61 3.2: Phys ica l Values of Beef Cattle 63 3.3: Beef Retention Function Fi les 65 3.4: Transportat ion Costs of Cattle and Dressed Beef Between Provinces and Between Canada and World 67 3.5: Demand D a t a at Nat ional Leve l 69 4.1: A Procedure for Model Val ida t ion 74 4.2: Comparison of Statistics Canada Est imates of Herd Size with Model Est imates 76 4.3: Retention Funct ion Elasticit ies 79 4.4: Retention Funct ion Elasticit ies in F A R M Model 81 4.5: H e r d Sizes by Province, M a r k e t Returns, Government Payment Levels and Beef sector Earnings for Base Case 83 4.6: Breeding H e r d Size by Province under Different Scenarios 87 4.7: H i g h Qual i ty Beef Yields on Feedlots 90 4.8: Ne t Interprovincial and Expor t Trade of Feedlot Calves and Year l ings 93 4.9: Ne t Interprovincial and Expor t Trade of H i g h Qual i ty Beef 95 4.10: Production Cash Costs 97 4.11: Usage of Bar ley on Beef Sectors 98 4.12: Ne t Beef Sector Earnings 100 vi i List of Figures 2.1: Derivation of Retention Function 25 2.2: Demand Curve and Retention Function facing Canadian Cattle Producers 28 3.1: General Structure of Model 35 3.2: Calf and Yealrling Ranching and Feeding Alternatives 42 3.3: Beef Production Matirx Using Retention Function Activities 44 3.4: Trade Block of Weaned Calves 47 3.5: Beef Demand Matrix for Beef Yields in Western Area 50 V l l l ACKNOWLEDGEMENTS I would like to express m y appreciation to m y major supervisor, John G r a h a m , for his personal comment to this research, and for his encouragement and generosity. I would like to thank T i m Hazeldine and H a r r y Paarsch for their suggestions and care in reviewing the final draft. I am grateful to Steven Gui ton and Pa t r i c i a B a r k m a n for their contribution in editing the Engl i sh composition of this work. Th i s thesis would not completed without their assistance. F ina l ly , I would l ike to thank m y family for encouraging and supporting me to continue m y education. ix C H A P T E R 1 I N T R O D U C T I O N This research attempts to measure and evaluate the impact of government payment programs upon regional production patterns and supply responses for the beef sector in Canada. Government assistance to a sector can take many different forms depending upon the way the policies or programs have been designed and implemented. However, direct financial transfers or payments from both provincial and federal sources conflict with the recent trend towards a liberalization of international agricultural trade. For example, the Uruguay Round of GATT negotiations launched in 1986 (GATT, 1986) and the recent Canada-U.S. free trade agreement (FTA) stress restricting the use of all direct and indirect subsidies and other measures affecting agricultural trade. Thus, examining the impact of a reduction in the level of government assistance and a move towards market prices in a single sector is timely and important. Beef producers make investment and production decisions based upon expected profits. Producer incomes and their cost structures are affected by government programs which in some instances supplement market returns and/or reduce costs, depending on the program and province involved. Both federal programs and provincial support programs exist and the current level of payments to producers varies accordingly. Changes in government payments to beef producers imply that herd size, representing a capital good, and the flow of beef to the market will be affected. Adherence to the GATT and FTA agreements will require that the Canadian 1 2 government reduce, equalize, or eliminate direct and indirect subsidies that are trade distorting. This change in agr icul tural policies is expected to affect the structure of the beef industry. M a r t i n and van Duren (1987) have estimated direct financial transfers (DFTs) to the beef sector by both provincial and federal governments. This study w i l l use their estimates to represent current levels of D F T payments to producers and then examine changes that result as our policies are adjusted more in line w i th those proposed under G A T T . Current D F T payments v a r y widely by province. F o r example, direct benefits to cow-calf producers are greatest in Quebec at $162 per head, while Mani toba is the lowest paying, $16 per head. A n y adjustment in payments to cow-calf producers wi l l change the expected future net benefits from the breeding herd. When future net benefits are decreased cow-calf producers w i l l reduce their herd size. When herd sizes are decreased, this expands aggregate short run supply to the market, changes beef prices, and affects interprovincial and international trade patterns. Over the longer-run, smaller herds imply less supply to markets. Regional price differences caused by local excess demand and/or supplies affect shipments or movements of cattle and dressed beef between provinces, and between Canada and the U . S . , and these trade movements trend to suppress fluctuations of cattle and beef prices. 1.1 BACKGROUND A t the aggregate level, an analysis of the beef sector and the many economic forces influencing market supplies and prices is extremely complex. However , cattle producers' economic behaviour at the f irm level can be considered wi th in a 3 traditional microeconomic framework. J a r v i s (1974) discussed cattle as economic goods and postulates cattle producers' behavior as follows: "Cattle are considered to be capi tal goods which are held by producers as long as their capital value in production exceeds their slaughter value. In essence, producers become portfolio managers seeking the optimal combination of different categories of animals to complement their non-cattle assets, given exis t ing conditions and future expectations." B y applying economic principles to cattle management it is possible to develop a theoretical model in which cattle producers maximize the discounted present value of profits from their breeding herd. If the maximized discounted present value of profits at the end of some period from reta ining a cow in the herd is greater than current slaughter value of that cow, cattle producers retain that cow and expand their breeding herd size through retention of heifers. This behaviour maximizes profits. However , when ranchers build up their herds supplies to the market decrease, and price increases in the short run . Retained calves over the long run wi l l add to market supplies. Al te rna t ive ly , in a reduction phase cow-calf ranchers sell or slaughter their cattle to minimize loss when future prices are expected to decrease. This , i n turn, results in a reduction of the breeding herd which accelerates the increases of supplies to the market , decreases prices further i n the short run but increases prices over the long run . These two scenarios account for the up and down cycle of prices and inventory levels in the cattle and beef industry. Gordon (1984) and Trapp (1987) have presented the same explanation as J a rv i s for this economic decision. Their long and short run analyses are the same, although the scenarios are developed differently. The i r analyt ical techniques wi l l be briefly reviewed in a later section. 4 In practice, producers are faced wi th several difficulties in at tempting to follow some of the economic principles detailed in this maximiz ing model. It is difficult to predict the future price of cattle because of imperfect information. Fur thermore , since the market mechanism alone does not determine profits, other important factors must be considered including government policies and programs, inter-provincial and international changes in policies and prices, feeding cost, etc. A s shown in Table 1.1, direct payments (a part ia l l ist ing of programs) to the beef sector have operated through various assistance programs over many years . F o r example, under the Livestock Special Assistance program, payments were provided to Albe r t a producers for cows and other qualifying stock in 1986. The amounts paid were $70.1 mil l ion. This program was introduced in response to the damaging effects of various weather conditions in 1985. Payments of $67.0 mil l ion under the Pra i r i e Livestock Drought Assistance were made in 1985 to help producers i n the four western provinces mainta in their breeding herds after the 1984 drought. Under the Winter ing Beef Cattle Assistance program, Quebec producers over the period 1980-1984 were provided financial assistance for wintering their cows. Fur thermore , each province has different assistance programs for the crop sector which affect the beef sector indirectly through feed supplies. Given these various assistance programs the amounts of government payments per head, in each province, can vary widely by year. These programs affect the profits of producers i f we assume that total returns consist of the marke t price and government payments from these assistance programs. However , the recent trend towards to liberalization of agricultural trade requires a reduction or an el iminat ion of government subsidies to producers. Changes in these payments wi l l affect returns 5 Table 1.1 A Partial Listing of Direct Payments to Livestock Producers Over the Period 1980-1986 ('000 Dollars) Mar. Que. Ont. Man. Sask. Alt. B.C. 1980 Herd Maintenance Wintering Beef Cattle Livestock Podder Procurement 4114 6030 12108 80 250 578 8 1981 Beef Cattle Assistance Herd Maintenance Compensation for Animal Losses Wintering Beef Cattle Livestock Podder Procurement 59 2381 3551 37133 1412 10496 1183 1586 13013 118 1355 2760 355 85 65 1982 Beef Cattle and Sheep Support Beef Cattle Assistance Beef Enhancement Herd Maintenance Compensation for Animal Losses Wintering Beef Cattle Livestock Compensation 20328 323 677 1470 3017 7034 5900 648 22 136 141611 331 13 1983 Beef Enhancement Wintering Beef Cattle Compensation for Animal Losses 15 2326 457 1265 6484 267 17 63 15 1984 Livestock Drought Wintering Beef Cattle Compensation for Animal Losses Livestock Transportation Beef Enhancement 1798 143 823 2838 283 45 21152 145 247 16142 307 28 1985 Livestock Drought Compensation for Animal Losses Livestock Transportation Beef Cow-Calf Assistance Beef Enhancement 57 100 22 638 1087 258 15 36379 42 385 29537 212 3972 14 1986 Livestock Special Assistance Livestock Drought Compensation for Animal Losses Livestock Transportation Beef Cow-Calf Assistance Beef Enhancement 131 46 766 300 1349 71 447 70087 41325 938 594 10 Source: Agriculture Economic Statistics, Cat 21-603E, 1987 6 to producers. Opt imal composition and size of the herd base and supplies to the market wi l l be affected. 1.2 PROBLEM STATEMENT The Canadian beef sector has been supported by various government assistance programs as noted. It is clear that they have increased profits to producers. Producers who equate marg ina l revenue wi th margina l cost wi l l tend to expand their capacities when governments make D F T payments to them or those not covering average costs under market price alone w i l l tend to stay in the industry. A p a r t from considerations of the social . welfare motivations and assuming no market failures the lack of exit by these high cost producers leads to inefficiencies in resource allocation. Subsidies to the beef sector result in social welfare losses since government payments come from taxpayers. Direct payments have differed by province. Producers receiving relatively smaller benefits have lobbied their respective governments and one often finds situations where one province w i l l introduce programs to counteract those of a neighbouring province. A n expansion of programs can contribute to the burden of government outlays. There are problems associated wi th this. One is the burden of budget. The second is the increased social cost arising from the difference between government payment levels and the value of beef output as given by the market . A move towards the l iberalization of agricultural trade w i l l require the elimination of trade-distorting programs. A s noted by War l ey (1987), the purpose is to lower the level of protection in agriculture and to allow greater scope for comparative advantage - expressed through natural market forces - to determine 7 economically efficient international patterns of production and exchange. Since Canada is a net exporter of live cattle and dressed beef to the U.S. and the American governments has already placed countervailing duties on our hog industry, there is the possibility that the U.S. could do the same to the cattle industry if it can be shown that assistance payments to the Canadian beef sector are harmful to the U.S. beef industry. To avoid these difficulties and to allow greater scope for comparative advantage in Canada and between our trading partners it- is essential that our industry considers and examines changes that will result in the different provinces as governments adjust their programs. Supply responses show different results according to the assumptions of the model. As noted by Tomek and Robinson (1981), the price elasticities of- supply and demand are critical in determining this impact. They describe the importance of elasticities as follows: . "The slope of the demand and supply schedules are critical in determining the costs to the government of supporting prices above equilibrium by making deficiency payments to producers. If the supply curve is relatively flat so that producers respond to the guaranteed price by adding substantially to total output, and if the demand curve is relatively steep so that a large reduction in price is required to induce consumers to buy the additional output, the gap between the guaranteed and market price will be large and hence costs to government will be high." Since elasticities are often difficult to estimate it is necessary to bear this in mind as one considers changes in the levels of assistance programs. 8 1.3 OBJECTIVES The major objective i n this research is to evaluate the role that both provincial and federal government policies and programs play in the beef sector as these relate to marke t supplies and demands, by province, and their impacts on the Canadian beef sector. The subobjectives of this study are: (1) To review theoretical models of the cattle industry and then to examine in detail the concept' of a "retention function" which shows the relationship between the expected prices and size of breeding herd and to examine the role that the current and expected cattle prices and profits (including market and non-market returns) play in determining investment or disinvestment behavior of beef producers. (2) To modify the Canad ian Regional Agr icu l tu ra l Model ( C R A M ) in order to allow herd size to increase or decrease as a function of changing expected profit levels. The closing stock (c/s) breeding herd size i n C R A M is currently given exogenously (generally set equal to opening stock) and so does not consider the economic behaviour of ranchers wi th in any single period. However, wi th in a specific period, opt imal breeding herd size w i l l change, given full information, i f full adjustment is possible. Th is study incorporates the concepts developed in objective (1) and therefore allows par t ia l adjustment of closing herd sizes. (3) To validate and verify the model, thus representing the current Canadian beef sector and policies as they now operate. (4) To examine changes in the beef industry when the government payments to the beef sector i n the different provinces are reduced or eliminated. More specifically, to examine changes in beef production levels, feed usage, beef slaughter 9 and beef trade that result from changes in government payments to this sector and draw policy conclusions therefrom. 1.4 RESEARCH PROCEDURES To fulfill the objectives described above the following procedures are adopted: (1) Based on economic theory and past empirical analysis , a retention function is developed which displays the relationship between cow herd size, current and expected prices, the total number of breeding heifers retained, slaughtered cattle and other variables. These concepts are executed to an aggregate level . Government payments which supplement marke t returns are also incorporated into this retention function relationship. Since the retention function derived is on the basis of the current and expected market price, the role of these is clarified. Al though we can define current market price, i t is hard to forecast future marke t prices. Returns to producers are assumed to be those received from the marke t and received v i a government programs. Government programs to the beef sector are detailed and differences in the level of payments between provinces noted. A model is presented to explain expected changes i n market conditions i f provinces move towards returns dedicated by market prices only. (2) In order to evaluate changes in supply and- demand conditions i n the beef sector under the scenario discussed above, the C R A M model is used. A revised C R A M which incorporates the above endogenization procedures w i l l be detailed. (3) In order to test the val idi ty of the results derived from the model, the methods suggested by M c C a r l (1984) are introduced. Several steps in model validation have been followed and these are presented. Val idat ion is examined p r imar i ly for the relationship between expected short-run and long run behavior of cattle producers and 10 the relationship between changes in prices and subsidies and herd sizes. Fluctuations in closing, cattle stock are captured from the model and these are compared with observed changes in herd size over t ime. M a r k e t supplies are estimated and compared to observed slaughter levels. (4) Results from the model and different scenarios are examined as these relate to changes in herd size, production cost, domestic and international trade, and beef incomes. These analyses w i l l be undertaken wi th different elasticities for the retention function, and the results evaluated. 1.5 THESIS OUTLINE The remain ing chapters are organized as follows: chapter 2 w i l l present the graphical and mathemat ica l methods used to generate the retention functions used in this analysis . In chapter 3, the empirical model as this relates to the beef sectors of the revised C R A M model is presented. The closing stock variables of activities that relate to closing livestock numbers for beef numbers are part ly endogenized. In addition, domestic demand and international trade relationships as these are modelled are explained. Mode l validation and results are presented in chapter 4. Chapter 5 wi l l summar ize this study and discuss some of the problems of developing this thesis. C H A P T E R 2 THEORETICAL CONSIDERATIONS The previous chapter suggested that the Canad ian beef sector w i l l change in size and structure as governments become less directly involved i n the industry following trends toward the liberalization of agr icul tura l trade. In this chapter we describe the roles that the government programs have played in the beef sector of the economy. In order to examine the role of government payments we establish a simplified model depicting structural changes in beef trade and production that m a y be expected as one moves in the direction of l iberal iz ing trade. A t the firm level, production decisions are based upon input and output prices. Output prices consist of two components; market prices and government payments . There are also input subsidies that may be of importance and details of payments made are noted. This chapter also reviews the economic structure of the beef sector in order to provide some background to the economic model presented. A review of government payment programs and policies as they affect this sector and some of the G A T T and free trade issue are also noted. 