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The B.C. mushroom industry : an analysis of demand and supply 1988

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THE B.C. MUSHROOM INDUSTRY: AN ANALYSIS OF DEMAND AND SUPPLY By Hsin Chung Huang B.Sc., The University of B r i t i s h Columbia, 1985 A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF SCIENCE i n THE FACULTY OF GRADUATE STUDIES Department of A g r i c u l t u r a l Economics We accept t h i s thesis as conforming to the required standard THE UNIVERSITY OF BRITISH COLUMBIA October 1988 © H s i n Chung Huang, 1988 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 of Agricultural Economics The University of British Columbia 1956 Main Mall Vancouver, Canada V6T 1Y3 D a t e October 13, 1988 DE-6(3/81) ABSTRACT The mushroom industry i n B r i t i s h Columbia markets and d i s t r i b u t e s through a central s e l l i n g agency under the trademark Money's Mushrooms. This member owned agency also exercises control, through production area quotas, on member production. This study analyses the market behavior of the B.C. mushroom ind u s t r y 1 , i n order to ascertain whether producers c o l l e c t i v e l y exercise monopoly control over the industry. The main s t r u c t u r a l components of the industry are described i n a mathematical model using a p a r t i a l equilibrium analysis. The parameters which a f f e c t demand are estimated with econometric equations. Supply- i s formulated by minimizing a cost function subject to a Constant E l a s t i c i t y of Substitution Production Fuction. A major feature i n supply i s the joint-product r e l a t i o n s h i p between mushrooms which are sold fresh and mushrooms which are sold processed. Policy implications a r i s i n g from the structure of the industry and i t s observed behavior i n the market are then analysed. The econometric analysis indicates that the demand for fresh mushrooms i n B.C. over the period 1982 to 1986 was influenced by own p r i c e , advertising and the pri c e of a complement, beef. The a b i l i t y of the association to set prices i n the fresh market i s confirmed by the r e s u l t s . In the processed market, i t was found 1In t h i s study, mushroom refer s to the commercially marketed v a r i e t y "Agaricus Bisporus". i i i that imported processed mushrooms are very close substitutes for domestic processed mushrooms. The factors which influence processed mushroom demand are consumer income, and p r i c e of imported processed mushrooms. A mathematical model of the industry i s formulated with two opposing models of market behavior -perfect competition, and monopoly power. The model generated r e s u l t s are then compared to actual market data. The r e s u l t s support a model of competitive market behavior i n the B.C. mushroom industry. That i s , producers do not c o l l e c t i v e l y , through the marketing association, set prices above competitive l e v e l s . In addition, the analysis indicates that the production quota i s not a binding input on production. Therefore, given the e x i s t i n g production technology, no s o c i e t a l welfare gains can be r e a l i z e d by increasing the t o t a l a l l o c a t i o n of quota i n the B.C. mushroom industry. I t i s concluded that the c e n t r a l i z e d marketing of mushrooms i n B.C. provides benefits to producers through scale economies i n inputs and i n marketing/distribution. However, the l i m i t e d powers that the association has a v a i l a b l e to enforce cooperation amongst members has recently placed the association i n f i n a n c i a l d i f f i c u l t i e s . S p e c i f i c a l l y , the low prices ( r e l a t i v e to cost of production) f o r processed mushrooms i n 1986 has recently resulted i n several growers opting out of the association i n favour of forming t h e i r own marketing agency. There was also a s i g n i f i c a n t increase i n volume of i l l e g a l sales i n 1986. The reduced volume of patronage, i l l e g a l sales, and competitive pressure from the i v newly formed marketing agency has resulted i n lower prices for members of the association. V TABLE OF CONTENTS ABSTRACT i i TABLE OF CONTENTS V LIST OF TABLES v i i i LIST OF FIGURES i x ACKNOWLEDGEMENTS X CHAPTER 1. INTRODUCTION 1 1.1 Problem Statement 3 1.2 Objectives of the Study 3 1.3 Research Procedure 4 1.4 Thesis Guide 5 1.5 History of the B.C. Mushroom Industry 6 1.6 Structure of the B.C. Mushroom Industry 8 1.6.1 Marketing Board 9 1.6.2 Fraser Valley Mushroom Growers Co-operative Association 9 1.6.3 Production Technology at the Producer Level 11 1.7 Growth of the National Industry 12 1.8 Unique Features of the B.C. Industry 16 1.9 Comparison of the B.C. Industry with Rest of Canada 18 1.10 P r i c i n g Conduct i n the B.C. Mushroom Industry . . 