2.1 GOVERNMENT PROGRAMS IN CANADA In this section we analyze government programs i n order to divide returns to producers into two elements; market returns and government payments. M a r t i n and van Duren (1987) classify government payments to cattle producers under three categories: direct, indirect payments and capital grants. The types of direct and indirect payments to producers can be grouped as follows: 1. subsidies to encourage production, 12 2. subsidies to compensate producers for low market returns, 3. payments to stabilize income, 4. subsidies to reduce expenditure on farm inputs and 5. payments to compensate producers for crop or livestock losses caused by extreme climate conditions, disease or other reasons. Programs which stabilize or supplement the price of livestock operate through the output market . Programs which reduce the costs of feed, agricultural labour or credit operate through the input market . Programs such as an imal research and extension affect productivity. M a r k e t information services, grants to slaughter facilities and grants for the establishment of an electronic auction are examples of programs which affect red meat producers through marke t infrastructure. Direct payments do not cover a l l payments made to farmers. M a r t i n and van D u r e n classify government payment to red meat producers as coming from three sources: Direc t F inanc ia l Transfer (DFT) , Other Government Expenditure (OGE) and Regulatory Transfer (RT). D F T covers the five direct government payment programs described above. O G E includes government expenditures not paid directly to red meat producers. Expenditures under this category include grants made to regional slaughter facilities, agr icul tural research, etc. R T expenditures affect market conditions without any direct public expenditures. Fo l lowing this classification of expenditures, programs are executed through four channels: output market, input markets, productivity factors and market infrastructure. Programs that increase productivity wi l l be not incorporated into this analysis because their impact is indirect and difficult to estimate. Expenditures on productivity factors and marke t infrastructure are executed through many different institutions 13 and intergovernmental agencies and their values are also difficult to estimate. Expenditures fall ing into this group are also ignored in this study and hence payments made under input and output programs only are included. These represent the major share of expenditure. • ' . Table 2.1 shows D F T ' s payments to cow-calf producers over the period 1981/82 to 1985/86. They represent an average level over this four year period. Payments are noted on per head basis and per $100 of cash receipts. A s indicated in Table 2.1, each province has received different amounts of government payments over this period. F o r example, it is shown that Quebec feedlot producers have received $161.61 per head while feedlot producers in Ontario have received $20.45 per head. In the cow-calf sector an addit ional $45.20 per $100 received from the market is paid to Quebec producers whereas i n Man i toba the estimate is $4.25. A s noted in the previous chapter, each province has implemented its own assistance programs i n order to affect returns to producers and thereby increase the size of the local industry. Payments to cattle producers are generally administered by several departments at both the federal and provincia l levels. Sometimes the terminology "top" loading versus "bottom" loading is used. "Top" loading programs generally subsidize output prices while "bottom" loading programs, affect input costs. That is , top loading programs increase prices to producers and therefore their response is a movement along the supply curve. Bottom loading programs lower the f irm's average cost curve and thereby shift the supply curve to the right. Government payments are simultaneously paid in output and input markets. It is, therefore, necessary to separate the effects of a shift in supply or a movement along the supply curve. 14 Table 2.1 Direct Financial Transfers From Provincial and Federal Government (Input and Output Programs Only - Average 81/82 to 85/86) Payment per Head Payment per $100 of Cash Receipts Cow-Calf Finish Cow-Calf Finish B.C. 52.39 70.64 11.96 8.31 Alt. 30.13 32.99 7.66 9.52 Sask. 40.68 44.39 10.13 13.81 Man. 16.41 40.09 4.25 5.39 Ont. 21.40 20.45 5.35 4.67 Que. 162.63 161.61 45.20 9.48 Mar. 40.93 35.10 9.70 16.98 Source: Martin and van Duren 15 2.2 BEEF TRADE Differences in support levels affect supply and demand conditions between provinces and between Canada and its other t rading partners. His tor ical ly , Eas te rn C a n a d a has an excess demand for beef, but Western Canada an excess supply of beef. Trade between these regions takes place in terms of dressed beef and live animals . Feedlot animals are finished in both Western Canada and Eas te rn Canada and beef products and livestock shipped. Trading patterns between Canada and the U . S . show similar movements. Samuelson (1952) formulated this trade model using the so-called "Koopmans-Hitchcock minimum-transport-cost" approach. In the model, geographic separation of two markets causes a price difference which is represented by the transportat ion cost, assuming no trade barriers. Inter-regional trade takes place when the transportation cost is less than the difference in prices resulting from positive excess demand in any one region. Trade between the regions continues unt i l excess demand becomes zero. The Samuelson formulation entailed given regional demand and supply levels. T a k a y a m a and Judge (1964) later endogenized these as demand and supply functions. They constructed a quadratic objective function which maximizes the net social payoff shown by the summation of producer's and consumer's surplus. Fo r the analysis of a spatial equil ibrium model, Tomek and Robinson (1981) noted several assumptions. These are restated to fit the beef cattle domestic trade block into sub-matrices of C R A M as follows: 1. A l l live and slaughter an imal and dressed beef to be traded i n each region are homogeneous with respect to quali ty and appearance. In addition, intermediate and final consumers for live animal and dressed beef are assumed to be 16 indifferent as to the source of supply. 2. No physical or institutional barriers exist to prevent the movement of live and slaughter animal and dressed beef. With these descriptions and assumptions of spatial equilibrium, beef cattle trade between provinces takes places and this is also associated with the larger American beef cattle market. Government intervention in the beef industry affects the determination of equilibrium prices and quantities in our market system. They affect the imports and exports of beef products through their influence upon production and consumption. In 1986, 90% of all Canadian exports of dressed beef and veal went to the U.S. while 40% of Canadian imports of dressed beef and veal came from the U.S. The United States imposes a tariff of 1 cent per pound for imported live cattle and two cents per pound for dressed beef and veal from Canada. For example, a cow of approximately 1100 lbs is levied $11 in tariffs when exported it to the U.S. Consequently, tariffs imposed by American governments at the border have minimal effect on the trade but health regulations and other indirect measures can be more important. Tariffs imposed on beef cattle and dressed beef and veal may restrict bilateral trade depending on their level. However, direct government assistance in its various forms may need to be withdrawn as a pre-condition to establish a non-tariff systems for the two countries. Elimination of government payments to a specific industry or commodity is consistent with the provisions of the General Agreement on Tariffs and Trade with respect to subsidies. The GATT agreement of the Uruguay Round in September 1986 states, in part, as follows: 17 "Negotiations shal l a im to achieve greater liberalization of trade in agriculture and br ing a l l measures affecting import access and export competition under strengthened and more operationally effective G A T T rules and disciplines, taking into account the general principles governing the negotiations, by: (1) improving market access through inter alia the reduction of import barriers; (2) improving the competitive environment by increasing disciplines on the use of a l l direct and indirect subsidies and other measures affecting directly and indirectly agricultural trade, including the phased reduction of their negative effects and dealing with their causes; (3) min imiz ing the adverse effects that sani tary and phytosani tary regulations and barriers can have on trade in agriculture, t ak ing into account the relevant international agreements." Canada and the Uni ted States have also agreed in principle to a free trade agreement in 1987 between themselves. The basic principles of the F T A va ry little from those of the G A T T . The objectives of the F T A are to "(1) el iminate barr iers to trade i n goods, (2) facilitate conditions of fair competition, (3) significantly expand liberalization of conditions for investment, etc." Specific to the beef t rading sectors (mainly, products and feed) the F T A aims as follows: (1) el iminat ing a l l agricul tural tariffs within 10 years, (2) to refrain from imposing or reimposing any quantitative restrictions on gra in and gra in products so long as there are no significant changes in grain support programs i n each country that would lead to significant change in imports from the other countries, (3) exempting each other from import restrictions imposed under their respective meat import laws, (4) agreeing that their p r imary goal wi th respect to agricul tural subsidies is to achieve, on a global basis, the elimination of a l l subsidies which distort agr icul tura l trade and agree to work together to achieve this goal, by methods such as mul t i la tera l trade negotiations like the U r u g u a y Round (Richard and Dearden, 1987). 18 Accordingly, the GATT talks and FTA agreement aim at reducing or eliminating the government assistance payments to Canadian beef producers over some planned horizon. It is assumed that the U.S. government will require the removal of Canadian government subsidies to the beef industry when the two countries phase into the free-trade stage and likewise for U.S. producers. In this case, the requirement of removal of government subsidies will be based on the GATT and FTA provisions as noted above. Even though there are arguments about advantages and disadvantages to freer-trade, Warley (1987) describes it as a necessity. This research concentrates on the beef sector and the changes expected as one attempts to implement some of the preconditions for freer trade. 2.3 INVESTMENT AND DISINVESTMENT BEHAVIOUR OF BEEF PRODUCERS The purpose of this section is to review theory which describes the cattle inventory cycle both in the short and long run periods. Since the number of cows to be retained or slaughtered is mainly related to how a farmer's assets will be changed into income, asset replacement principles are introduced following the early work of Chisholm (1966) and Perrin (1972). According to Chisholm, who criticized and expanded upon earlier work by Faris (1960), the aim in replacement problems is to select the particular production period for assets which, over a planning horizon, will maximize the net present value of future profits. In selecting the particular production period, the following elements of marginal cost with respect to time are important: (a) the annual operating costs or annual variable cost, 19 (b) the interest on the total revenue obtainable from sale of the asset, and (c) the amortized value of the net re turn. The relative value of future earnings versus present earnings is calculated using a discounted rate which represents either the cost of capital , the returns on alternative investments or time preference. Per r in (1972), following Chisho lm, states that the optimal time to replace assets is when the present value of margina l revenue is equal to the present value of margina l opportunity cost. The optimal replacement age is determined over an infinite time period without consideration of the uncertainty of the future stream. B u r t (1965) introduced elements of chance into the decision process. Problems caused by fire, insects, death, disease and physical injury as they affect agr icul tural capital goods are important factors i n the replacement cri terion. H e introduces a probability distribution of asset life into the uncertain future earning s t ream i n order, to consider production risk. He then develops the relationship between the compounded interest rate and an exponential distribution function using the probability of asset life over a continuous time period. The replacement criterion follows the conditions equating the expected present value of marg ina l revenue to expected margina l cost over an infinite time horizon. Bentley, Waters and S h u m w a y (1976) developed a model useful i n determining the optimal replacement age of a brood cow by extending the work of Bur t , Chisholm and Per r in . However, they assumed constant input and output prices. They assumed herd size to be constant and they also assumed a given planning horizon. Mel ton (1980) followed this up by incorporating technical change i n the form of genetic progress of cows into a model. The optimal replacement age under average 20 1967-1976 cattle prices, and al lowing for changes in genetic factors was determined. He illustrates the cattle cycle over a given period in view of prices and number of cows culled and replaced. One of the more important aspects of the cattle industry is the cattle producers' behaviour in response to changes in cattle prices over both the short and long run. A s described in the previous chapter, J a rv i s and Gordon distinguished between cattle producer's response over the short run and long run. They state that the supply curve is negative in the short run but becomes, positive in the long run. Paarsch (1985) analyzes the cow-calf sector on the basis of the Ja rv i s ' s and Faus tmann 's models. H e argues that the cow sale date can va ry depending upon the selling decision a producer makes. H e assumes that the beef price per unit of weight is constant over t ime, that cow-calf/feedlot operator herd is of homogeneous age and qual i ty and that each animal in the herd has the same calving/growth properties. F i r s t , based on the work by J a rv i s , Paarsch derives comparative static rules for the economic behaviour of feedlot and cow-calf producers. The analysis shows that the sale date of each an imal in the feedlot herd is positively related wi th price changes. This result is s imi lar to the Ja rv i s results for heifers and cows over the long run . However , the cow-calf producers in his comparative static analysis can not determine the sale date for beef price changes. According to his argument, at the opt imum age, cow-calf producers equate the expected marg ina l revenue product from postponement (the expected value of a calf plus the value of a cow's weight gain) wi th the marg ina l cost of postponement (the one period feeding costs, the interest foregone on last period's potential income, plus additional cost of calving). Given these first order conditions for maximiz ing the expected discounted profits, he derives the relationship between changes in sale date and changes in beef price. This relationship shows an indeterrminancy of sale date. Accord ing to his argument, "since cow-calf operators can use brood cows for either calf or meat production, when the price of beef rises," the ambiguous relationship suggests, "that brood cows become relat ively more profitable as meat-producers than as calf-producers. Thus cow-calf operators w i l l seek to sell off older cows. B u t w i t h beef price increases, feeding costs are relat ively lower, and cows as meat producers are kept longer, so that the capital gains created by weight gain can be captured." The holding or selling of a cow when beef prices rise is indeterminant, and depends on the expected bir th rate and weight gain. Second, he derives another comparative static analysis for feedlot/cow-calf operators using a modification of the Faus tmann model. In this modification, he assumes an infinite time horizon for an objective function and considers the present discounted value of a perpetual s tream of profits. G i v e n this additional assumption and the modified objective function, a comparative static analysis for feedlot operators shows that the relationship between the sale date and price is negative. According to his argument, this means that the opportunity cost of interest foregone on potential profit from all future herds increases more in proportion than the rise in beef price. Tha t is , "sale is brought forward because the sale of future herds is relat ively more lucrative than before." O n the other hand, the economic behaviour of cow-calf producers in the modification of Faus tmann 's model shows s imilar results as those based on the Ja rv i s work. A s shown in Paarsch's study, the feedlot/cow-calf producers' economic 22 behaviour can be varied depending on the model specification. This research wi l l use assumptions and methods different from those of Paarsch. Even though the changes in weight gain and the probability of birth rate can be considered, this paper does not consider the weight gain for cows as being possible. This paper uses five categories of cattle. That is, after a calf has grown, it becomes heifer or steer and then cow or bul l . Based on these an imal flows i n the model, each category of cattle is considered as a class by itself. W i t h each animal belonging to one category, the model in this paper does not consider weight gain wi th in any one category. Another reason for not al lowing for weight gains for cows in this paper is that based on the tradit ional practice of ranchers cows are generally culled in the fall after they have tested for pregnancy. A n i m a l s that are not ca r ry ing a calf w i l l be culled. In addition, cows are sometimes culled in the spring when they lose a calf. Ranchers w i l l then attempt to replace that cow through purchases i n the open market . A th i rd option, although not very common, is for ranchers to hold culled cows i n the fall and attempt to feed them for a short period. In this situation ranchers are generally attempting to add weight lost during the summer when carried on rough pasture. They are also attempting to take advantage of the price differences one finds i n the market between when most cows are sold in the fall (generally November) and market prices in J a n u a r y and February when supplies to the marke t are reduced substantially. Weight gain can be added through this feeding. The benefits from weight gain can be captured over the short-run. However , i f a producer wants to keep a cow for breeding purposes then that an imal must be carried over the winter and summer grazing period. Dur ing the winter she is pregnant and she can only be sold after her calf is weaned in the fa l l . 