2 0 1.11 Recent Developments 22 1.11.1 Barriers to Entry i n the B.C. Mushroom Industry 22 1.11.2 Production Withdrawal 24 v i 1.11.3 The Marketing Contract and Problems of Enforcement 25 1.11.4 Factors A f f e c t i n g the V i a b i l i t y of the F.V.M.G.C.A 26 2. A MATHEMATICAL MODEL OF THE B.C. MUSHROOM INDUSTRY . . . 28 2.1 Demand Model 29 2.2 Supply Model 34 2.3 Modelling Market Equilibrium 36 2.4 The Concept of Consumer Surplus 38 2.5 Fina n c i a l Analysis of Production Quota 39 3. CONSUMER DEMAND THEORY, ECONOMETRIC MODELLING AND ESTIMATION 45 3.1 Consumer Demand Theory 45 3.1.1 C l a s s i c a l Consumer Demand Theory 46 3.1.2 Extension of the C l a s s i c a l Theory of Consumer Demand 49 3.1.3 Single Equation Demand Estimation 50 3.2 The Demand for Mushrooms i n B.C 52 3.2.1 Demand for Fresh Mushrooms 52 3.2.2 Advertising and Demand 56 3.2.3 Demand for Processed Mushrooms 61 3.3 Econometric Estimation and Results of Demand for Mushrooms 64 3.3.1 Fresh Demand Equations 64 3.3.2 Demand E l a s t i c i t i e s for Fresh Mushrooms . . 70 3.3.3 Processed Demand Equations 72 3.3.4 E l a s t i c i t y of Price F l e x i b i l i t y f o r Processed Mushrooms 73 v i i 3.4 Cost of Production Model 75 3.4.1 Assumptions 76 3.4.2 The Cost of Production Model 80 3.4.3 Results of the Cost of Production Model . . 85 4. RESULTS OF THE MATHEMATICAL MODEL OF THE BRITISH COLUMBIA MUSHROOM INDUSTRY . . 86 4.1 Monopoly versus Competitive P r i c i n g , 1986 . . . . 87 4.2 Monopoly versus Competitive P r i c i n g , 1983 to 1986 93 4.3 The Payback Period for Quota 95 5. SUMMARY, CONCLUSIONS AND POLICY IMPLICATIONS 98 5.1 Summary and Conclusions 98 5.2 Policy Implications 100 5.2.1 The Problem of Processed Mushroom Imports . 101 5.2.2 Producer Unity 104 BIBILIOGRAPHY 106 APPENDIX A 108 APPENDIX B I l l v i i i LIST OF TABLES Table 1.1 Total Growing Area, Production, and Y i e l d of Mushrooms i n Canada 13 Table 1.2 Total Production and Value of Mushrooms i n B.C. . 15 Table 1.3 Total Production and Value of Mushrooms i n Canada 15 TABLE 1.4 Capital Investment and Yields, per square foot of Growing Area, for B.C. and the Rest of Canada 19 Table 3.1 Res t r i c t i o n s on the System of Demand Equations . 48 Table 3.2 Econometric Estimates of Fresh Mushroom Demand Linear and Stock Adjustment Models 66 Table 3.3 Econometric Estimates of Fresh Mushroom Demand Cumulative E f f e c t s and Koyck Lag Models 67 Table 3.4 Demand E l a s t i c i t i e s f or Fresh Mushrooms Calculated at the Means 70 Table 3.5 Price Dependent Demand Model 72 Table 3.5 C o e f f i c i e n t s of Price F l e x i b i l i t i e s f o r Processed Demand Function, Calculated at the Means . . . . 74 Table 4.1 Market Quantity, Price, Input Levels, 1986 . . . 89 Table 4.2 Monopoly P r i c i n g Model, with Quota Constraint, 1986 89 Table 4.3 Competitive P r i c i n g Model, with Quota Constraint, 1986 89 Table 4.4 Competitive P r i c i n g Model, no Quota Constraint, 1986 89 Table 4.5 Industry Welfare E f f e c t s of Moving from Competitive to Monopoly P r i c i n g , with Current Quota, 1986 90 ix LIST OF FIGURES Figure 1.1 The B.C. Mushroom Industry 1986 2 Figure 2.1 B.C. Fresh Market Demand 31 Figure 2.2 Fresh Market Demand (out of B.C.) 31 Figure 2.3 Derived Demand by Other Processors 31 Figure 2.4 Derived Demand for B.C. Processed 31 Figure 2.5 Welfare E f f e c t s of Supply Control 38 Figure 3.1 Indifference Curve for the U t i l i t y Function (1) 46 Figure 4.1 "Optimal" Prices as a Percentage of Actual Prices 94 Figure 4.2 "Optimal" Quantities a Percentage of Actual Quantities 94 X ACKNOWLEDGEMENTS I would l i k e to thank the members of my th e s i s committee, Tim Hazledine, John Graham, George Kennedy, Jim Forbes, and Dick Johnson. Thanks e s p e c i a l l y to Tim, my main th e s i s supervisor, for h i s generous contributions to t h i s t h e s i s . I benefitted greatly from h i s support and enthusiasm. Thanks are also due to Rick Barichello, who obtained the funding f o r t h i s project. Most of a l l , I would l i k e to thank my parents, who have supported me from the beginning. CHAPTER 1 INTRODUCTION The mushroom industry i n B r i t i s h Columbia i s the only one i n Canada that markets and d i s t r i b u t e s through a central s e l l i n g agency. Most producers i n B.C. belong to the Fraser Valley Mushroom Grower's Cooperative Association (F.V.M.G.C.A.). This member owned agency i s responsible for d i s t r i b u t i o n of a l l fresh and processed mushrooms c u l t i v a t e d i n the agency area. 2 The association has an aggressive marketing campaign; the trademark "Money's Mushrooms" has become almost synonymous with fresh mushrooms i n B.C. Mushrooms are also processed i n the association's own cannery and marketed under the Money's l a b e l i n every province of Canada. In addition, the association owns and operates a farm i n southern Alberta which serves the l o c a l market. In 1986, t o t a l mushroom p r o d u c t i o n i n B.C. was approximately 34.8 m i l l i o n pounds of which 49 percent was marketed as fresh and 51 percent as processed. Total crop value 2Non-member producers operate outside the Lower Mainland and are not subject to the rules and regulations of the B r i t i s h Columbia Mushroom Marketing Board. Non-member producers accounted f o r less than 5 % of t o t a l B.C. production i n 1986. 1 2 at the wholesale l e v e l was 36.2 m i l l i o n d o l l a r s . This figure places mushrooms f i r s t i n terms of vegetable crop value i n B.C. For Canada, mushrooms are ranked second i n vegetable crop value, behind potatoes ( S t a t i s t i c s Canada 22-203, 22-008). For 1986, a breakdown of the production and disappearance of mushrooms by end use i s provided i n Figure 1.1 below. TOTAL PRODUCTION 34.8 MILLION LBS. FRESH 49 % PROCESSED 51 % OUT OF B.C. 12 % OTHER PROCESSORS 6 % F.V.M.G.C.A. CANNERY 45 % Figure 1.1 The B.C. Mushroom Industry 1986 3 1.1 Problem Statement The B.C. mushroom industry has two features which makes i t unique i n Canada. The industry i s regulated by quotas on the area of production. Also, producers c o l l e c t i v e l y own and support a sing l e marketing agent, the F.V.M.G.C.A. These features have important implications for producer returns. On the production side, r e s t r i c t i o n s on production area may d i s t o r t the use of resources, and therefore a f f e c t the cost of production. On the marketing side, producer returns may be enhanced by c o n t r o l l i n g the p r i c e (or quantity) i n the market. The magnitude of the benefits to the producer from the quota depends on the structure of the market and the degree of control that producers c o l l e c t i v e l y are able to exert, through the marketing agency, on the market for mushrooms. To q u a n t i t a t i v e l y assess the degree of producer control over the mushroom market i n B.C., a model of the industry, describing the main s t r u c t u r a l relationships which a f f e c t supply and demand, can be formulated. 1.2 Objectives of the Study The main objective of t h i s study i s to analyse the quota on production area i n the B.C. mushroom industry, and determine whether producers use the quota to exercise monopoly p r i c i n g control over the industry. 4 Sub-objectives for t h i s study are: (1) To describe the B.C. mushroom industry (2) To construct a cost of production model f o r the B.C. mushroom industry. (3) To formulate and estimate an econometric model describing the market forces which a f f e c t the demand for mushrooms i n produced i n B.C. This w i l l include demand functions for fresh and processed mushrooms. As well, estimates of various demand e l a s t i c i t i e s w i l l be computed. (4) To formulate a mathematical model of the B.C. mushroom industry, incorporating the r e s u l t s of the cost of production and demand models, with p a r t i c u l a r emphasis on the e f f e c t s of the production quota. (5) To use t h i s model to analyse the welfare implications a r i s i n g from the structure of the industry. (6) To draw p o l i c y implications for the B.C. mushroom industry. 