23 Instead of al lowing for weight gain by cows as shown in Paarsch 's specification, this study assumes that expected prices are incorporated into the model and cow-calf operators have animals of heterogeneous categories in their herd. Weight gain by cows wi thin a single production cycle are not catered to. E v e n though younger replacements and cows can gain weight in their ear ly years, their weight gain generally remains constant over several years and tends to fall sl ightly as cows become older. Therefore, cows culled are taken to be a given weight and i t is assumed that ranchers do not have the option of at tempting to add weight in the fall . It is also noted that b i r th rates for cows increase i n the earlier parts of their life cycle and then fall off gradually. In this study b i r th rates are exogenously given at average levels for each province and weight gain by cows is ignored. Rosen (1986) suggests that the decisions of cattle producers at the f i rm level are based upon their v iew of whether price changes are t ransi tory or permanent. A shock that results in a permanent increase in feed prices relative to market price increases current market supply, and reduces breeding herd inventories. Permanent increases in beef prices are associated wi th smaller marke t supplies in the short r un but in the longer-run supplies are increased. O n the other hand a transi tory increase in price of beef increases immediate supplies to the market because ranchers w i l l generally sell more immediately in order to maximize their benefits from the transitory price increase. Future supplies w i l l be reduced because ranchers w i l l need to make up for the decrease in herd size that resulted from this earlier selling off. Trapp develops investment and disinvestment rules for fluctuating herd sizes. To maximize profits in the herd, cattle producers have to find the opt imal cull ing 24 age and herd size. He defines the optimal culling age as that at which the discounted earnings for a cow over her next year of production plus her discounted marke t value at the end of that year is equal to her current market value. Given the opt imal cull ing age, i f the net present value is greater than zero, cattle producers t ry to retain animals which have positive net present values. In addition, cattle producers w i l l want to purchase replacements. Conversely, when the given opt imal cul l ing age is applied to each animal , the animals having negative net present value are culled. Culls are not restricted to any specific age. Rather, cull ing occurs sequentially start ing wi th the age group showing the largest negative net present value in the herd. The culling is continued unti l no remaining age group shows a negative present value. The age group with the the largest negative present value is generally the oldest age group in the herd. Therefore, in order to max imize the profits of the entire herd size, herd size is expanded (invested) or contracted (disinvested) every year unt i l discounted marginal cost is equated wi th the discounted marg ina l revenue. G i v e n these considerations, this research assumes that the cattle producers w i l l re ta in cows i f the expected discounted value (discounted net earning plus the discounted expected market value) is greater than the current value. The number of animals retained i n the herd is positively related to the discounted expected value of each an imal . A positive relationships implies the contraction of current supply into the marke t . These relationships wi l l be described graphically as shown in Figure 2.1. I f the expected. future price (P ) of cattle increases relative to that the current price (P ), cattle producers w i l l be encouraged to keep their stocks instead of e sell ing them. The relationship between P and the number of cattle retained Panel (b) Panel (a) Figure 2.1: Derivation of Retention Function 26 wi l l be called the "retention" function as shown in panel (a) of Figure 2.1. Panel (b) of Figure 2.1 describes the reaction of cattle producers using e "expected" price (P ) in some future marke t period as this relates to current price c • . e c c (P ). In order to show this relationship between the P and P , P is taken as e c c c given and then P w i l l be equal to P , greater than P or less than P . 6 c 6 c Panel (b) of F igure 2.1 shows that relative prices between P " and P (P / P ) are less than, equal to, or greater than 1. Panel (c) of Figure 2.1 shows that the supply curve of cattle to the market and is function of the current prices . In general, Q C = f ( P c , P e , P f ) (1) f where P is price of feed. The relationships between the dependent variable and the independent variable in equation (1) are shown as follows: 9 Q C / 9 P C > 0 9 Q c / 9 P e < 0 9 Q c / 9 P f < 0 Panel (d) in Figure 2.1 shows the relationship between number of cattle retained (Q^) and number of cattle sold current ly (Q C ) , since the total number of R c cattle (Q plus Q ) is given. Pane l (d) represents the total balance of cattle, showing the relationships between the number of cattle to be sold and retained. That is, 9 Q R / 9 Q C < 0 (2) U s i n g those relationships in panel (b), (c) and (d) we can construct the e R relationship between P and Q . Pane l (a) and (c) show market supplies and e c e c number of animals retained. If P is greater than P (i.e. P /P > 1), they may reduce market supplies and increase their herd size as shown by the broken line. As shown in panel (a), the curve of the retention function has a positive slope. At this point, for simplicity, we suppose that the inflow of and outflow of cattle at R each period are the same so that Q can be interpreted as the number of cattle expected to be sold in the future. Consequently, the retention function becomes a supply function of cattle at different times. Gordon (1984) states that beef and livestock prices in Canada are bounded by import and export prices. Trade between the U.S and Canada accounts for approximately 90% of total Canadian exports of cattle and calves and 85% of Canadian exports of total dressed beef and veal. Changes in the U.S. price of beef or livestock prices affect Canadian beef prices and, in turn, the behaviour of ranchers. Gordon explains this relationship using the demand curve as shown in panel (a) of Figure 2.2 -- the import ceiling price becomes an upper bound for beef prices and the export floor price becomes a lower bound for prices in Canada. He does not, however, show the specific range between import ceiling (P^ ) and export EX I EX floor price (P ). He defines P and P as follows as: I u s P = P ' ' + Transportation cost from U.S. to Canada + Tariff P^^= pu"s" - Transportation cost from Canada to U.S. - Tariff where P ' ' = price of beef products in the U.S. Even though the particular range is not specified, Gordon's bound concept of prices is introduced to limit the retention function shown in Figure 2.1. Adding P^  EX and P to Figure 2.1, the retention function can be redrawn as shown in panel (b) of Figure 2.2. Beef price and number of cows to be retained depends on these 28 Price ($) Panel (a) D 0 q Quantity Price($) p a n e l (b) Import Ceiling Export Floor . .0 - • Quantity F i g u r e 2.2:Demand Curve and Retention Function facing Canadian Cattle Producers 29 prices established in the market and the rancher 's future expectation of the current prices. It is unnecessary to specify "current and expected" price in the procedure used to derive the retention function. Econometric models have used "expected" price based on a geometrically declining average of past prices such as the autogressive process, moving average, autogressive/moving average, etc. In addition, expected prices may be estimated in reduced form from the concept of rat ional expectation by using al l of the available information at the current t ime. The estimation of expected price simply represents a trend or a relationship between other variables. In other words, it is difficult to forecast any specific values to be incorporated into the programming model. Therefore price changes are often taken as exogenous to models and in this analysis w i l l be allowed to va ry between the bound levels set by the U . S . market . Current and expected beef prices received by cattle producers are assumed to be derived as follows; P = P M + G P (4) c c c P = P M + G P (5), e e e where P = Prices per head received by producers, P M = M a r k e t prices per head received by producers, G P = Government payments per head received by producers, c = Curren t t ime, e = Future time. In this study market prices both current and future are held constant and only government payments change. G i v e n an adherence to the principles of G A T T and 30 the recent free trade agreements, G P g is expected to decrease or be el iminated entirely. 2.4 DEMAND CONSIDERATIONS To model the industry it is necessary to consider both supply and demand. To facilitate the analysis , we assume that the demand function is l inear and endogenous in own prices following the method of Duloy and Nor ton (1975). A s described in deriving the retention function, we introduce upper and flower bounds for the price assuming the U . S . market size is approximately ten times the Canad ian market and therefore sets import and export prices. The relationship between Canadian and Amer i can beef prices can be represented in a simple diagram. In panel (a) of Figure 2.2, D D ' shows the Canadian domestic function for dressed beef. The import ceiling price (P^) is defined as the price of beef in the U . S . in Canadian dollars plus transportat ion costs to E X . Canadian markets plus a tariff. The export floor price (P ) is defined as the beef I E X price in the U . S . less transportation costs to the U . S . less a tariff. P and P represent the range in which the Canadian price w i l l be varied relative to the U . S . price. The larger size of the U . S . market relative to the Canadian marke t has a number of important implications for the shape of the aggregate demand curve for I E X beef. If Canadian prices va ry within the range P to P , the relevant portion of E X the demand curve is domestic demand. If Canadian prices fall below P and Canada is an exporter, then Canadian beef becomes competitive in U . S . markets and the relevant demand curve for Canadian cattle producers is the domestic demand plus the U . S . demand for Canadian beef. This demand can be d rawn horizontal at price (segment CE) to indicate the assumption that Canadian exports to the U . S . wi l l not affect U . S . beef prices. Meanwhi le , i f Canadian prices rise above P \ U . S . beef becomes competitive on Canad ian markets. A reduction in Canadian beef supply below Oq would result in U . S . beef entering in Canadian market and prices being reduced to P^. Consequently, in this case the relevant demand curve for Canadian producers is horizontal at price P^ (segment A B ) . The demand curve facing Canadian beef producers is thus represented in panel (a) of Figure 2 .2 . Based on these assumptions about the demand curve, we can specify the l inear demand curve for segment B C in panel (a) of Figure 2.2 as follows: P = a + b * Q (1) where a > 0.0, b < 0.0, P is the beef price and Q is the quanti ty demanded. This equation provides the following revenue equation for producers: T R = P * Q =(a-b*Q)*Q = a*Q - b * Q 2 (2) where T R is total revenue. W e can find the "quasi" consumer surplus under the demand equation (1) as follows: 2 W = f P dQ = J(a-b*Q) d Q = a*Q - 0 .5*b*Q z (3) where W is "quasi" consumer surplus. Equations (2) and (3) are represented in quadratic forms. The method of incorporating these equations into the mathematical programming model has shown by Duloy and Norton ( 1973 ) . 32 2.5 SUMMARY The purpose of this chapter was to present a theoretical f ramework for the structure of the beef sector. In order to analyze liberalized agr icul tura l trade, requir ing the reduction and/or elimination of the government subsidies, the payments to the beef sector were presented. The impacts of e l iminat ing the government payments on the beef sector were reviewed on the basis of the aforementioned theoretical considerations. Based on the investment and disinvestment rules and the economic behaviour of cattle producers changes in future profit levels are expected and these changes should, in turn, lead to changes in industry size and structure. CHAPTER 3 A N EMPIRICAL MODEL OF THE B E E F SECTOR The beef inventory model presented in the previous chapter is developed in this section as an empir ica l model in which the Canadian beef sector is modelled. Par ts of C R A M ' s structure as these relate to the beef components thereof wi l l be detailed. Since C R A M describes both the crop and livestock sectors in each province, it is unnecessary to present and detail the structure of the entire C R A M model in order to develop and describe the behaviour of cattle producers. This has been done elsewhere (Webber,er al, 1986) Livestock sectors in C R A M model include the beef and dairy cattle, hog and poultry production, marke t ing and trade components of these industries. Only the beef cattle sector is examined in this paper in a par t ia l equil ibrium analysis in which the agr icul tura l sector of the economy alone is considered. Interactions between the beef sector and other agricul tural sectors are explicit ly accounted for in this analysis since the beef sector is l inked to these other sectors within the C R A M model framework, n keeping wi th the C R A M structure, a beef sub-block is adapted for the empir ical testing of the beef cattle inventory model. 3.1 THE GENERAL STRUCTURE OF CRAM This section presents a general overview of the model in order that the beef components thereof m a y be related to the rest of the agricultural economy. The C R A M model details both crop and livestock sectors dealing wi th both supply and demand sides, l inks between these sectors, trade between provinces and trade 33 34 between Canada and other nations. The broad objectives of C R A M when the model was developed in 1986 included the specification, estimation and validation of a regional model of the Canadian crop and livestock sectors. Several subobjectives in the earlier work were specified, these being: (1) . To conceptualize a model that divides the country into a number of regions wi th special emphasis given to a disaggregation of the Pra i r i e region into 22 crop production regions. This regional disaggregation was chosen because cropping activities in the provinces were being emphasized and yet the link between livestock herds in each of the provinces and the crop sectors is important . Pol i t ical boundaries were recognized wi th the livestock sector being specified at a provincial level, and trade takes place between provinces, but wi th in each of the provinces several crop producing regions are specified. (2) . To develop a data base that specifies technical relationships between inputs and outputs, resource constraints and cost coefficients. These input/output coefficients represent feasible production alternatives for each of the activities in the model. (3) . To detail the economic activities that represent major crop and livestock production opportunities for each of the regions and transportat ion routes from production to market ing areas. (4) . To evaluate the economic impact of the introduction of medium-qual i ty wheat on the Prai r ies and on Canadian agriculture and to examine the impacts of alternative freight rate structures for moving Pra i r ie grain on the agr icul tura l economies of both the eastern and western provinces. The model represented seven provincial regions: B r i t i s h Columbia , Alber ta , PRODUCT ICH INVENTORY TRADE DOMESTIC DEMAND K«t -o»Cs » i c n T HAND SIDt Province 1 (Ve . t e r t O Province 2 (W*rt«rn) Province 3 (E&itarh) c k< s o n ft. '— Crop LIvt • tock . Ueic t o t Hstlonil C CL o i * u jt V o •> CL o v> u M 0 « • > o. o u L) -X v a « > c M « u rt k. «j f- —' * M a. o u o 5\ > Ck O u U .* u o • • > o u V o w - J Ob]«ctlv« function + + + + + + -f T -1 c l . C*«h Costa + e l . l + ci.a + c1.1 + Cl.< 4- + Cl.« + + c1.10 + C1.U <_ a Crop A2.1 + A2,2 A 2 , » + i » » (Wcatarrt) Livestock + Crop Proline* 2 A4,J ^ 4 A«,9 x4,10 °4, 11 {Wvstarn) Liv«itock A5,4 • »S,U «*.» Crop A6,S At,6 (E*«t«rn) Llvsatock A7,6 *7.11 i » j Port 1 Crop (Wattsrn) i 0 Port 2 Crop (L*at«rn) i 0 Crop A10,1 * A10,J A10,S •1 °10,16 i 0 Lirtstock AU,2 A l l , 4 All*» +1 i 0 Livestock Tr*d« Poo »1T,11 i 0 World Livestock •13,11 Struct tar t l loundi »2 »4 »6 »7 » U »11 »1* A14 Figure 3.1: Genral_ Structure of Model CO. 36 Saskatchewan, Man i toba , Ontario, Quebec and the Mar i t imes . E a c h region has four major submatrices--each referring to either production, trade, domestic demand or inventories of commodities. Under these basic concepts, Figure 3.1 shows the general structure of C R A M . Supply and demand balances between producing regions, demand points, and interprovincia l movements and imports and exports are i l lustrated. The symbols used in F igure 3.1 are defined as follows: A . . : submatr ix i n the i ^ row, j * ^ column position of a larger matr ix , B . :set of s t ructura l bounds associated wi th column set, J C. . :row vector in the i^ row, j^1 column position of a larger matr ix , dealing wi th costs or prices, th Cj :row vector of objective function coefficient in the j column position. D . . :diagonal m a t r i x i n the I^1 row, j ' * 1 column position, Rj :set of r ight hand side values associated wi th the i ^ row set. superscript " + " : a l l values of mat r ix or vector are non-negative superscript "-" : a l l values of mat r ix or vector are non-positive a : positive coefficient a : negative coefficient b : s t ructural bound The general structure of the model is i l lustrated in Figure 3.1. The objective function row of the model accounts for a maximizat ion of consumer and producer surplus incurred by those sectors specified in the model. In order to detail the logic of the s t ruc tura l specification of the livestock activities consider submatrices A 9 „, A g ^ a n d A ^ ^ Submat r ix A ^ ^ represents the use by livestock of gra in or forages produced by the cropping sector. Rows and columns wi th in submatr ix A g ^ account for other inputs to the livestock, numbers and transfers of animals from one category to another wi th in the time period, and they deal w i th livestock yields which are accounted for at the provincial level. Submat r ix ^ accounts for yields i in province 1, which supplies a national pool, wi th supply ( A - ^ ^, A ^ 4 and A ^ g) being balanced wi th use ( D ^ A t the provincia l level , supply (Ag ^) * s shipped to other provinces or to export (Ag ^ ) and provincia l use or demand is specified (Dg ^ ) . There are also livestock t rading activities i n the model that move livestock or livestock products between province, between provinces and a national pool, and to export. These are i l lustrated through A ^ A,_ ^ and A^ , ^ which draw from, or add to, provincial supplies and through A ^ ^ which draws from or deposits into the national pool. Exports may take place from this pool, or from the provinces directly. C R A M has, since its original development, been modified in each of its different sectors or sub-matrices without changes i n the basic structure of the model. Specific changes are detailed elsewhere (Webber, et al). Th is section wi l l briefly review the revised beef sector and then more details on each of the changes wi l l be noted. 3.2 AN OVERVIEW OF MAJOR CHANGES In the ini t ia l specification of the beef production ma t r ix , cattle numbers of closing stock were given exogenously, and were generally set equal to opening stock numbers wi th in some period. This assumption, being for long-run analysis, did not allow for any changes i n cattle numbers wi th respect to price fluctuations wi th in a single period. The period modelled by C R A M was one year and it was assumed that an equilibrium situation was being examined in which the size of the herd would not change wi th in the year. Revisions incorporated in this study endogenizes closing cattle numbers in accordance wi th price or other variable changes during the 38 period. A s noted i n chapter 2, cattle producers are assumed to respond to changes in cattle prices. Therefore, to reflect changes in cattle prices, the retention function derived in chapter 2 is incorporated into the beef production matr ix of C R A M . Hence opening and closing stock numbers are no longer necessarily set equal and, in par t icular , closing stock numbers are adjusted to changes in other variables wi th in the model. In addition to shorter-run adjustments within a year, longer-run adjustments m a y also be evaluated. The approach followed allows opening stock numbers to be adjusted based upon some longer-run equi l ibr ium position that ranchers wi l l adjust to for changes in both product price and input cost levels, and these changes affect herd size levels. Th is allows opening and closing herd size to be set a priori at some level , and changes wi th in a production year may also be examined. The method of incorporating this adjustment in C R A M is also detailed in this section. It is difficult to forecast future prices. Both future product and input prices are important because in their economic behavior cattle producers respond to changes by compar ing current price and profit levels wi th possible changes in the future. To derive expected price changes both market prices changes and government policy changes must be anticipated. A s noted earlier, the current fa rm gate price to producers is assumed to consist of two components, marke t price and government payments. M a r k e t price is determined by the forces of supply and demand and Canadian prices are often assumed to be exogenously determined by market forces in the larger U . S . market . Government payments represent the amounts paid to each producer, often based on herd sizes, and government policies change over time. The reason for dividing farm 39 gate returns into two components is to examine the economic impacts of reducing or eliminating payments to the beef sector. To simplify the incorporation of expected price changes into the model, the elasticity of price response of producers to returns received from government payment sources is assumed to be similar to that for returns from the market price. It is possible to change this assumption but a literature search has not found studies that have catered to this problem. That is, estimates of supply elasticities for own market price changes as distinguished from these for changes in payments from governments are not available. Accounting rows and columns have also been added to the model in order to account for the values of economic activities in each province. These relate specifically to the livestock sector and include production levels, interprovincial trade, export levels, government payments, cash costs, and feed usage. These values facilitate the calculations of net sector earning for livestock producers. In the earlier version of CRAM, domestic demand levels for beef were predetermined. The revised CRAM modifies this using an endogenized demand curve. The purpose of incorporating an endogenized demand curve into the model is to find the market clearing price. This requires the estimation of appropriate elasticities for each commodity in the model and requires a quadratic objective function which can measure consumer surplus areas. This formulation and approach is detailed later. It is also assumed that Canada is a price taker with the U.S. setting price. However, depending on Canadian supply and demand, Canadian price can differ from that of the U.S. as noted earlier. For example, if Canada is an exporter, local demand price will differ by transportation costs (tariffs ignored) and this is represented by a 40 position on the demand curve different to the exogenous U . S . price. The objective function was previously specified as value added to the agr icul tura l sector and did not evaluate the changes in net producer and consumer surplus. The demand activities account only for the areas under the demand function i n the competitive economy. W i t h the implementation of the endogenized demand function for a l l commodities, consumer and producer surplus concepts are now used to model a competitive economy. 3.3 THE BEEF SECTOR OF CRAM This section details the approach used to model production activities, trade activities, the retention function component of the production sector and demand activities. D a t a detailing these components of the model is presented. 3.3.1 Beef Production Activities The beef production block is reviewed in order to detail its structure and describe the beef production activities in the model. For convenience, beef producers are divided into two types of operators; cow-calf, and feedlot producers. Producers ca r ry beef animals specified as cows, replacements, stockers, bulls, feedlot yearl ings and calves i n their herd. Producers feed six kinds of animals and produce calves and replacements. Cow-calf producers sell calves or sometimes carry animals through to heavier weight. Feedlot operators purchase calves from cow-calf producers and then feed to maximize profits. A simple beef cycle describing these two types of operators is represented in 41 Figure 3.2. A s a starting point, calves in the current period (t) are born around M a r c h . Cow-calf operators allow cows and calves to graze upon open range unt i l the end of the fal l . The weaned calves are then either sold to feedlot operators or retained as stockers over to the next period (t+1). Stackers carried in as opening stock wi l l be either sold as l ight feeders, retained and slaughtered as feedlot yearlings, or bred as replacements and feedlot yearlings. Bred replacements wi l l either become cows producing calves or be culled depending on the requirements of the rancher at the time the cul l ing decision is made or on market conditions. Cows generally are kept to produce a cal f every year for about ten years. Feedlot operators buy weaned calves or feedlot calves from cow-calf producers. Feedlot calves at the next period (t+1) are grown as feedlot yearlings being fed high protein/ feed requirements. The beef production ma t r i x representing Figure 3.2 is specified in a linear programming format represented by F igure 3.3. Rows in the model are grouped as follows: 1. Government payments: an accounting row in the model which keeps track of payments to producers on a per head basis. 2. Input requirements: rows that specify inputs required per unit of each activity in a traditional Leontief production function sense: 2.1) cash costs, 2.2) forage, 2.3) pasture, 2.4) barley. 3. Beef opening stock: the r ight hand side of the model that represent the current investment level for producers. F i g u r e 3.8: C a l f and Year l ing Ranching and_ Feeding Alternatives 43 4. Beef balance rows: balance equations that keep track of an imal flows between classes wi th in the time period of the model. 5. Constraints on number of replacements: technical constraints that must be specified in order to keep track of production relationship between various animal classes in the model. These include replacement ratio and cul l ratios. 6. Beef closing stock: the right hand sides at the end of the period representing balances required for continuous production by cow-calf operators and feeders. 7. Beef yield: output dur ing the production period is categorized as three items; number of beef slaughtered, A B C beef yield, and D beef yield. 8. Bul l s : rows in the model that specify the ratio bulls per cow. A l l column activities in this section of the beef production submatr ix m a y be grouped into five major sets, namely: 1. opening stock activities 2. wi th in year activities 3. closing stock activities 4. retention function activities 5. government payment. The opening and closing stocks are divided into six categories as shown in Figure 3.3. F i r s t , the number of animals in each of these six categories at opening stock is given exogenously as a right hand side variable in the appropriate constraint. Second, there are six "within year" groups, four of which are used as balance row categories. The other two rows are used as replacement ratio rows. T h i r d , the number of animals i n each of these categories as closing stock (except of bulls) is determined endogenously through balance and replacement ratios, w i th their own elasticities, from the retention function. Opening Stock Closing Stock Slaughter Bulls Retention Fn. Activities 5 c • S 2 X. * c «; Z - -T < j( - -• •= o T3 T3 ffl « W I*. In Feedlot yearlings Culled replacements Breeding herd Replacements Stockers Feedlot calves Feedlot L. yearlings m *9 S " s = * "1 • ° m ° •* o v *% — -* - * 3 ^ n x o (2 (Z < O/S Bulls Culled Bulls C/S Bulls Culled bull. Slaughter Reduced Cow Cull ! a £ £ f • 0. • «J 4J J > r s ! - i 5 c *» 2 *. -£ ~ " « ° o „ X> oJ ^ —. — j «•= t; -a -o * OJ O- X 41 V O •• V J o « J) CQ Ct£ 03 U. U. Government Payment T T a a 1 £ 0 Cash Cost a a a a a a a a a a a a a £ 0 Provincial Forage Crop Pasture Balance Barley a a a a a a a a a a a a a a a a a a a a a a a a a a £ 0 £ 0 £ 0 Beef • Breeding herd Opening Replacements Stockers Stockers Feedlot Calves Feedlot L. yearlings I 1 I 1 I £ a £ a £ a £ a £ a Beef Breeding herd Balance Replacements . Weaned Calves Yearlings Culled Replacements i " a , "a a "a a" 1 1 1 1 T l l i l 1 1 1 £ 0 £ 0 £ 0 £ 0 £ 0 Beef Breeding herd Cloaing . Replcements Stockers Stockers Feedlot calves Feedlot L. yearlings T T I T T a a a a a £ 0 £ 0 £ 0 £ 0 £ 0 Provincial Heifers and Steers livestock Cows and Bulla Yield Total cattle A B C beef D boef a a T % T 1 1 a a Z a 1 1 T l l i T a 1 l a X a i T X a £ 0 £ 0 £ 0 £ 0 * 0 Bulls (VS Bulla Balance O S Bulls Slaughter 1 X T 1 T X 1 £ a £ 0 £ T £ 0 Flfiinj 3.1 JW Production Matr ix Using Retention Function Activit ies 45 The annual diet of an an imal consists of a mixture of forage, pasture and barley. A s the stage of the life cycle model spans a calendar year, the diet is split between opening stock act ivi ty numbers and the corresponding closing stock columns. The spli t is based on the relat ive length of the growth stages and animal categories dur ing the year. Feed is d r a w n from a provincial supply which can be supplemented by grains shipped between provinces as required. A certain proportion of the opening breeding herd is culled yielding D grade beef. The remaining breeding herd and opening replacements transfer as opening stock to produce calves based on an average provincial b i r th rate during the current period (t). Weaned calves f inish the current period (t) as either a stocker or a feedlot calf yielding A B C grade beef for the next period (t+1). Stackers carried over from the previous period (t-l) s tart the current period (t) as yearlings. They are assigned to one of four categories dur ing the current period (t): feedlot yearlings, feedlot long yearlings, replacements for breeding and closing stock bulls. Those replacements exceeding the closing stock replacement requirements are culled yielding A B C grade beef at period (t). In addition, the feedlot calves, yearlings and long yearl ings produce high qual i ty beef; the yield per an imal va ry ing wi th the category. The slaughter of feedlot long yearl ings is adjusted for death loss. Meanwhi le , the number of closing stock animals except bulls is endogenously determined by their corresponding elasticities shown in the retention function activities of Figure 3.3. 3.3.2 The Trade Block A s described in chapter 2, we assume that beef and live animals are traded based on price differences between regions and transportation costs. These two basic 46 factors are incorporated into the spatial equil ibrium model. Trade levels are based on production and demand levels wi th production being determined by the relative size of the herd in each of the provinces and upon producer decisions. Figure 3.4 details how beef trade between provinces, or between a province and the rest of the world is specified in C R A M . Since most external Canad ian beef trade involves the U . S . , this analysis w i l l then define trade between Canada and al l countries as trade wi th the U . S . alone. In addition, a livestock pool acting as an intermediate trading location is included in the model and this pool m a y trade wi th any province and the rest of the world since it is inefficient to identify a l l shipping routes and incorporate them into the model. A s a pre-condition of this pool, the shipped-out quantities from the pool are a lways less than or equal to those shipped-in. The reason is that the pool does not have any capacities for producing or consuming beef and acts only as a trading place. The quantities shipped v i a the pool avoid defining a l l specific routes. There are seven types of beef shipment activities in the trade blocks of C R A M : slaughter heifers and steers, cows, bulls, feeder (or weaned) calves, feedlot yearlings, high and low quality beef. Since trade for any one of these commodities is modelled in a s imilar fashion the mat r ix structure and their explanations are s imilar to that for weaned calves, presented in Figure 3.4. For a more detailed explanation, a portion of the weaned calves trade mat r ix is described as follows. The columns consist of eight sets of activities: 1. Interprovincial trade 2. Trade between each province and pool 3. Imports of each province from the world Interprovincial Trndt Trade between Province & Pool Inlerprovincial Trnde N'et Exports Net Imports Aggregate Import Cost Trad Levc Imp. Exp. J « cZ « £ S S e SSSS3SS3333 o o o o o o o o o o G.a.Tuo.0. 22332 — n « C 3 3 3 3 3 3 c = i OCfa. 3 3 c o o o o o o > > > :^  > 222S2S 1-S o 32 < < < to co wS ^ ^ o cy • c -' " ^ a 0 1 c a "o"o"o"o"o O 0 0 o o 'a. o. a. a. a. ooo • s l ! = si < (/> O Gfz. •i e ' - « o S - 2 £ c 3 °-2 < i o 5 o ore. 5 •-S c J * « o o — « ™ c ?. o £ S o o ? Obj. a 7 s 0 T.C. a a a a i a a . a a a a a a a a a a a a a a a a a a a a a a s 0 B/A Alt Suk. M.n. Ont Que. Pool Wor. H I T T r 1 1 1 T T T i l l T T T I T T 1 1 1 1 1 1 TTTI I T T T T •T l l l l i T T T l l l 1 1 1 I 1 1 i i n IT i T £ 0 £ 0 £ Q £ 0 £ 0 £ 1 S 0 Exp. Alt Suk. Man. Ont Que. Pool Wor. 1 l 1 1 I 1 1 1 1 1 1 l l l l -l 1 1 1 1 1 l l l i i i i i i T 1 T T T T I S 0 £ 0 i 0 £ 0 5 0 £ 0 £ 0 Imp. AIL. Suk. Man. Ont Que. Pool Wor. l 1 l l l l . 1 1 1 1 l 1 1 1 1 1 l l l l l l l l l 1 1 1 1 1 1 T T T T l l 1 £ 0 £ 0 £ 0 £ 0 £ 0 £ 0 £ 0 T.C. Alt Suk. M u . Ont Que. Pool Wor. a a > a a a a a a a a a a a a a a a a 1 T T ' T T T T £ 0 £ 0 £ 0 £ 0 £ 0 £ 0 £ 0 Hcun Trade Block of Weaned Calve. 48 4. Exports of each province to the world 5. Net exports to each destination 6. Net imports from each destination 7. Aggregate import cost for each destination 8. Exports and imports at the national level. The rows consist of five categories: 1. Transportat ion costs (recorded at national level) 2. Beef balance rows at each location: each province, pool, world 3. Export rows at each location: each province, pool, world 4. Import rows at each location: each province, pool, world 5. Import costs at each location: each province, pool, world The cost of the shipment appears as " + a" in the national transportation cost row and this is summed into the objective function of the model. In the balance rows i n Figure 3.4, " + represents shipments of weaned calves from the originating point and to destination. For example, exports from Albe r t a to Saskatchewan, Man i toba , Ontar io , pool and the world are shown as +1 and draw upon supplies while imports are shown as -1 and add to supplies. In addition, net exports (or imports) i n the world rows provide revenue (or cost) into the objective function at the nat ional level . Tha t is, the trade activities column section at the national level summar izes the net external trade for weaned calves. If exports exceed imports then Canada receives income corresponding to the positive coefficients in the objective function row. However , i f imports are greater than exports, then a payment is required. Based on the balance rows, export and import rows account for the traded numbers for each originating point and destination. F ina l ly , import cost rows and columns account for transportation costs of import animals from 6 49 originating points. 3.3.3 The Beef Demand Block A s noted in the previous chapter, the objective function of a model is derived from a linear demand curve wi th quantity demand being a function of prices. A quadratic function requires a special algorithm. To overcome this, Hadley (1964) suggested a technique for approximation of non-linear variables involved in constraints or an objective function. Based on this mathematical technique, Duloy and Norton (1975) solved the quadratic problem by linear approximation. M c C a r l and Tice (1982) note the efficiency of l inearizing non-linear variables as follows: "One would apply a quadratic programming algori thm that would work on the Kuhn-Tucker conditions of the problem. This leads to a larger system of equations and also requires the complementary conditions to be dealt wi th . Efficiency software for large problems of this sort is not widely available. The approximation problems above then m a y be desirable for large problems that are to a great extent l inear w i t h a few quadratic variables Approximizat ion of quadratic variables does not make any significant errors." W i t h these advantages of approximation, the objective function from the derived beef demand curve i n C R A M takes the form of a step-wise function. Based on this approach, F igure 3.5 illustrates the beef demand mat r ix for high and low quality beef in western Canada. It contains five sets of basic equations: the weighted values of population for distr ibution of demand in Eas te rn Canada and Western Canada which can be on a population basis for the provinces involved or a per capita disappearance basis, total revenue rows and column activities, beef price, quantities demanded and convexity constraints. The ini t ia l value 50 E o,_8 linearized Activities I linearized Activities *> s! o o 0 0 %. D. 31x2x3x4x5x8x7x8x0x10 H P. yl y2 y3 y4 y5 y8 y7 yfl vfl yl 0 ObJ. a a a a a a a a a a a a a a a a a a a a HQ ac. b«ef Alt Suit Man. Revenue Price Demand Convex Constraint a a a _ a a a a a a a a a a 1^  a a a a a a a a a a I a a a a a a a a a a 1 1 1 1 1 1 1 1 1 1 r 50 so so so so so <0 <0 LQ ac. beef Alt Sdflk. Han. Revenue Price Demand Convex Constraint a a a a a a a a a a a a a a l a a a a a a a a a a I a a a a a a a a a a 1 1 1 1 1 1 1 1 1 1 i 50 50 <o 50 50 50 50 Figure 3.5: Beef Demand matrix for Beef Yields in Western Area 51 for the beef price coefficient is the upper bound price (i.e. the import ceiling price) and the last value is the lower bound price (i.e. the export floor price) as i l lustrated in figure 2.2. Given the estimated elasticities, values of the objective function, total revenue and demand quantities are calculated according to a set of prices which is divided into ten steps wi th in these two bound levels. D a t a corresponding to F igure 3.5 is presented later. 