1.3 Research Procedure To achieve the objectives outlined above, the mushroom industry i n B.C. w i l l be modelled using a p a r t i a l equilibrium analysis. Using economic theory, the variables which a f f e c t demand and supply of mushrooms i n B.C. w i l l be s p e c i f i e d . Two models of market behavior w i l l be examined. Perfect competition 5 w i l l be modelled by equating p r i c e and marginal cost i n the model. Monopoly behavior w i l l be modelled by equating marginal revenue to marginal cost. The parameters which a f f e c t demand w i l l be estimated with econometric r e l a t i o n s h i p s . A numerical estimate of the e f f e c t that p r i c e has on the quantity of mushrooms demanded by consumers w i l l then be calculated, holding a l l other variables constant. The parameters which a f f e c t supply w i l l be modelled using a l i n e a r cost function, minimized subject to a Constant E l a s t i c i t y of Substitution (CES) production function. From the cost minimization problem, a supply function can be derived with output l e v e l , p r i c e of inputs, e l a s t i c i t y of s u b s t i t u t i o n between inputs, and returns to scale as parameters. Some of the parameters which are neccessary to specify the supply function are then estimated. S p e c i f i c a l l y , a cost of production model w i l l be estimated i n order to obtain values f o r pr i c e s of inputs i n the supply function. A range of pl a u s i b l e values for returns to scale and e l a s t i c i t y of substitution w i l l be assumed, based on personal communication with producers i n the industry. Actual market data w i l l then be used to c a l i b r a t e the model, and market c l e a r i n g prices and quantities are calculated f o r the two models of market behavior, perfect competition and monopoly. 1.4 Thesis Guide The plan of t h i s study i s as follows: 6 Chapter 1 i s a description of the B.C. mushroom industry, including some comparisons with the national industry. In Chapter 2, a mathematical model of the B.C. mushroom industry i s formulated, with p a r t i c u l a r emphasis on the production quota. S p e c i f i c a l l y , the analysis w i l l determine whether production quota has enabled the industry to behave i n a monopolistic manner. A p a r t i a l equilibrium analysis i s employed f o r two models of market behavior -perfect competition and monopoly. The parameters which are needed i n the mathematical model are estimated i n Chapter 3. Section one i s a b r i e f discussion of consumer demand theory. In section two, market demand for mushrooms produced i n B.C. i s estimated using econometric equations. Demand functions for fresh and processed mushrooms are estimated. These provide the parameters f o r demand i n the mathematical model. Section 4 presents a cost of production model f o r mushrooms i n B.C. The cost of inputs are used as parameters for the production function i n the mathematical model described i n Chapter 2. The r e s u l t s of the mathematical model of the B.C. mushroom industry are presented i n Chapter 4. Chapter 5 i s a discussion of the conclusions and p o l i c y implications which a r i s e from the r e s u l t s of t h i s study. 1.5 History of the B.C. Mushroom Industry Mushrooms were c u l t i v a t e d i n B.C. long before the formation of the F.V.M.G.C.A. In 1928, William T. Money, one of the f i r s t 7 growers, started a farm i n Burnaby. Several other farms were also i n operation throughout the Fraser Valley. In 1931 a c o l l e c t i v e agreement was made amongst the growers to allow W. Money to take over marketing of mushrooms. The agreement enabled producers to concentrate f u l l - t i m e on mushroom production, leaving the job of sales and promotion to W. Money. By 1936, production had reached a point where fresh mushroom supply exceeded demand. As a r e s u l t , the Money Canning Co. was formed to provide an alt e r n a t i v e means of marketing the surplus that could not be sold i n the fresh market. When W. Money r e t i r e d i n 1956, the F.V.M.G.C.A. was formed to take over d i s t r i b u t i o n of mushrooms. The trademark Money's Mushrooms was purchased at the same time for marketing of fresh mushrooms. In 1963, several new growers formed t h e i r own company, Huntingdon Mushroom Company, which marketed i n d i r e c t competition with the F.V.M.G.C.A. In 1964, yet another company was formed, c a l l e d the United Mushroom Growers. A quote from Walter L o e f f l e r , a producer who has been i n the industry f o r many years, summarizes the si t u a t i o n , " Competition was f i e r c e and mushroom prices dropped d r a s t i c a l l y . Many went out of business- others were barely hanging on". In 1966, the B.C. Mushroom Marketing Board (B.C.M.M.B.) was formed to bring producers together under a c o l l e c t i v e marketing umbrella and put an end to the i n s t a b i l i t y which was at that time c h a r a c t e r i s t i c of the industry. The F.V.M.G.C.A. was chosen to 8 be the sole s e l l i n g agency for producers i n B.C. Packing and marketing costs were financed by a commission on sales of member production. R e s t r i c t i o n s on entry of new producers, i n the form of quotas on area of production, were introduced i n 1976. Producers were required to r e g i s t e r e x i s t i n g production area with the B.C.M.M.B., and a l i c e n s i n g fee for quota was u t i l i z e d as a means of r a i s i n g c a p i t a l to finance the purchase of the association's own packing f a c i l i t i e s . In 1979, the F.V.M.G.C.A. opened i t s own processing plant with the assistance of an ARDSA grant. The Money's Trademark for processed mushrooms, which was s t i l l under private ownership, was also purchased. In 1982, production area quotas were increased to meet growing demand for fresh mushrooms. Of the t o t a l stock of new quota, 95 percent was to be allocated to e x i s t i n g producers who applied for expansion, and the remaining 5 percent for po t e n t i a l new producers. No new producers entered the industry. 1.6 Structure of the B.C. Mushroom Industry The B.C. mushroom industry can be s p l i t up into three l e v e l s , the Marketing Board, the producer owned association, and the producers. 9 1.6.1 Marketing Board The B.C. Mushroom Marketing Board i s the governing body of the mushroom industry i n B.C. The board acts as the l i a i s o n between the government and the mushroom industry. Some of the board's duties include l i c e n s i n g producers, and l i c e n s i n g square footage of growing area. To finance i t s a c t i v i t i e s , the B.CM.M.B. has a levy per pound of production (in 1986, 1/3 cent per pound). Every year producers are required to sign a contract promising to d e l i v e r 100 percent of production to the board's designated s e l l i n g agency, the F.V.M.G.C.A. Members of the board are elected from producers. 1.6.2 Fraser Valley Mushroom Growers Co-operative Association The F.V.M.G.C.A. i s a member owned cooperative association. I t i s con t r o l l e d by a Board of Directors, whose members are elected from producers i n the industry. The nature of the association as a grower's cooperative exempts i t from income tax, because a l l income which i s earned i s d i s t r i b u t e d back to members. A l l o c a t i o n of growing area to members i s determined by the association. The association s e l l s fresh mushrooms to wholesalers and r e t a i l e r s , and processors (e.g., Campbell's Soup). Processed products canned by the association are sold d i r e c t l y (Money's label) as well as through various sales agents as no name brands 10 (e.g., Scotch Buy). Each month receipts from sales are d i s t r i b u t e d to growers a f t e r deducting a commission to cover operating expenses for mushrooms delivered during that month. The commission i s usually g r e a t e r than the a c t u a l operating expenses, leaving the association with a p r o f i t . This p r o f i t i s d i s t r i b u t e d to members at the end of the year. Each member's share of the d i s t r i b u t i o n i s based on the volume of patronage. Members of the association are assessed a one time fee for each square foot of licensed growing area ( $1.00 per f t 2 i n 1986) to finance a c q u i s i t i o n of the member owned c a p i t a l f a c i l i t i e s of the F.V.M.G.C.A. In return, the association markets members' production and provides growing supplies at cost. The association also operates a composting wharf which provides compost to growers at cost. This service i s of special s i g n i f i c a n c e to smaller producers who would not f i n d i t economically f e a s i b l e to produce t h e i r own compost without enlargening the scale of t h e i r operation. The c a p i t a l investment required to produce t h i s input i s quite large. Also, the production of compost i s a very s p e c i a l i z e d process which requires excellent management and technical s k i l l s . In addition, producers enjoy the advantages of not having to compete with each other f o r purchase of of a very important input used i n the production of compost, namely horse manure. For these reasons, the majority of producers