3.4 INCORPORATION OF RETENTION FUNCTION INTO MODELS The retention function was derived in the previous chapter in order to relate beef producers' behaviour to future price variat ions. In this section, a more detailed description of this function wi l l be presented as i t is incorporated into the model. The retention function is closely related to investment (or disinvestment) rules proposed by Trapp . These rules follow and substitute for some of the basic approaches suggested in his paper, even though Trapp uses a different methodology to solve his model. A s a s tar t ing point, Trapp sets up a discounted net present value objective function to maximize profits by v a r y i n g herd size for cattle producers. The objective is to find the opt imal cul l ing age which maximizes the net present value when future price is different to that of the current price. The necessary condition to satisfy the objective function is to select that age at which the discounted net earnings for a cow over her next year of production plus her discounted market value at the end of that year is equal to her current market value. A t this time the choice variable is the optimal cull ing age. I f this net present value at the optimal cul l ing age is greater than zero, the heifer w i l l be placed in the herd. 52 Otherwise, the heifer or cow will be sold for slaughter. Since each cow in the herd is of a different age, it is important to note that the optimal culling age depends on the conditions noted above and it can be expected that older animals will be culled - before younger animals. When new heifers are added into the herd and optimal culling age is extended, the herd size is expanded as a result of this investment by cattle producers. Changes in herds sizes often implies changes in both fixed and variable costs. Conversely, disinvestment can occur by cattle producers and this too will change optimal replacement times. Variations of herd size over time are closely related to fixed and variable production costs. Changes in herd size will affect total costs per unit of product. Variations in herd size, by adding or culling animals, will change average production costs if some factors are fixed and the discounted net present value flows of all other assets currently being held by cattle producers. Decisions to expand herd size by adding replacements eventually drive up fixed producion cost per unit and hence total costs. Likewise, contraction from a larger herd size will change average costs. Therefore, to maximize the net present value for the entire herd it is necessary to consider changes in fixed costs as herd size is expanded or contracted. Hence, the decision rule becomes a comparison of discounted marginal revenues for the entire herd with that of discounted marginal costs. To operationalize these rules, a large amount of information is required a priori including: 1. the expected prices of feeders, slaughter and cull cows over relatively long time horizons between 8 and 16 years, 2. the age distribution of all cows in the herd, 53 3. expected feed and maintenance costs of a cow/calf pair over the planning horizon, 4. expected weaning rates of calves born to a cow at various ages, 5. expected death losses of cows at various ages, 6. expected weaning weights of a heifer or steer raised by a cow of a given age. It is unreasonable to expect that this type of information for cows of different ages over a long time horizon w i l l be readily available at aggregate levels. However , u t i l iz ing some of Trapp's assumptions it is possible to determine whether beef cattle divided by sex and some age groups should be retained or culled over a short time horizon. G i v e n that Trapp 's rules are difficult to incorporate into the C R A M model an alternative approach has been proposed. Other reasons for not following Trapp 's approach include (a) a mult i-year period ranging of 8 to 16 years is required, (b) i t would be also necessary to disaggregate the herd size by age groups, (c) data required for his analysis is not available. I f the preceding information were available and a special a lgori thm for solving the problem was constructed, then it would be feasible to also allow for investment and disinvestment decision rules more accurately. Instead, econometrically estimated behavioral responses of retention functions w i l l be used. In i t ia l ly , it is necessary to specify the relationship between inventory of beef cattle of the various classes and price changes. Assume the general form of the stock retention function is as follows; S = S(X), X = ( x i> x 2 x n } ' ( 1 ) 54 Taking the total differential for equation (1) dS = Z 9S/9x.* dx. (2) where the right hand side term determines the amount of change in the retained stock, S, resulting from an infinitesimal change in one of the independent variables. If we assume that the retention function is linear for simplification,. S = a„ + a *x. + a *x„ + + a *x " (3) 0 1 1 2 2 n n Then, taking partial derivatives for equation (3) with respect to X, ds/dx.= a. (i=l, n)' (4) Equation (2) can be changed as follows, dS= Ea.*dx. (5) In discrete time, equation (5) can be written for a specific choice variable i (i.e. ceteris paribus except variable i) as the following difference equation: S t + 1 " S t = a i * ( x t + l " x t } ( 6 ) where Sfc = Stock at time t (opening stock), Sj. + ^ = Stock at time t+1 (closing stock), x. = Level of variable i at time t (current price), i,t x. = Level of variable i at time t+1 (expected price). 1 j t i _L The elasticity of the retention function with respect to x. can be defined as follows: E= (dS/dx.)*(x. ,/S) (7) 1 1. b Therefore, each partial derivative can be derived from the corresponding elasticity as follows: 55 a. = dS/dx. = (S7x. J * E (8) 1 I t i , t Consequently, given the opening stock (S^.), the levels of each independent var iable (x.) at time t and t+1, and the set of elasticities, the closing stock ( S t + ^ ) can be computed. In the previous section the beef production mat r ix was explained in order to describe the relationship between production activities wi th in a single period. The beef production mat r ix contained the retention function activities showing this par t i a l enodogenization of the closing stocks. Opt imal closing stocks are determined by the future price of the beef an imal w i th the constraints noted above. Therefore, the coefficients, a., derived in this section were incorporated into the beef production mat r ix . Wi thout the right hand side value prespecified as i n the earlier version of C R A M , the size of closing stocks is determined according to the given elasticities of the retention function. A n estimation of elasticity for each animal class specified is required. . In chapter 4 different elasticities are provided for these different an ima l categories. 3.5 THE EQUATIONS OF THE BEEF MODEL The preceding sections described the structure of the beef model w i t h reference to representative mat r ix tableaus. This section more clearly restates i n equation form each equation defined in this portion of C R A M . Some of these equations define other variables not specific to the beef sector but necessary to l ink the beef sector wi th the rest of the economy. A numeric definition of variables and coefficients is avoided in order to clarify this presentation. 56 A. Beef sector constraints 1. Beef opening stocks NUMBER OF EACH < TYPE OF ANIMAL FED AT START OF YEAR 2. Beef balance rows (a) Cow balance COWS RETAINED AT YEAR < END + CULLED REPLACEMENTS SPECIFIED OPENING STOCKS OF EACH TYPE OF ANIMAL COWS AT START OF YEAR - CULLED COWS + REPLACEMENTS AT START OF YEAR - COW AND REPLACEMENT DEATH LOSS (b) Weaned calf balance STOCKERS + FEEDLOT CALVES RETAINED AT YEAR END + FEEDER CALVES SHIPPED OUT OF PROVINCE BIRTHRATE TIMES (COWS + REPLACEMENTS) AT START OF YEAR + DAIRY CALVES TRANSFERRED TO FEEDLOT + FEEDER CALVES SHIPPED INTO PROVINCE (c) Yearling balance FEEDLOT YEARLINGS + REPLACEMENT HEIFERS AND BULLS + FEEDLOT LONG YEARLINGS (d) Bull balance NUMBER OF BULLS RETAINED AT YEAR END (e) Replacement heifer cull REPLACEMENTS CULLED STOCKERS AT START OF YEAR BULLS AT START OF YEAR + REPLACEMENT BULLS < REPLACEMENTS AT START OF YEAR (f) Bull cull 57 CULL RATE TIMES BULLS AT START OF YEAR NUMBER OF EACH TYPE OF ANIMAL RETAINED AT YEAR END NUMBER OF BULLS CULLED 3. Beef closing stocks SPECIFIED STOCK CHANGE COEFFICIENT TIMES NUMBER OF EACH TYPE OF ANIMAL AT START OF YEAR 4. Number of beef animals slaughtered NUMBER SLAUGHTERED 5. High and low quality beef balance (HQB NUMBER OF BEEF AND DAIRY COWS SLAUGHTERED + NUMBER OF FEEDLOT CALVES AT START OF YEAR + NUMBER OF FEEDLOT LONG YEARLINGS AT START OF YEAR ADJUSTED FOR DEATH LOSS + NUMBER OF FEEDLOT YEARLINGS + NUMBER OF REPLACEMENTS CULLED + NUMBER OF BULLS CULLED + NET IMPORT OF SLAUGHTER ANIMALS and LQB) QUANTITY OF DRESSED HQB (LQB) SHIPPED OUT OF PROVINCE + NUMBER OF SLAUGHTER ANIMALS SHIPPED OUT OF PROVINCE TIMES AVERAGE HQB (LQB) YIELD OF EACH ANIMAL + QUANTITY OF HQB (LQB) REQUIRED TO MEET PROVINCIAL PORTION OF DOMESTIC DEMAND 6. Government payments to beef sector (a) Cow-calf subsector GOVERNMENT PAYMENTS TO COW-CALF RANCHERS < NUMBER OF ANIMALS SLAUGHTERED IN PROVINCE TIMES AVERAGE HQB (LQB) YIELD OF EACH + QUANTITY OF DRESSED HQB(LQB) SHIPPED INTO PROVINCE NUMBER OF COWS, REPLACEMENTS, AND STOCKERS TIMES 58 GOVERNMENT PAYMENT ASSOCIATED WITH EACH (b) Feedlot subsector GOVERNMENT PAYMENTS TO FEEDLOT NUMBER OF FEEDLOT ANIMALS SLAUGHTERED TIMES AVERAGE GOVERNMENT PAYMENT 7. Convexity constraint for demand functions THIS CONSTRAINT ENSURES THAT ONLY ONE STEP (OR A COMBINATION OF TWO ADJACENT STEPS) WILL BE CHOSEN ON THE DEMAND FUNCTION. 8. Total level government payments TOTAL LEVEL OF B. Accounting rows 1. Cash costs (a) Cow-calf and feedlot LEVELS OF GOVERNMENT GOVERNMENT PAYMENTS PAYMENTS FROM EACH SECTOR CASH COSTS TO BEEF SECTOR (b) Feedlot only OPENING + CLOSING OF ALL TYPES OF ANIMALS TIMES CASH COSTS ASSOCIATED WITH EACH TYPE + NUMBER OF YEARLINGS PRODUCED TIMES YEARLING CASH COSTS CASH COSTS TO FEEDLOTS OPENING + CLOSING STOCKS OF FEEDLOT CALVES AND FEEDLOT LONG YEARLINGS TIMES CASH COSTS ASSOCIATED WITH EACH + NUMBER OF YEARLINGS PRODUCED TIMES YEARLING CASH COSTS 5 9 2. Feed use AMOUNT OF EACH TYPE OF FEED USED IN FEEDLOT SECTOR 3. Provincial yields (a) Cow-calf and feedlot AMOUNT OF HQB (LQB) PRODUCED BY BEEF SECTOR (b) Feedlot OPENING + CLOSING STOCKS OF FEEDLOT CALVES AND FEEDLOT LONG YEARLINGS TIMES AMOUNT OF EACH TYPE OF FEED REQUIRED BY EACH + NUMBER OF FEEDLOT YEARLINGS PRODUCED TIMES YEARLING FEED REQUIREMENTS TOTAL NUMBER OF BEEF ANIMALS SLAUGHTERED TIMES AVERAGE HQB (LQB) YIELD OF EACH AMOUNT OF HQB(LQB) PRODUCED BY FEEDLOT SECTOR 4. Production cost NUMBER OF FEEDLOT CALVES, YEARLINGS AND LONG YEARLINGS SLAUGHTERED TIMES AVERAGE HQB (LQB) YIELD OF EACH TOTAL PROVINCIAL COSTS TOTAL LIVESTOCK COSTS + TOTAL CROP COSTS C. Objective function MAXIMIZE TOTAL AREA UNDER CHOSEN STEP OF DOMESTIC DEMAND CURVE FOR EACH COMMODITY + REVENUE FROM EXPORTS TO WORLD - COST OF IMPORTS FROM WORLD -TOTAL CASH COSTS OF PRODUCTION FOR CROPS AND LIVESTOCK 60 - T R A N S P O R T A T I O N C O S T S ( R E G I O N T O P R O V I N C E , I N T E R P R O V I N C I A L , A N D I N T E R N A T I O N A L ) + T O T A L L E V E L O F G O V E R N M E N T P A Y M E N T S T O A G R I C U L T U R A L S E C T O R These s t ructura l equations show that the beef sector is closely l inked wi th other sectors par t icular ly the grains and forage sectors and the dai ry sector. A s s u m i n g that these l inks are ignored, it is possible to analyze changes in the beef sector alone or i f not ignored changes in one sector and its impacts on another. Fo r example, feed grain prices impact upon beef production decisions and these l inks are specified in C R A M . 3.6 THE EMPIRICAL MODEL This section w i l l present portions of the data base as specified as in C R A M as these pertain to the model and matrices. The activities i n the model, as noted in the previous section, are composed of three major sectors: production, shipment and market ing. Since most of the data used in C R A M is detailed elsewhere i n a Technical Report (Webber, et a l , 1988), this paper w i l l only describe part of this data as it relates to this study. 3.6.1 Beef Data Files Costs, feeding requirements and yield data for each class of animal specified in the model for each of the provincial herds are required. These data for Alber ta are presented i n Table 3.1 i n order to il lustrate these data needs. E a c h row corresponds to the act ivi ty given to a part icular category of beef. The first four columns specify the inputs, and the last two columns specify the yields to be Table 3.1 Input Requirements and Y i e l d by A n i m a l Category in Alber ta CowsReplacements Feedlot Feedlot Stocker Feed.L. Bul ls Calves Year l ings Year l ings Cash Cost 26.33 13.00 9.29 6.38 5.03 16.52 26.33 (Dollars) Forage 2.39 2.39 1.832 0.515 1.02 0.283 2.37 (Tonnes) Pasture 3.324 3.324 -- 1.49 4.32 (Tonnes) Bar ley -- -- 59.755 46.067 14.96 47.01 (Bushels) A B C beef -- 533.8 618.67 671.83 -- 718.8 Pounds) D beef 597.6 -- -- - -- -- 866.2 (Pounds) 62 expected from each animal category. Cash costs are estimates of the cost to car ry one an imal over one year. The pasture, forage and barley requirements specify possible diets required to feed one animal in a part icular category over one year. The A B C beef and D beef categories of high and low quali ty beef specify the yields from culled and fed animals . The product from younger beef animals is usual ly high quali ty beef ( A B C grade). Cows and bulls result in low quality beef (D grade). A n i m a l s transfer from one category to another as they pass through the beef cycle. Consequently, some intermediate animal class categories have no yield associated wi th them (e.g. stocker, pasture yearling). 3.6.2 B e e f C o e f f i c i e n t F i l e s Table 3.2 specifies biological parameters for the beef herd such as cull ing rates, replacement ratios, calving rates, and death rates, and cul l ing rates for each provincial herd. These coefficients are important in that supply demand balances for the balance rows in Figure 3.2 are dependent upon these coefficients: provincial cull rates, replacement ratios, calving rates and other herd related rates. The cull ing rate represents that proportion of the beef cow herd is culled annual ly . The replacement ratio is used to determine the number of beef heifers reserved as replacement for the breeding herd, and the calving rate determines the number of calves entering the herd. C a l f loss and cattle deaths represent the proportion of the cal f and cattle lost annually. 63 Table 3,2 Physical Values of Beef Cattle (Percentages) Province Cull Replacement Calving Calf Cattle Bull Rate Ratio Rate Losses Deaths Cull B.C. 0.15 0.195 0.74 0.099 0.031 0.377 Alt. 0.09 0.135 0.89 0.044 0.025 0.377 Sask. 0.115 0.160 0.85 0.081 0.023 0.377 Man. 0.15 0.195 0.86 0.090 0.020 0.377 Ont. 0.15 0.195 0.72 0.078 0.026 0.377 Que. 0.08 0.195 0.78 0.078 0.019 0.377 Mar. 0.15 0.195 0.71 0.093 0.02 0.377 64 3.6.3 Beef Retention Function Files The retention function files for beef are specified for each province corresponding to five categories of beef -- cows, replacements, stockers, feedlot calves and feedlot long yearlings. Retention function information, as shown in Table 3.3, is specified by animal type and includes: opening stock level number of arguments in the retention function where each argument is a variable determining closing herd size for each argument: (1) elasticity of stocks with respect to price of the good, (2) current market price of the good, (3) current government payment to producer of the good, (4) expected market price, (5) expected government payment to producer. For example, in Table 3.3 beef cattle stocks are a function of the price of beef and the price of feed grain. All prices and payments are expressed as a percentage of current market price which is set at 100% (i.e. government payments are expressed as dollars per $100 of market receipts). The government payment (adjusted for any division of market price from the index of 100) is added to the market price to determine the effective price, or unit revenue, to the producer. The percentage change in effective producer price is determined exogenously through changes in market forces and changes in policies as these affect producers. Elasticities shown in Table 3.3 for each animal category will be explained in more detail later when the different scenarios to be analyzed are detailed. Given the above information, the closing stock level can be determined, and the closing stock coefficient is then calculated as the closing stock divided by the Table 3.3 Beef Retention Function Files Category of Beef Option Coefficient Number of Arguments Opening Rang Stocks COWS ELAS = 0.25 ELAS = -0.22 REPLACEMENT ELAS = 0.44 ELAS = -0.22 STOCKERS ELAS = 0.20 ELAS = -0.20 FEEDERS ELAS = 0.20 ELAS = -0.20 F.L.Y. ELAS = 0.50 ELAS = -0.30 1 1.0 CMKT=100 CUGP = 7.66 CMKT=100 CUGP = 1 1.0 CMKT=100 CUGP = 7.66 CMKT=100 CUGP = CMKT=100 CMKT=100 1.0 CUGP = 7.66 CUGP = 1 1.0 CMKT=100 CUGP = 7.66 CMKT=100 CUGP = 1 1.0 CMKT=100 CUGP = 7.66 CMKT=100 CUGP = EMKT=100 EMKT = EMKT=100 EMKT = EMKT=100 EMKT = EMKT=100 EMKT : EMKT=100 EMKT = EMKT=100 EMKT = EMKT=100 EMKT-EMKT=100 EMKT-EMKT=100 EMKT-EMKT=1'00 EMKT = 1,130,000 0.£ 138,000 0.£ 1,008,510 0.£ 273,093 0.£ 225,902 0.1 CMKT = CURRENT MARKET PRICE CUGP = CURRENT GOVERNMENT PAYMENTS EMKT = EXPECTED MARKET PRICE EXGP = EXPECTED GOVERNMENT PAYMENTS 66 opening stock level. The range parameter is used to set a biological l imi t on the change in stock levels, and is expressed as a proportion of opening stocks. The two additional items specified in Table 3.3 are the option number and the closing stock coefficient. Three options for determining closing stocks are allowed. If option 1 is specified, then the closing stock coefficient provided w i l l be used. Option 2 is the retention function approach described above. Option 3 al lows one to specify the lower bound on closing stocks as the right hand side of the appropriate constraint. I f option 1 is requested then the opening stock levels specified i n the retention function file should be equivalent to the corresponding opening stock values in the ' r ight hand sides' file. 3.6.4 Government Payments Government payments are associated wi th production activities in the model. Table 2.1 described in section 2.1 sets the level of payments to producers in the base case examined in this study. For accounting purposes, government payments are recorded at each provincial level. Payments are calculated first to the provincial level, and then aggregated to the national level from which they are transferred to the objective function. Thus , the level and distr ibution of payments w i l l affect the solution. Government payments also affect the solution v i a the stock retention functions as explained in the previous section. 3.6.5 Transportation Cost Data A s noted in the previous section, shipment of beef or live animals is based on the concept of a spatial equil ibrium model. Transpor ta t ion costs are considered to Table 3.4 Transportation Costs of Cattle and Dressed Beef Between Provinces and Between Canada and World Routes' Slaughter Feeder Feeder Dressed Heifer &Steer Calves Yearlings Beef ($/10001b) ($/5001b) ($/7001b) ($/lb) B.C. to Alt. ± 35.130 ± 17.565 ± 36.35 -0.021 Alt. to Sas. 24.321 ± 12.211 -18.46 — Alt. to Man. 45.940 ± 23.070 ~ — Alt. to Ont. 116.202 58.101 87.15 0.070 Alt. to Que. 137.821 - - 0.083 Alt. to Mar. — — — 0.098 Sask. to Man. 21.619 — 16.31 — Sask. to Ont. 91.881 — 68.91 0.056 Sask. to Que. 113.500 ~ — 0.069 Sask. to Mar. 140.262 — — 0.084 Man. to Ont. ± 70.262 35.131 52.70 0.042 Man. to Que. 91.881 — 68.91 0.056 Man. to Mar. — — — 0.071 Ont. to Que. ± 21.619 ± 10.810 ± 16.22 ± 0.015 Ont. to Mar. ± 48.643 24.321 -36.48 0.029 Mar. to Que. 27.024 -13.512 - -0.017 B.C. to Wor. 3.783 ± 1.892 2.84 -0.202 Alt. to Wor. ± 9.458 4.729 7.10 0.006 Sas. to Wor. 8.918 4.459 6.69 0.005 Man. to Wor. ± 3.783 1.892 2.84 0.002 Ont. to Wor. ± 7.026 ± 1.892 -5.27 -0.204 Que. to Wor. 3.783 ± 1.892 — -0.202 Mar. to Wor. ± 3.783 1.892 — -0.202 Note "±" means the costs of shipment out and in. (i.e. 35.130 means B.C. to Alt. or Alt to B.C.) "-" means the opposite direction. (i.e. -0.021 in B.C. to Alt. is the cost of Alt. to B.C.) 68 be important in determining shipped amounts. Table 3.4 represents transportation costs for live animals and dressed beef between some of the regions defined in the model, for example, between B . C . and Alber ta . Since shipments can be executed in both directions or one way only, a " ± " in Table 3.4 means that trade routes in both directions due to price differences between two provinces are specified in the model. Some trade routes are not specified to reduce model size. However a l l trade routes are data deriven and are generated as required. 3.6.6 Demand Data Domestic demands for beef are generally specified at western, eastern or nat ional levels. In the older version of the C R A M model, a fixed domestic price was stated in the objective function and a fixed level of consumption was specified in the s t ructural bounds section. In this case domestic demand had to be met before dressed beef and live cattle could be exported or imports needed to take place. If no bound is placed on consumption then domestic demand was perfectly elastic. If we change the assumption of exogenous prices in the demand function, the objective function becomes quadratic and this is approximated by piece-wise linear segments. The following additional information must be specified in the domestic demand file: 1. demand function parameters including a point on the curve (price-quantity pair), and the demand elasticity, 2. the segment of the demand curve to be considered, 3. the step function row codes for the price- quantity pairs, and for the convexity constraint. A revenue row is also specified. The step function w i l l be calculated over the segment of the demand curve Table 3.5 Demand Data at National Level Import Export Elasticity Price price HQ Beef 4336 3390 0.74 LQ Beef 2920 2400 0.41 Weighted Values of Population B.C. 0.39 Ont. 0.50 Alt. 0.32 Que. 0.37 Sask. 0.14 Mar. 0.13 Man. 0.15 70 specified. This segment is defined by an upper and lower bound price. The upper bound becomes the import price and the lower bound the export price as noted . in chapter 2. The export and import prices include both transportation and tariff effects. When a l inear approximation is requested for beef demand, its price in the objective function is replaced by a set of areas under the demand curve corresponding to the various steps. F o r this reason, the objective function is no longer net revenue, but rather consumer plus producer surplus. In order to allow for consumption i n each province, demand levels once calculated on a western or eastern Canada basis are distributed to each provincia l base on population or per capita consumption levels. Table 3.5 shows demand elasticity, upper and lower bound and weighted values of the population. 3.7 SUMMARY The purpose of this chapter was to present an empir ical basis for the beef model considered in the previous chapter and to describe its structure and data. In order to develop the empirical model in the beef sector, the overal l framework of C R A M was considered. Production, trade and demand matricies related to the beef sector were also detailed. The method of incorporating the elasticities of the retention function into the production mat r ix were described. In addition, behavioural equations included in each mat r ix were specified. Information and data used to determine the coefficients of s tructural equations were explained in this chapter. CHAPTER 4 RESULTS This chapter details the results of the study. There are five sections. Section 4.1 examines problems in model validation and describes the procedures followed in order to validate the model developed in this study. Section 4.2 provides a basis for the sensitivity analysis conducted based upon different own elasticity parameters selected in this study. These retention function elasticities are important because results depend . on the values chosen. Section 4.3 briefly introduces some of the economic measures selected to summarize and characterize in the beef sector in the base case where 1986 is selected as the base year. Section 4.4 analyzes the results from the model and details some of the changes that may be expected if government payments to producers are removed. Section 4.5 briefly summarizes this chapter. 4.1 MODEL VALIDATION The model developed in this study examines and evaluates changes in the Canadian beef sector under both the current and future policies as these relate to this sector. It is therefore important to consider whether the model adequately abstracts from reality and is useful as a policy analysis tool. On the issue of validation, McCarl (1984) suggests; "A model need not mirror the perceived reality perfectly; rather it needs to abstract "adequately" for the model's anticipated use Exercise of model validation, referring to activities designed to determine the usefulness of a model, can improve model credibility; provide a "better" platform from which to make policy or operational decision recommendations; contribute to evidence on the usefulness and applicability 71 72 of theory and modeling methods; provide insights into proper ways of modeling; and increase the likelihood of models and their results being used by decision makers." He argues further that models can be used for three purposes: structural exploration, prediction, and prescription. The current model is developed for structural exploration and to examine the consequences of el iminat ing the government payments i n beef sector. Val ida t ion for predictive power is also important since; (a) it indicates the degree to which predictions should be believed, (b) it helps in avoiding prediction errors result ing from inval id models, and (c) i t permits statements regarding the model's abi l i ty to predict. G iven this background, M c C a r l presents seven categories or methods to attempt validat ion as follows: 1. P lausibi l i ty test — this test examines whether the model creates "plausible" results. 2. Possibil i ty test — this test examines whether it is possible for the model to duplicate a situation real is t ical ly. 3. Supply function test — this test examines whether the model's marg ina l cost of production is close to the observed price. 4. D u a l supply function test — this test examines whether production at the observed price is close to the observed production. Here, prices are fixed at the expected price, and output compared wi th actual output. 5. Predict ion test — this test examines the abili ty of the model to predict outcomes, when specified wi th parameters "identical" to those leading to that outcome. 6. Predictive change test — models m a y not need to predict exactly as long as 73 they predict the magnitude or possibly even the direction of change accurately. 7. Predictive t racking test — the ability to predict change on time m a y be inadequate i n terms of validation. Val ida t ion of the beef model detailed in this paper follows several of the procedures presented by M c C a r l . The basic procedures followed are listed in Table 4.1. Ini t ial specifications of the model did result in infeasibilities and solutions which meant misspecification of the structure. Misspecification requires re-examination of the logic, equations and data. In these tests, it was part icularly difficult to examine the beef sector of the model ignoring the non-beef sectors. The agricul tural economy is too closely linked. Transfer of feed supplies from the crop sectors to the beef sector, the transfer of calves from the dairy sector to the beef herd, the shipment of beef and animals between provinces and other links makes it difficult to val idate the beef model on a single sector basis, or on a province by province basis. Inconsistencies in various data sources and the classification of animals by the var ious age categories required assumptions regarding bir th and death rates and a transfer or ageing of animals from one category "to another. Agricul ture Canada classifications and statistics are different from those of Statistics Canada. In terms of val idat ion over the short run , the typical accounting flow of opening stock plus bir ths , plus transfers and shipments in , are equal or less than closing stock, plus sales, plus deaths, plus transfers out and shipments out. In the evaluation of government payments the ex post number of cattle without payment to producers are less than ex ante ones wi th payments. But , the size of the herd in Canada has shown fluctuations over time depending on price and profit levels of the industry and these are cyclical . Therefore, an accounting of an imal stocks by category and provinces over a ten year horizon was necessary to validate livestock balances for different 74 Table 4.1 A Procedure for Model Validation Step 1. Enter the parameters, constraints, alternatives, etc. which implement the particular validation test. Step 2. Obtain a solution to the model. Step 3. Evaluate the results. There are two possibilities for the results. Either the model has been solved with an answer or the model has failed. (a) If the model has "failed", discover why. Programming models may either unbounded or infeasible. Simulation models may exhibit numerical difficulties or may incorporate equations which can not feasibly represent the particular variable values. Repair the model and go to Step 2; otherwise go to Step 6. (b) If the model has a solution, then utilize association measures to discover the degree of correspondence between the outcomes set and the model solution. These measures should be applied to all possible output variables, and imputed prices. Aggregates, such as income and total land area, should be examined. Go to Step 4 if measures indicate a sufficient degree of association. Go to Step 5 otherwise. Step.4 Prepare to do a more complex validation test going to or, going to Step 1, or determine that the model is not invalid for use and terminate the validation. Step 5. Consider whether (a) the "reality" parameter-outcome set data are consistent and correctly calculated, (b) the data are properly entered into the model structure, and (c) the assumptions underlying the model structure are proper and correct. If the deficiencies in the model leading to the invalid solution are corrected, go to Step 2 and repeat the validation test, otherwise go to Step 6. Step 6. If the model is judged invalid then consider whether the model needs to be revised, discarded or qualified. If the model is revised then go back 'to either Step 2 or one of the earlier validation tests dependents upon the extent of model revision. If the model is qualified then either continue this validation text -- if there is anything remaining to be done (go to Step 2), move on to higher validation texts (go to Step 1), or accept the model for use (terminate the validation exercise with qualifications). Source: McCarl (1984) 75 provincial herd sizes. Es t imates of these livestock data are described in the next section. Steps 2 and 3 described in Table 4.1 lead to a solution to the model and an evaluation of the results. In considering the "possibility test", questions regarding the abili ty of the model to duplicate the 1986 base are examined. After examining many different solutions, solutions of the model consistent wi th outcome sets are used and reported. Tests also involved f ixing decision variables at set levels and examining model results. The year 1986 is used as the base year, although part of the input series involves annual data over the five year period 1982 to 1986. The levels of livestock activities i n the model, as reported, are those for 1986. In terms of the predictive change test where the magnitude or even the direction of change needs to be considered the model has been examined closely. A s indicated, following the predictive change test, models m a y not need to predict exactly provided they predict the magnitude or possibly even the direction of change accurately. In this research, impacts of an elimination of government payment on beef economic activities are carefully reviewed in terms of the beef cattle theory represented by J a r v i s and Trapp . Three different scenarios of predictive values are obtained and these v a r y wi th the different elasticities assumed. The elasticities used in the base case are derived from the F A R M model and extensive testing and validation of this model over approximately fifteen years, when used in a forecasting and policy analysis sense, has been done. G iven the complexity of model validation, par t ia l results of the possibility test are noted in Table 4.2. The classification of the beef herd into the livestock classes is required since the volume of slaughter beef supplied to the marke t is a function Table 4.2 Comparison of Statistics Canada Est imates of Herd Size wi th Model Est imates Number of Cattle on J a n u a r y ls t(1986) — Statistics Canada ('000 Head) Cows Heifers Steers Calves Bu l l s Tota l B . C . 180.0 43.0 34.0 220.5 11.5 489.0 A l t . 1130.0 271.0 315.0 1075.0 61.0 2852.0 Sask. 760.0 154.0 110.0 590.0 37.0 1651.0 M a n . 325.0 87.0 73.0 280.0 18.0 783.0 Western 2395.0 555.0 532.0 2165.5 127.5 5775.0 Ont. 325.0 268.0 405.0 700.0 30.0 1728.0 Que. 172.0 50.0 47.5 263.0 27.5 560.0 M a r . 56.2 •27.5 36.8 88.4 4.8 213.7 Eas te rn 553.2 345.5 489.3 1051.4 62.3 2501.7 Canada 2948.2 900.5 1021.3 3216.9 189.8 8276.7 Source: Livestock and animal products statistics, (Cat. 23-203), 1986. Opening Stock Numbers in Model ('000 Head) Breeding Replacement Stokers F . L o n g Feedlot Bul l s Tota l H e r d Year l ings Calves B . C . 180.0 37.0 103.6 40.0 59.5 12.5 432.6 A l t . 1130.0 138.0 1008.5 225.9 316.1 64.0 2882.5 Sask. 760.0 111.0 490.4 153.0 106.3 38.0 1658.7 M a n . 325.0 55.0 230.5 61.6 100.9 19.0 792.0 Western 2395.0 341.0 1833.0 480.5 582.8 133.5 5765.8 Ont . 325.0 93.0 432.9 507.3 352.0 31.0 1741.2 Que. 172.0 40.0 129.8 17.0 310.2 27.0 696.0 M a r . 56.2 15.1 51.1 0.0 59.4 4.8 186.6 Eas te rn 553.2 148.1 613.8 524.3 721.6 62.8 2623.8 Canada 2948.2 489.1 2446.8 1004.8 1304.4 196.3 8389.6 77 of these categories. A comparison of Statistics Canada an imal categories and numbers wi th categories used in this study is shown. Est imates of Statistics Canada data needed to be redefined based on the production schedule for cow-calf and feedlot operators defined in this research. The classification categories of Statistics Canada are not suitable from a biological modeling aspect. A s shown i n Table 4.2, there are smal l differences between observed opening stock numbers and model estimates. In summary , the literature dealing wi th model validation suggests that the process is par t ly scientific and part ly subjective. The approach adopted in this study is to examine all results under the many different scenarios and test for inconsistencies between the model and observed behavior and results. 4.2 THE SCENARIOS TO BE EVALUATED Opening stock numbers in the beef sector are important i n that these determine beef supplies to the market , trade, feed usage levels and eventually market prices. Current opening stock levels have been established based upon investment behavior. A s described earlier, herd size changes w i l l v a r y wi th changes in the level of government payments depending on the response of producers' retention functions and assumptions regarding different elasticities. Econometr ical ly , it is difficult to estimate cow-calf elasticities for supply responses to the marke t on a regional basis and by each category of an imal . Estimates of supply elasticities va ry depending on the researcher, the structure of the model, the time frame and other considerations. Therefore, any estimate of the impacts of changes i n government policies wi th respect to payment levels to producers w i l l depend upon the elasticity 78 estimates used. Th i s research provides three scenarios using different supply elasticities and changes to the Canadian beef sector in a comparative static sense are reported. A s noted i n the previous chapter, the retention function has a positive slope wi th respect to future prices. Th i s characteristic is associated wi th a long-run supply response of animals at the fa rm level. A s Ja rv i s and Gordon argued, the supply curve of beef an imals over the short run can be negative but becomes positive over the long run. G i v e n this result and since this study deals wi th a long run equil ibrium situation, several elasticities, as shown in Table 4.3, are extracted from the published l i teratures. Genera l ly , the estimated elasticities ranges from 0.4 to 1.83. Wi th in these ranges this study selects estimates from three sources in order to evaluate the changes in the base solution. Solutions are defined at specified points on the retention function. The base case represents a case wi th government payments set at their current levels. Unde r this si tuation opening and closing stock numbers are set exogenously. H e r d sizes are based on observed levels for 1986. Scenario #1: Elast ici t ies provided by the F A R M model as estimated from various functions related to the Canadian beef sector. The beef sector of the F A R M model has been revised and reestimated over an extended period. The estimates shown in Table 4.4 are the most recent. This model estimates the livestock inventory function on a quar ter ly period covering the period from the first quarter of 1972 to the fourth quarter of 1983 for eastern and western Canada. Provinc ia l supply or demand elasticities are not estimated. The model is dynamic and simultaneous because it uses the simulated values of lagged endogenous variables and Table 4.3 Retention Function Elasticit ies Elas t ic i ty Country Time Period Period of A n a l y s i s F A R M See Table 4.4 Canada L o n g R u n 1972-1983 Gardner 0.6 U . S . L o n g R u n 1910-1980 Gordon 1.41 Canada Long R u n 1956-1982 Goddard 1.83 Canada L o n g R u n 1970-1980 0.4 U . S . L o n g R u n 1970-1980 1.00 E C L o n g R u n 1970-1980 0.42 N e w Zealand L o n g R u n 1970-1980 0.45 Japan Long R u n 1970-1980 Tyers & 0.6 Canada L o n g R u n 1961-1983 Anderson 0.72 U . S . Long R u n 1961-1983 1.02 E C Long R u n 1961-1983 0.80 J apan Long R u n 1961-1983 80 also uses the simulated values of the endogenous variables on the right-hand side of the equations. Even though some of the behavioral equations w i th in the regression model m a y be debated, and i t has some statistically insignificant estimates, the model, as a whole, fits well when simulated over a historical or forecast period. Therefore, we adopt the estimated elasticities provided i n Table 4.4, from the F A R M model, as our most important scenario results in this study. Scenario #2: Gardner(1987) has provided estimates of elasticities of the U . S . agricultural commodities estimated using a production function approach. H i s model was estimated using annual data over 1910 to 1980. H i s own-price and lagged dependent variables are long run in a Ner lovian sense. H i s estimated own price elasticity for herd size, as shown in Table 4.3, is 0.6. Th is value is greater than the elasticities of beef cow numbers for the F A R M model in the west and less than elasticity of only feeder yearlings in east. In the empir ica l tests we examine the impacts of using this estimated elasticity wi th the assumption that supply response of the beef producers in a l l provinces is equal and given as 0.6. Scenario #3: Gordon has studied the Canadian cattle sectors and focused on herd size inventories at the aggregate level. H i s estimated model is based on the Cobb-Douglas functional form. The estimation procedure includes an autoregressive integrated moving average ( A R I M A ) to represent the expectation process for prices. The model is examined in terms of the cow-calf producers and data covers from 1956 to 1982. He also used cross sectional data. The estimated long run elasticity in his model, as shown in Table 4.3, is 1.41 and represents the response to price changes for a l l the animals held by a rancher. This estimate is derived for the aggregate level wi th a focus on the western Canada. Th i s estimate is greater than Table 4.4 Retention Funct ion Elast ici t ies in F A R M Model O w n Price Elasticit ies Feed Price Elast ies Western Eas te rn Western Eas t e rn Canada Canada Canada Canada Cows 0.25 0.40 -0.22 -0.14 Replacement 0.44 0.40 -0.22 -0.14 Stackers 0.20 0.25 -0.22 -0.14 Feeders 0.20 0.25 -0.20 -0.08 F . Year l ings 0.50 0.75 -0.20 -0.08 82 that provided by the F A R M model and Gardner and is chosen i n this study to represent a fa i r ly elastic response to price changes. H a r l i n g and Thomson (1983) have analyzed the economic effects of government intervention on Canadian agriculture using supply and demand curves. In their analysis they set the range of m i n i m u m and m a x i m u m elasticities for the beef sector between 0.56 and 1.87. Therefore, elasticity values of the latter two cases (i.e. 0.6 and 1.41) are considered reasonable even though they do not represent the properties for a l l classes of each animal and province in the model. Goddard (1988) and Tyers and Anderson (1988), as shown i n Table 4.3, estimate long-run supply elasticities for several countries. U s i n g the H a r l i n g and Thomson method of analysis , the estimates of supply elasticities set a range of 0.4 to 1.83 as m i n i m u m and m a x i m u m values. However , as shown i n Table 4.4, elasticities from F A R M model range from 0.2 to 0.75 for each animal in western and eastern Canada . These values are more detailed than others and these min imum values w i l l be used i n this study. The largest elasticity of the long run supply curve in Table 4.3 is 1.83. Even though this value can be used as a m a x i m u m value, Gordon's estimate is chosen as more suitable because it is closer in range to the estimates of the F A R M model. 