choose to purchase compost from the wharf. Any p r o f i t s which are made by the composting wharf are also d i s t r i b u t e d back to users of the f a c i l i t y , pro rata, at the end of each year. 1.6.3 Production Technology at the Producer Level Mushrooms are grown year round indoors under highly c o n t r o l l e d conditions. An average crop cycle l a s t s two and a h a l f to three months. The preparatory stage usually l a s t s s i x weeks, followed by s i x weeks of cropping. At the end of each growing cycle, a l l of the material substrate on which the mushrooms grow must be cleaned out of the buildings and new material loaded i n for the next cycle. Several growing rooms are employed on a ro t a t i o n basis, usually weekly (eg. load a bu i l d i n g every Saturday). In t h i s way, mushrooms are cropped on a continual basis, the production from growing rooms which are cleaned out being replaced by rooms which are ready for harvesting. The v a r i a t i o n i n supply of mushrooms from week to week i s small. The lag between the time a production decision i s made and i t s r e a l i z a t i o n (six weeks) i s quite short i n comparison to vegetable crops which are grown on an annual basis. The implication of a l l t h i s may be reduced v a r i a b i l i t y i n p r i c e due to factors which are exogenous to the producer (e.g., changing consumer tastes) because producers can quite quickly adjust production l e v e l s by stepping up/down the length of the growing 12 cycle. However, i n the short run, c a p i t a l l i m i t a t i o n s place an upper bound (the maximum capacity of the farm) and a lower bound (fixed c a p i t a l costs which are incurred regardless of the l e v e l of production) on the s i z e of the adjustments. Producers are not l i k e l y to want to vary production dramatically, as continuity i n employment of e x i s t i n g labourers i s desirable from the viewpoint of s t a b i l i t y . Mushrooms which are sold on the fresh market are produced as a j o i n t product with mushrooms which are sold on the processed market. That i s , the two categories of mushrooms are not produced separately. The difference between fresh and processed mushrooms i s based on a measure of q u a l i t y as determined by size, shape, and colour c r i t e r i a . Mushrooms which meet a minimum qu a l i t y l e v e l are graded for sale into the fresh market. Mushrooms which are below t h i s l e v e l of q u a l i t y are processed. Production of mushrooms always involves a c e r t a i n proportion of the t o t a l which does not meet the fresh q u a l i t y c r i t e r i a . As producer pr i c e s for fresh mushrooms i s higher than for processed mushrooms, producers s t r i v e to obtain as high a proportion of fresh as possible. 1.7 Growth of the National Industry Mushrooms are produced i n almost every region of Canada, with major producing centres i n southwestern B.C. and southern Ontario. In 1985, production i n Ontario was estimated to be 55 13 percent of t o t a l Canadian production. B.C.'s share of domestic production was 30 percent. Between 1975 and 1985, domestic production increased by approximately 160 percent, with an increase i n growing area of only 42.9 percent (see Table 1.1). This production increase was a r e s u l t of productivity increases i n terms of lbs per square foot of c u l t i v a t e d area (2.57 to 3.93) and more i n t e n s i f i e d usage of e x i s t i n g growing area. The number of crops c u l t i v a t e d has increased from 3.45 to 4.93 crops per year. Table 1.1 Total Growing Area, Production, and Y i e l d of Mushrooms i n Canada t o t a l t o t a l crops lbs year area lbs per y r a per f1 1985 6574 99411 3.93 3.85 1984 6124 92325 3.84 3.92 1983 6017 82613 3.75 3.67 1982 6838 78512 3.59 3.20 1981 6710 72112 3.66 2.94 1980 N/Ac 64517 N/A N/A 1979 N/A 54584 N/A N/A 1978 5573 51230 3.50 2.62 1977 5422 46150 3.54 2.40 1976 4913 43782 3.38 2.64 1975 4601 40798 3.45 2.57 Source: S t a t i s t i c s Canada (22-003) Mushroom Growers Survey (annual) a c a l c u l a t e d , t o t a l area harvested/total area c u l t i v a t e d ^calculated, t o t a l l b s / t o t a l area harvested CN/A, data not available Increased production has been channeled to both processed 14 and fresh markets, however closer inspection of the data reveal regional differences. Fresh market disappearance of mushrooms i n B.C. increased sharply between 