4.3 ANALYSIS OF THE BASE CASE It is important to review provincial herd sizes and government payment levels for the base year of the model. The base year for this analysis is 1986 and opening stock numbers of herd sizes are noted in Table 4.5. Shares of total government payments to the beef sector in each provinces are estimated from Table 4.5 H e r d Sizes by Province, M a r k e t Returns , Government Payment Levels and Beef Sector Earnings for Base Case Herd % of Market % of Gov't % of Total Size Total Earnings Earn, t Payments Earn, t Earning ('000 Hd.) (%) ($ Mil.) (%) ($ Mil.) (%) ($ Mil.) B.C. 399.10 5.16 40.13 69.15 17.9 30.85 58.0 Alt. 2839.50 36.69 517.91 87.48 74.1 12.52 592.0 Sask. 1640.80 21.20 178.85 79.51 46.1 20.49 224.9 Man. 764.70 9.88 137.01 88.10 18.5 11.90 155.5 Western 5644.10 72.94 873.90 84.80 156.6 15.20 1030.5 Ont. 1489.10 19.24 248.72 91.34 23.6 8.66 272.3 Que. 454.50 5.87 60.28 50.97 58.0 49.03 118.3 Mar. 150.70 0.00 24.15 82.35 5.2 17.65 . 29.3 Eastern 2094.30 27.06 333.15 79.34 86.7 20.66 419.9 Canada 7738.40 100.00 1207.05 83.22 243.34 16.78 1450.39 Note f: Provincia l share as % of total provincia l earnings. 84 average payment levels made over the 1981/82 to 1985/86. M a r k e t earnings and beef incomes are estimated wi th the given herd sizes and represents results for the base case. Fo r convenience, the provinces represented in Table 4.5 are divided on a western and eastern Canada basis. Herd composition is divided into five categories: cows, replacements, stackers, feedlot yearlings and calves. In terms of herd size, Alber ta ' s share is largest wi th 37% of the total herd, Saskatchewan is next w i th 21% and Ontario and Mani toba hold 19% and 10% respectively of total herd size. The western provinces' share of the aggregate herd size is 73%, while that of eastern area is 27%. The larger relative share for Western Canada implies that most of the economic activities associated wi th this sector such as production, earnings and other economic indicators are higher in this region of the country. Total government payments to the beef sector i n the base situation are estimated to be $243.3 mi l l ion . This expenditure varies by provinces depending upon herd sizes and payment levels and by the relative sizes of the cow-calf and finishing operators. The beef sector in the Saskatchewan, Mani toba and Ontario receives payments generally less than the relative size of their cow-calf herds while Quebec wi th only 5.9% of the national cow herd receives 23.8% of the total amount of government payments. Based on herd size and sales, market earnings are estimated. M a r k e t earnings are estimated as slaughter numbers or shipments mult ipl ied by farm gate price. In the absence of a l l government payments these amounts are $1.2 billion. Total sector income is $1.4 bill ion. Hence 17% of this is in the form of government payments. Even though marke t earnings in each province are related to herd sizes, 85 the large share of beef income, in Quebec, from government payments distorts this relationship. Fo r example, herd sizes are s imilar between B . C . and Quebec, at approximately 400 thousand head, while beef income in Quebec is twice that in B . C . Despite the relatively large shares that government payments represent of beef sector gross earnings, the recent trade trend toward liberalization wi l l require a reduction or el iminat ion of the government payments to the beef sector. In section 4.4 the three scenarios chosen represent alternative levels of production, trade, cash costs and income, and other changes that m a y be expected when these payments are el iminated, given the elasticities of retention function assumed. 4.4 ANALYSIS OF EACH SCENARIO Under the scenarios reported i n this section one is examining changes that m a y be expected, on a province by province basis, i f government payments to producers are eliminated. Aside from selecting different supply elasticities and report ing changes for each of these parameters it is also feasible to examine policy changes that would reduce payments rather than eliminate them. The model structure would allow for this scenario based on l ikely policy changes wi th in individual provinces or i f agreements between provinces are assumed. For example, an e l iminat ion of a l l input programs, wi th output payments remaining, could be assumed and the changes reported. The range of alternatives that could be considered is extensive. This study has chosen to examine responses that m a y be expected i n e l iminat ing all payments for a l l provinces and details estimates for different supply elasticities. The results are analyzed in terms of a comparative static analys is . Table 4.6 to 4.13 w i l l show these changes. A s noted in the previous 86 section, scenario #1 has different own-price elasticities and feed elasticities for both Western and Eas te rn Canada and they differ by an imal category. These are no provincial differences wi th in each of these two regions. A n own-price elasticity of 0.6 is assumed in scenario #2 and 1.41 in scenario #3 for a l l categories of animals in Canada. 4.4.1 Changes in Herd Sizes Present herd size in each province represents a starting point for this analysis. Current ly , as shown i n Table 2.1, Quebec receives the largest payments per head in the cow-calf sector and investment decisions and herd sizes of producers in each of the provinces have been influenced by these levels. The relationships between herd sizes and total government payments on a province by province basis were shown in the previous section. It is assumed that a l l producers wi l l change their herd sizes following a reduction or an e l iminat ion of government payments. The relative changes w i l l depend upon the relative shares received from the market i n each of the provinces and upon the changes i n expected government payment levels. A t the national level the change in the breeding herd size is downwards wi th a range of 2% for scenario #1 and 12% for scenario #3. Percentage changes are shown in brackets below absolute changes for each scenario. Comparing the base case wi th scenario #1, the herd size i n Quebec is reduced by approximately 10% whereas the adjustment for most other provinces is about 2%. Mani toba cow-calf producers who receive the least assistance (i.e. $16 .41 per head) among al l provinces do not show much change by comparison wi th other provinces. Changes in Manitoba 's breeding herd size amount to 0.98% i n scenario #1. In scenario #2 and Table 4.6 Breeding Herd Size by Province under different Scenarios (Cows, Replacements, and Stockers) ('000 Head) Base Case Scenario #1 Scenario #2 Scenario #3 B.C. 320.6 311.9 (-2.71) 300.2 (-6.36) 272.4 (-15.03) Alt. 2276.5 2238.3 (-1.68) 2178.4 (-4.31) 2047.2 (-10.07) Sask. 1361.3 1329.9 (-2.31) 1286.7 (-5.48) 11.84.8 (-12.97) Man. 610.5 604.5 (-0.98) 595.6 (-2.44) 575.4 (-5.75) Western 4568.9 4484.9 (-1.85) 4360.9 (-4.55) 4079.8 (-10.70) Ont. 850.9 836.7 (-1.67) 825.3 (-3.01) 790.0 (-7.16) Que. 341.8 305.4 (-10.65) 277.9 (-18.70) 191.8 (-43.89) Mar. 122.3 118.6 (-3.03) 115.8 (-5.31) 107.1 (-12.43) Eastern 1315 1260.7 (-4.13) 1219 (-7.30) 1088.9 (-17.19) Canada 5883.9 5745.3 (-2.36) 5579.9 (-5.17) 5168.7 (-12.16) 88 3 which have larger elasticities than those of scenario #1 adjustments are much larger. Changes in herd size are generally proportional to the supply elasticities used. At the provincial level, if base case and scenario #3 are compared, the following changes in breeding herd are noted: B.C. down 15%, Alberta down 10%, Saskatchewan down 13%, Manitoba down 6%, Ontario down 7%, Quebec down 44% and Maritime down 12%. Each province shows fairly dramatic changes, proportional to the elasticity of retention function, as one moves to a situation where government payments are eliminated. 4.4.2 Changes in Supplies to Market Beef supplies to the market are closely related to changes in the breeding herd size. These are also influenced by slaughtering capacities and per unit cost of slaughtering cattle. In the model, bounds on slaughter animals are based on provincial slaughter capacities. Capacity limitations also have a role in determining the transfer flow of animals from lower capacity locations to higher ones. Lockhart (1987) notes that the per unit cost of slaughtering cattle relative to the major United States plants is a major concern of the western Canadian packing firms. Most of the western packing firms do not always have sufficient capacity to slaughter cattle which are fed in western regions. Animals can also be supplied and slaughtered in the United States. He notes that western Canadian livestock is moved into eastern Canada and United States for slaughter when the price spread exceeds the transfer cost. Thus, western Canadian firms not only compete among themselves but also with eastern Canadian and United States firms for a share of the available 89 supply of fat livestock for the fresh beef and processed meats markets. The per unit cost of slaughtering cattle is thus an important element of the firms' financial performance. Given these considerations, Table 4.7 provides an estimate of the high quality beef production levels. As noted in the previous discussion, a reduction of herd sizes in each province affects production levels. The percentage changes under each scenario are shown in brackets. Positive increases in high quality beef yields for some provinces, in Table 4.7, can be explained by the imports of live animals from other provinces. Feed costs, excess capacities and unit cost for beef slaughter result in a transfer of live animals between provinces. Another important consideration is that payments to the finishing sector differ by province. As noted in Table 2.1, Quebec producers in the finishing sector received payments amounting to $161.60 per head while Ontario producers have received amounts of $20.45 per head. Ontario has supported this sector at a lower level than other provinces and therefore is at a competitive advantage when subsidies are removed. In this sense, if the base case and scenario #1 are compared at the provincial levels, high quality beef yield in Quebec is down significantly by 19.4% while that in Ontario is up by approximately 3.5% in spite of a herd size reduction of 1.6%. Therefore, when payments to this sector are eliminated the observed impacts will vary by province. Since shipments of animals increase to Ontario, the changes noted are observed. In general, because of shipments between western and eastern regions, there is a positive 0.94% increase in production in eastern Canada but a 4.2% decrease in western Canada as shown in scenario #1 of Table 4.7 However, high quality beef yields in scenario #2 and #3 are dramatically reduced in Table 4.7 High Quality Beef Yields on Feedlots ('000 Tonnes) Base Case Scenario #1 Scenario #2 Scenario #3 B.C. 20.5 20.1 (-2.14) 19.1 (-7.20) 16.9 (-17.50) Alt. 260.9 257.4 (-1.32) 249.6 (-4,32) 234.4 (-10.14) Sask. 58.5 52.6 (-10.03) 55.1 (-5.83) 50.5 (-13.71) Man. 71.5 63.9 (-10.69) 62.5 (-12.53) 48.1 (-32.80) Western 411.4 394.0 (-4.23) 386.3 (-6.11) 349.9 (-14.95) Ont. 164.4 170.2 (3.53) 158.0 (-3.93) 149.0 (-9.35) Que. 26.2 21.5 (-19.44) 23.0 (-13.46) 21.0 (-20.97) Mar. 12.7 13.9 (10.14) "12.8 (1.12) 12.6 (-0.80) Eastern 203.7 205.6 (0.94) 193.8 (-4.86) 182.6 (-10.34) Canada 615.1 599.6 (-2.52) 580.1 (-5.70) 532.5 (-13.43) 91 both eastern and western Canada because of smaller herd sizes. At the aggregate level, decreases of the high quality beef amount to 3%, 6% and 13% in each scenario as compared with base case. Larger changes at the provincial levels are noted. Hence, the amount of high quality beef produced is closely related to the smaller herd sizes noted. 4.4.3 Interprovincial Trade and Export . In chapter 2, the retention function was bounded by the export price on the lower level and by import price at the upper level. Given that export and import prices are held constant exogenously, domestic beef demand is assumed to be relatively stable and is endogenized by the demand function within the bounds. Based on these assumptions, changes in herd sizes, as noted in Table 4.6, influence interprovincial movements and the exports of live animals more dramatically than demand levels. In Table 4.8 and 4.9, a positive sign implies net exports and a negative sign implies net imports. Before describing these shipment results, we need to understand the methods of modeling shipment activities in this programming framework. The following example is used: The reduction in herd size resulting from the elimination of government payments changes the size of the interprovincial trade and exports. It is relatively difficult to examine interprovincial trade since cost data on alternative routes and modes of transport, finishing and slaughter costs, retail margins and other factors affecting the market are difficult to specify accurately. For example, if we assume that the transportation cost of a animal from Saskatchewan to Manitoba is $10, from Manitoba to Ontario $15, while direct from Saskatchewan to Ontario it is $27, then Manitoba may appear to be importing when it is only an interim destination. Transportation costs between Saskatchewan and Ontario, in 92 reality, may be less than the summation costs for the indirect route noted above. Therefore, the solution from the programming model, depending on the method of defining transport routes, can appear differently from the actual situation. To overcome some of these difficulties, interprovincial trade is analyzed based on western/ eastern regions. As shown in Table 4.8, Canada in the base case is a net exporter of feedlot yearlings and calves. Net exports are estimated as the difference between exports and imports for the western and eastern areas. In the base case, net exports in the western region are 258 thousand head and net imports in the eastern region are 230 thousand head. Thus, Canada exports 28 net thousand head to the U.S. as a domestic surplus. As a result of the elimination of government payments and the decrease in farmer's returns and herd sizes, there is a decrease in net exports of live animals. Under scenario #1 eastern Canada increases imports by 75,000 head from the base of 230 thousand head and western Canada decreases their exports by 36,000 head from 258 thousand. Therefore, Canada imports a net 12 thousand head in scenario #1. At a regional level-, western Canada in scenario #1 and 3, maintains an export position regardless of reduction of the breeding herd size. Furthermore, exported amounts for western Canada increase with the elimination of government payments. In base case it exports 258 thousand head while under scenario #1 to #3 it exports 294, 280 and 320 thousand head respectively. This change is difficult to account for but it is related to high quality beef export levels. Fat animals can be sold to the market or processed and then sold in beef. The relationship between costs and returns in these two market levels needs to be accurately captured. If Table 4.8 Net Interprovincial and Export Trade of Feedlot Calves and Yearlings ('000 Heads) Base Case Scenario #1 Scenario #2 Scenario #3 B.C. 28.4 27.0 28.0 27.4 (-4.75) (-1.37) (-3.38) Alt. -94.9 -98.2 -87.2 -76.5 (3.39) (-8.13) (-19.38) Sask. 347.7 359.1 331.2 308.5 (3.28) (-4.74) (-11.28) Man. -23.6 5.7 7,8 60.1 (-124.30) (-133.24) (-355.05) Western 257.5 293.7 279.8 319.5 (14.04) (8.64) (24.05) Ont. -398.7 -434.0 -391.5 -381.1 (8.84) (-1.83) (-4.42) Que. 155.1 120.7 106.8 84.1 (-22.19) (-31.10) (-45.76) Mar. 13.9 7.4 11.6 10.3 (-46.57) (-16.48) (-25.79) Eastern -229.8 -305.9 -273.0 -286.7 (33.12) (18.82) (24.76) Net Export 27.8 -12.2 6.8 32.8 (-143.94) (-75.60) (18.12) 94 not, the decrease in dressed beef exports can offset this increase in fat cattle exports. The changes also relate to the excess supply position of western Canada relative to its trading partner — eastern Canada. As noted in Table 4.6, changes in the breeding herd size in eastern Canada are greater than those in western Canada. Breeding herd sizes in western Canada are adjusted downwards to 1.8%, 4.5% and 10.7% for each scenario, but are 4%, 7% and 17% down respectively in eastern Canada. These more significant changes in the breeding herd sizes in eastern Canada change its demands for fat cattle relative to the base situation. Under these considerations, imports of feedlot calves and yearlings, in eastern „ Canada, are adjusted upwards to 33%, 19% and 25% for each scenario. Together with changes in the interregional shipments, it is expected that Canadian net export position for live animals will change. Table 4.8 does not show explicitly that the current net export position for feedlot yearling and calves will be maintained. It is thought that export numbers of live animals are dependent upon the elasticities of the retention function. However, the base case for high quality beef in Table 4.9 shows that each province is either an exporter or importer. In base case, Alberta, Saskatchewan and Manitoba are exporters but the other provinces are importers. If base case and each scenario are compared, export amounts in western Canada are adjusted downwards by 7%, 10% and 24% respectively as one moves to increasing elasticities of retention function. At the national level exports of high quality beef change fairly dramatically with changes of 17%, 38% and 89% respectively for each scenario. This means that Canada in the base case exports 93 thousand tonnes of high quality beef but in scenario #1 this decrease to 77 thousand tonnes, to 58 thousand tonnes in scenario #2 and to 10 thousand tonnes in scenario #3. These decreasing amounts in each Table 4.9 Ne t Interprovincial and Expor t Trade of H i g h Qua l i ty Beef ('000 Tonnes) Base Case Scenario #1 Scenario #2 Scenario #3 B . C . -40.3 -40.7 -41.8 -43.9 (1.09) (3.78) (8.91) A l t . 210.3 206.8 199.0 183.9 (-1.64) (-5.35) (-12.55) Sask. 37.1 21.8 33.7 25.8 (-41.33) (-9.20) (-30.54) M a n . 48.8 50.7 39.9 28.8 (3.79) (-18.29) (-41.10) Western 255.9 238.5 230.8 194.5 (-6.79) (-9.81) (-23.98) Ont. -13.0 -7.2 -19.5 -28.4 (-44.75) (49.59) (117.96) Que. -113.1 -118.2 -116.6 -118.6 (4.58) (3.17) (4.94) M a r . -37.1 -35.8 -37.0 -37.2 (-3.46) (-0.38) (0.27) Eas te rn -163.2 -161.3 -173.1 -184.2 (-1.18) (6.07) (12.89) Ne t Expor t 92.7 77.3 57.7 10.3 (-16.65) (-37.77) (-88.89) 96 scenario are roughly proportional to the elasticities of retention function assumed. 