1980-1981, but has since that time remained steady at 12.5 to 13 m i l l i o n pounds annually. The r e l a t i v e l y stable fresh market demand may be due to the currently high l e v e l s of consumption being close the l i m i t s of consumer demand. In 1985, per capita consumption i n B.C. was 4.3 lbs while the national average was 3.1 lbs . In fact, consumption i n the greater Vancouver area i s currently the highest i n the world. Potential fo r fresh market expansion appear to be excellent i n eastern Canada, as disappearance of fresh mushrooms have increased at an average annual rate of approximately 15 percent over the l a s t decade. Nationally, processed mushroom disappearance has exhibited a strong upward trend. However, much of the increased demand has been supplied by imports from P a c i f i c Rim countries such as Korea, China and Taiwan. In eastern Canada, domestically processed quantities have v i r t u a l l y remained unchanged since 1975. In B.C., processed quantities have increased dramatically (Table 1.2), but the pressure of imports has caused prices to decline i n recent years. Over 73 percent of domestic demand for processed mushrooms was supplied by imports i n 1985. Table 1.2 Total Production and Value of Mushrooms i n B.C year FRESH quantity •000 l b value •000$ pr i c e per l b a PROCESSED quantity '000 l b value •000$ pr i c e per lb' 1985 15332 25871 1.69 17063 11085 0.65 1984 15492 24679 1.59 15734 9990 0.63 1983 14506 21026 1.45 16346 10071 0.62 1982 13092 18517 1.41 11999 7988 0.67 1981 12624 16648 1.32 6948 5299 0.76 1980 11372 12616 1.11 6487 4663 0.72 1979 9479 9615 1.01 4534 3245 0.72 1978 9576 8744 0.91 3545 2125 0.60 1977 7361 6610 0.90 3549 2131 0.60 1976 6319 5189 0.82 1797 896 0.50 1975 5321 3859 0.73 1926 949 0.49 Source: S t a t i s t i c s Canada (22-003) Mushroom Growers Survey (annual) awholesale p r i c e , calculated as value/quantity Table 1.3 Total Production and Value of Mushrooms i n Canada (excluding B.C.) FRESH PROCESSED quantity '000 l b value pr i c e quantity value p r i c e year •000$ per l b a '000 l b '000$ per l b a 1985 54520 77577 1.42 12496 9726 0.78 1984 49869 70504 1.41 11230 8900 0.79 1983 40884 56821 1.39 10877 8204 0.75 1982 39271 52819 1.34 14150 10975 0.78 1981 38640 49540 1.28 13900 11077 0.80 1980 35329 39780 1.13 10823 8624 0.79 1979 31522 33619 1.07 9049 6745 0.75 1978 28397 27191 0.96 9712 6362 0.66 1977 23723 21681 0.91 11517 6868 0.60 1976 21886 17788 0.81 13780 7232 0.52 1975 17348 13374 0.77 16202 8025 0.50 Source: S t a t i s t i c s Canada (22-003) Mushroom Growers Survey (annual) awholesale price, calculated as value/quantity 16 1.8 Unique Features of the B.C. Industry Centralized marketing/sales/promotion through the Fraser Valley Mushroom Grower's Cooperative Association has resulted i n widespread acceptance of mushrooms by food r e t a i l e r s as an e s s e n t i a l commodity i n the vegetable section of stores. The a b i l i t y of the industry to supply mushrooms on a year round basis with r e g u l a r i t y i s probably the single most important reason for the high l e v e l s of consumption i n B.C. The closeness of the industry to a large urban centre (Vancouver and the lower mainland) f a c i l i t a t e s e f f i c i e n t d e l i v e r y of the product to r e t a i l o utlets, a factor which i s very important given the r e l a t i v e l y short shelf l i f e mushrooms have i n comparison to other vegetable crops. In addition, the association has control over prices i n the fresh market. This i s made possible by d i v e r t i n g any product that i s not sold fresh into the processing plant which i s also owned by the association. The mushroom industry i n B.C. supplies more than 90 percent of fresh mushrooms consumed i n B.C. I t i s one of the few vegetable commodity industries which i s able to consistently do so on a year round basis. The small quantities (less than 10 percent) that a r r i v e from the United States (Washington, Oregon) do not yet pose a serious threat to the fresh market i n B.C., as American production capacity i s currently not enough to supply larger shipments into B.C. In addition, the p o t e n t i a l f o r fresh market expansion i s much greater i n the U.S. P a c i f i c Northwest 17 than i n B.C., where per capita consumption i s already the highest i n North America. Imports from the U.S. are currently favored by a low t a r i f f of only 5 percent ad valorem