4.4.4 Analysis of Production Cash Costs and Feed Grain Use Levels The el imination of payments results in cattle producers decreasing their herd size, and consequently the derived demand use of inputs falls. Suppliers of inputs w i l l be concerned about changes that decrease the size of their market. A s shown i n Table 4.10, the el iminat ion of . payments reduces input costs for al l provinces, although the magnitude of the decline varies. Production cash costs in Table 4.10 are calculated as herd sizes times cash cost per head. The proportional decrease in cash costs shown in Table 4.10 is almost s imi lar to that of breeding herd size changes noted i n Table 4.6. A t the national level cash costs in the base case are $129 mill ion, they are $126 mi l l ion , $123 mil l ion and $114 mil l ion in each scenario respectively; representing decreases of 2.5%, 4.9% and 11.5%. In the base case Alberta 's cash costs are $48 mil l ion, Saskatchewan and Ontario spend $28 mil l ion and $22 mil l ion respectively. Quebec's cash costs are $7.4 mil l ion. These decrease by as much as 11%, 16% and 37% for each of the three scenarios in Quebec. It is also important to note changes in the feed use patterns as these relate to the scenarios reported. In the beef sector, feed can be of three categories — forage, pasture and barley. Since the cost of barley fed is the most important feed cash cost i tem, changes in the amount of barley fed are shown in Table 4.11. The reduction i n herd size noted in Table 4.6 decreases bar ley use due to a reduced derived demand from cattle producers. Table 4.10 shows that at the national level estimated bar ley use in the base case is 4.1 mil l ion tonnes for the beef sector. Under the scenarios reported use levels decline 2%, 5% and 12%. Quebec feeds Table 4.10 Production Cash Costs ,($ Million) Base Case Scenario #1 Scenario #2 Scenario #3 B.C. 7.0 6.9 6.6 6.0 (-1.95) (-5.50) (-14.15) Alt. 48.4 47.5 46.4 43.7 (-1.69) (-4.13) (-9.68) Sask. 28.3 27.4 26.8 24.7 - (-3.01) (-5.33) (-12.60) Man. 13.7 13.3 13.2 12.4 (-2.46) (-3.89) (-9.63) Western 97.3 95.2 92.9 86.8 (-2.20) (-4.55) (-10.84) Ont. 22.1 21.9 21.5 20.8 (-0.75) (-2.49) (-5.95) Que. 7.4 6.6 6.2 4.7 (-11.49) (-16.28) (-37.21) Mar. 2.4 2.4 2.3 2.2 (-1.32) (-4.11) (-10.10) Eastern 31.9 30.9 30.1 27.6 (-3.28) (-5.82) (-13.53) Canada 129.3 126.1 123.0 114.4 (-2.47) (-4.86) (-11.51) Table 4.11 Usage of Barley on Beef Sectors ('000 Tonnes) Base Case Scenario #1 Scenario #2 Scenario #3 B.C. 151.6 149.0 (-1.72) 140.6 (-7.26) 125.7 (-17.10) Alt. 1812.5 1790.3 (-1.23) 1734.7 (-4.29) 1630.0 (-10.07) Sask. 517.6 479.0 (-7.47) 488.1 (-5.71) 448.1 (-13.44) Man. 478.8 439.6 (-8.19) 430.4 (-10.10) 353.2 (-26.24) Western 2960.5 2857.8 (-3.47) 2793.8 (-5.63) 2556.9 (-13.63) Ont. 899.3 922.4 (2.57) 879.2 (-2.24) 851.1 (-5.36) Que. 156.0 132.3 (-15.17) 132.6 (-15.00) 111.9 (-28.26) Mar. 70.1 74.6 (6.43) 69.5 (-0.76) 67.2 (-4.14) Eastern 1125.3 1129.3 (0.35) 1081.3 (-3.91) 1030.2 ' (-8.46) Canada 4085.8 3987.0 (-2.42) 3875.1 (-5.16) 3587.1 (-12.21) 99 relat ively less because of the greater reduction in the size of the herd relative to that of other provinces. However , there are positive changes in Ontario and Mar i t imes in scenario #1. This positive change is closely related to changes in shipments of animals from other provinces to Ontario and Mar i t imes . In general, this movement is from western to eastern Canada, but numbers are fair ly sensitive to changes in some of transportation costs and other coefficients of the model. 4.4.5 Beef Sector Earnings Table 4.12 estimates beef income by summar iz ing the changes described in the sections above. It is- important to analyze beef sector incomes as this is an important target which often influences the position taken by farmers and government policy makers, both federal and provincial. Ne t sector earnings are calculated as total revenue minus total variable costs of production. Total revenue is derived as production mult ipl ied by farmgate price. The revenue is adjusted for changes in the value of inventory, shipments of live animals out of the sector are credited as revenue, and government payments received by the beef sectors are also treated as income. Shipments between provinces of animals are important and are accounted for in the sense that the exporting province is credited and the import ing province debited. O n the cost side, total variable cash costs are a summation of cash production costs, feed costs, and the value of shipments into the sector, as well as the transportat ion costs which accrue to the import ing province. Ne t beef sector earnings in the base case amount to $1.45 bi l l ion. A s shown i n Table 4.5, government payments in the base case amounted to $243 mil l ion and 100 T a b l e 4.12 Ne t Beef Sectors Earnings ($ Mill ion) Base Case Scenario #1 Scenario #2 Scenario #3 B . C . 58.0 39.5 (-31.94) 43.7 (-24.64) 49.3 (-15.08) A l t . 592.0 508.7 (-14.07) 493.6 (-16.62) 462.6 (-21.87) Sask. 224.9 168.5 (-25.10) 162.9 (-27.59) 140.6 (-37.50) M a n . 155.5 123.3 (-20.69) 121.1 (-22.12) 97.7 (-37.18) Western 1030.5 840.0 (-18.48) 821.4 (-20.29) 750.1 (-27.21) Ont. 272.3 259.8 (-4.59) 242.3 -(-11.03) 230.3 (-15.43) Que. 118.3 50.6 (-57.23) 52.2 (-55.89) 45.3 (-61.69) M a r . 29.3 26.0 (-11.33) 24.2 (-17.45) 23.6 (-19.58) Eas tern 419.9 336.4 (-19.89) 318.6 (-24.12) 299.2 (-28.75) Canada 1450.4 1176.4 (-18.89) 1140.0 (-21.40) 1049.3 (-27.65) 101 therefore net sector earnings in the absence of government payments amount to $1.2 bill ion. Ea rn ings for each scenario, which represents a no government subsidy situation, are $1.2 bil l ion, $1.1 bill ion and $1.0 bill ion respectively. A t the national level beef sector earnings fal l by 19% for scenario #1, by 21% and 28% respectively for scenario #2 and 3. Government payments in the base case amount to approximately 17% of total sector earnings and therefore when these are eliminated a corresponding reduction i n the beef sector earnings is noted. In scenario #2 and 3 the reduction is substantial more than the changes noted in breeding herd size. Fo r example, at the aggregate level herd size under scenario #3 is decreased by 12% but sector earnings fall 27%. Interprovincial changes for these sector earnings m a y be examined by comparing the base case to that of scenario #1 where no government payments are made. In B . C . earnings are down 32%, in Albe r t a by 14%, in Saskatchewan by 25%, in Man i toba by 21%, in Ontario by 5%, in Quebec by 57% and in Mar i t imes by 11%. These changes correspond approximately to the amounts of government payments i n terms of relative values of total beef earnings noted in Table 4.5. This scenario assumed no market price changes or feed price changes and therefore the results are not surpr is ing in this sense. However , the results are interesting in that some of the interrelationships between herd sizes, production levels, trade flows and sector earnings are clarified. In scenario # 2 and 3 beef sector earnings fall quite substantial ly based on changes in the breeding herd size. A t the national level the earnings decline by 21% and 28% respectively. Earnings in Quebec, in scenario #3, declines by 62% wi th respect to the base case. Hence, the elimination of government payments does affect net sector earnings of beef producers and the impact on net change varies by province. 102 4.5 SUMMARY In summary , the scenarios examined show that current breeding herd size w i l l be reduced in the case of an elimination of government payment. A s noted in the previous section, when $243 mil l ion of government payments are eliminated, beef sector earnings are reduced by more than this amount. E v e n though the reduction of beef sector earning is dependent upon the estimates of the retention function, it is expected that elimination of government payments w i l l change the structure of Canadian beef industry. The model in this study assumes that U . S . beef prices are held constant. The results are obtained using comparat ive static analysis . If U . S . beef prices are not held constant and a dynamic analys is or perhaps change in other assumptions is considered, results described in the previous section wi l l vary . CHAPTER 5 SUMMARY AND CONCLUSIONS The study has described changes i n the Canadian beef sector as these relate to changes i n policies and programs which involve direct government payments to producers. This chapter summarizes the results, conclusions are drawn, and recommendations for further study are provided. 5.1 SUMMARY AND CONCLUSION A move towards liberalization of agricul tural trade may benefit or cost different producers in different sectors depending on the subsector one is dealing wi th and the policy changes dealt wi th . E v e n though trade between countries is an internat ional issue, it directly or indirectly affects the domestic industry. Executing the principles of G A T T and F T A provides gains and losses to different groups and in this sense an elimination of subsidies may threaten the stability and income levels of different agricul tural sectors differently. Agr icul tura l production is seasonal and biological. International market forces can result in fair ly dramatic price changes and therefore producers can be vulnerable to these forces. This study has analyzed the Canad ian beef sector wi th the assumption that the beef sector wi l l follow the move towards l iberalization of agricul tural trade. E a c h provincial government has assistance programs which protect and/or increase livestock producers' incomes. Direct payment programs encourage production, and they add to producers' incomes and impact upon trade levels. M a r t i n and van D u r e n have shown that direct and indirect government payments per head for beef 103 104 producers varies widely by provinces. This study has assumed that supply responses of producers depend on current and future returns of an animal . It is assumed that the amount received by cattle producers per an imal consists of a market re turn and a payment from government in the form of a subsidy. Fol lowing a move towards liberalized agricultural trade, government subsidies to producers are el iminated (or reduced), and, therefore, future returns received by cattle producers come f rom the marke t only. Changes in future earnings are associated wi th investment and disinvestment rules of decision-makers. There is a positive relationship between the expected price of beef and herd size over the long run . A n y reduction of herd size leads to changes in excess demand and supplies. These situations result in changes in quantities shipped between provinces and between Canada and U . S . Chapter 3 detailed the analyt ical methodology and data sets used in this study. The C R A M model was introduced i n order to incorporate the situations developed i n chapter 2 into the empir ical model. The beef sector submatrices in C R A M detailed the method of modeling beef production, trade and demand wi th in this model. Supply response to changes i n prices is related to coefficients of supply elasticities specified for the retention function used i n this study. D a t a sets were explained in order to detail the coefficients in these given submatrices and structural equations. In chapter 4 results of the study are presented. Three different supply elasticities were introduced in order to cover some ranges between m i n i m u m and m a x i m u m changes. Changes that m a y be expected at a regional level as government payments to the beef sector are examined. Curren t ly , total estimated government 105 payments to the cattle producers are approximately $243 mil l ion. The share of payments versus market returns ranges from 49 to 9 percent depending on the province. U s i n g a comparative static analysis, this study has shown that the el iminat ion of government subsidies leads to changes i n the structure of the Canad ian cattle industry. The size of the breeding herd size at the aggregate level was estimated to decrease by two to twelve percent depending upon the elasticities of the retention function assumed. The base case for this analysis is 1986 and opening stock numbers of cows, replacements and stockers are approximately 7.7 mil l ion head at the national level. In terms of herd size Alber ta share is largest w i th 37% of the total herd, Saska tchewan has 21% and Mani toba and Ontario fall relat ively further down wi th approximately 19% and 10% of the total herd size. The beef sector in the P ra i r i e province and Ontario receives generally less in payments than in the relative herd size. Quebec wi th only 5.9% of the national cow herd receives 23.8% of the total amount of government payments. Changes between the base case and each of the scenarios are analyzed in terms of aggregated measures. A t the national level the change in the breeding herd size is downwards wi th a range of 2% for scenario #1 and 12% for scenario #3. These scenarios represent different supply elasticity situations. Comparing the base case wi th scenario #1, herd size in Quebec is reduced by approximately 10% whereas the adjustment for most other provinces is about 2%. Quebec producers in the finishing sector received payments amounting to $161.60 per head, while Ontario producers have received amounts of $20.45 per head. Ontar io has supported this sector at a lower level than other provinces and 106 therefore is at a competitive advantage when subsidies are removed. In this sense, i f the base case and scenario #1 are compared at the provincial levels, high quality beef yield in Quebec is down significantly by 19.4% while that in Ontario is up by approximately 3.5% in spite of a herd size reduction of 1.6%. Therefore, when payments to this sector are eliminated the observed impacts wi l l va ry by province. Canada , in the base case, is a net exporter of feedlot yearlings and calves. In the base case, net exports in the western region amount to 258 thousand head and net imports in the eastern region are 230 thousand head. Thus, Canada exports 28 net thousand head to the U . S . as . a domestic surplus. A s a result of the elimination of government payments and the decrease i n farmer's returns and herd sizes, there is a decrease in net exports of live animals. Under scenario #1 eastern Canada increases imports by 75,000 head from the base of 230 thousand head and western Canada decreases their exports by 36,000 head from 258 thousand. Therefore, Canada imports a net 12 thousand head in scenario #1. Government payments to the beef sector are $243 mil l ion in the base case. In absolute amounts, beef sector net earnings decline by approximately $273 mil l ion, $310 mil l ion and $401 mil l ion for each of the three scenarios. These amounts are greater than the absolute decline i n government payments. E v e n though the government saves $243 mil l ion in subsidies to the beef sector, net losses exceed this by $30 mil l ion in scenario #1, by $67 mi l l ion i n scenario #2 and by $158 mil l ion in scenario #3. In conclusion, a move towards liberalized agricultural trade causes net losses in the sector earnings for beef producers. The net losses are proportional to the values of the elasticities assumed for retention functions. It should be noted that in this analysis U . S . prices which are exogenous are held constant. In a 107 mult i la tera l agreement where al l national governments decrease subsidy payment levels this assumption m a y be questioned. 5.2 RECOMMENDATIONS FOR FURTHER STUDY. The beef sector model and approach detailed in this study required several restr ict ing assumptions. Th is section suggests some improvement of the model's analyt ica l abili ty through a relaxation of some of these assumptions. F i r s t , any reduction of government subsidies is expected to be implemented over some time horizon rather than being treated as a single change. It is possibly to examine this scenario using parametric programming methods. This approach can solve the model wi th proportional decreases in subsidies unt i l the full reduction is achieved over some planned horizon and therefore the time path of adjustment changes could be reported. This analysis was comparative and static. Second, throughout this study, U . S . beef cattle prices have been held constant. Fol lowing the principles of G A T T and F T A , the U . S . government w i l l also reduce or eliminate subsidies to its agricultural sectors and this m a y impact upon U . S . prices and therefore change Canad ian market conditions for exports. In this s tudy U . S . prices were held constant but i f prices rise because of a decrease in supplies to the marke t then this could offset some of the income losses noted i n this study. Gardner (1987) has estimated farm commodity support price programs as a percent of the world price for the Uni ted . States. The Amer i can beef cattle sector is protected through import tariffs and voluntary restraint agreements. A m e r i c a n beef prices have been supported, on average, two to three percent above wor ld prices dur ing 1985/1986 and hence direct government payments to the A m e r i c a n beef sector 108 are relat ively unimportant. However , corn, wheat and barley, which are inputs in cattle production, have been supported an average of fifteen to twenty-five percent above world prices dur ing 1985-1986. A s noted in the previous section, government payments to the crop sector are indirectly related to the beef sector and estimates of these on market prices need to be considered. If these payments to U . S . beef and crop sector are reduced or el iminated, U . S . cattle prices should not be held constant. Th i rd , elasticities of the retention functions specified in this study should be more specific to the needs of this analysis . Elasticit ies from the F A R M model have been estimated according to each category of beef cattle in western and eastern Canada. Provincia l elasticities are preferable. The elasticities as estimated by Gardner and Gorden were estimated for U . S . and Canada without classification according to an imal category and region. Since each province has its own supply characteristics in the agricultural economy, elasticities of the retention function, for each beef an imal category, in each province, would be more satisfactory. Four th , feed for cow-calf and feedlot producers includes forage, pasture and barley needs. Al though variat ions in diet are possible there is room for improvement in the specification of the diets, par t icular ly the forage component thereof. This addition of more feeds and an allowance for changes i n diets by costs in the beef production submatrices w i l l provide a more accurate representation of some of the feeding options facing producers. F i f th , this study assumed that the retention function has a positive slope for the future expected price and the number of retained animals. Expected price times the number of retained animals w i l l give an expected revenue to cattle producers. 109 This expected revenue function, differentiated wi th respect to prices, m a y have the shape of convex curve wi th positive second derivatives. In order to incorporate these characteristics of the retention function into the model, it is recommended that separable or integer programming methods be investigated. Since a common aspect of these two programming methods is to move from small values of any s tar t ing point to larger values wi th in an allowance of constraints, it is possible to find solutions of the quadratic objective function allowing for a convex total revenue curve. This situation is val id over a short-run planning horizon. It is difficult to say which of these recommendations is most important i f further work is to be undertaken. It depends on the problem or issue to be analyzed. BIBILOGRAPHY Agricul ture Canada , "Agr icu l tu re Economic Statistics.", Cat . 21-603E, Ottawa, 1987. Agricul ture Canada , "Livestock and A n i m a l Products Statistics.", (Cat. 23-203), 1986. Bentley, Ernest , J ames , R . Waters , and C. Richard Shumway . "Determining Opt imal _ Elements ." S. J . A g r . 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"Issues Fac ing Agricul ture in the G A T T Negotiations" Can . J . A g .  Econ. . 35(1987):515-534. Webber, C . A . , J . D . G r a h a m , and K . K . K l e i n . The Structure of C R A M : A Canadian  Regional Agr icu l tu ra l Model . Dept. of Agr i cu l tu ra l Economics, Univers i ty of B r i t i s h Columbia, 1986. Webber, C A . and J . D . G r a h a m . A Regional A n a l y s i s of Direct Government  Assistance Programs in Canada and Their Impacts on the Beef and Hog Sectors. Dept. of Agr icu l tu ra l Economics, Un ive r s i t y of B r i t i s h Columbia , 1988. 

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