plus 5 cents per pound. In contrast, mushrooms going from B.C. into the U.S. face a t a r i f f of 25 percent plus 5 cents per pound. The existence of the association has made i t possible for small, family operated farms to be economically v i a b l e . Without the f a c i l i t i e s that the association provides, each farm would have to package, market and d e l i v e r i t s own production. Also, the association operated compost wharf eliminates the need for each producer to invest i n the c a p i t a l equipment required to prepare t h i s major input. Undoubtedly, many B.C. producers would have to increase i n s i z e to take advantage of scale economies i f the services provided by the association were not av a i l a b l e . Mushroom production i n B.C. i s co n t r o l l e d by a l l o c a t i n g production quotas i n terms of square footage of growing area to producers. Since productivity per unit of c u l t i v a t e d area i s vari a b l e , the r e s u l t i s an industry which does not exhib i t firm control over quantities which are placed on the market. Yields have increased as a r e s u l t of ongoing technical innovations i n c a p i t a l and crop management. This trend of increasing p r o d u c t i v i t y shows no sign of slowing down, p a r t i c u l a r l y i n l i g h t of continuing research on new hybrid s t r a i n s of mushrooms, delayed release nutrient supplementation, shorter crop cycles, etc. In addition, each producer has some f l e x i b i l i t y i n deciding the intensiveness of usage for e x i s t i n g square footage. 18 1.9 Comparison of the B.C. Industry with Rest of Canada Mushroom farms i n the rest of Canada are predominantly large firm type operations. The farms are much larger than t h e i r B.C. counterparts, enabling d i v i s i o n of a farm into i n d i v i d u a l units which s p e c i a l i z e i n production, packing and shipping, and marketing. This i s p a r t i c u l a r l y true i n Ontario, the province with the largest volume of mushroom production i n Canada. In 1986, the Canadian Mushroom Growers Association reported 24 producers i n Ontario, compared to 73 i n B.C. Mushroom farms i n the other provinces are more c a p i t a l intensive than t h e i r B.C. counterparts, as each farm must have i t s own f a c i l i t i e s f or a l l phases of production, packaging and marketing. Table 1.4 compares c a p i t a l investment per square foot of growing area. The B.C. industry consistently has a smaller c a p i t a l investment per unit of c u l t i v a t e d area than the other provinces. The data for B.C. does not include c a p i t a l value of the F.V.M.G.C.A., but adjusted figures have been calculated, and the r e s u l t s of a consistently lower c a p i t a l investment than the rest of Canada s t i l l hold t r u e . 3 Mushroom production i s a labour intensive process. Rising production costs, p a r t i c u l a r l y labour, have motivated farmers to increase productivity. In B.C. y i e l d s per square foot increased from 6.53 i n 1975 to 15.09 i n 1985 (Table 1.4). Many c a p i t a l -'Adjusted figures are not reported, as c a p i t a l value for the association f a c i l i t i e s i s c o n f i d e n t i a l . 19 innovations have been adopted i n the l a s t decade which have allowed savings i n labour and enhancements i n y i e l d . Capital i n t e n s i f i c a t i o n i n the industry i s apparent i n the increases i n c a p i t a l investment per unit of c u l t i v a t e d area. In B.C., c a p i t a l investment per square foot increased from $ 5.77 i n 1975 to $ 13.85 i n 1985 (Table 1.4). However, these innovations have only been r e a l i z e d i n the preparatory stages of mushroom production. Labour requirements fo r the cropping stage have remained unchanged. Harvesting i s the sing l e most labour intensive stage, with costs that can range from 15 to 20 percent of t o t a l production costs. TABLE 1.4 Capital Investment and Yields, per square foot of Growing Area, for B.C. and the Rest of Canada BRITISH COLUMBIA REST OF CANADA year c a p / f t 2 a l b / f t / y e a r 2 b c a p / f t 2 a b / f t / y e a r 2 b 1985 $ 13.85 15.09 $ 24.73 15.14 1984 12.24 14.50 23.51 15.39 1983 14.55 14.56 23.07 13.28 1982 14.33 11.83 19.78 11.33 1981 13.85 9.32 20.27 11.39 1980 N/Ac N/A N/A N/A 1979 N/A N/A N/A N/A 1978 8.54 7.83 12.29 7.96 1977 7.72 6.63 9.72 6.92 1976 6.77 5.88 9.17 7.14 1975 5.77 6.53 8.22 6.32 Source: S t a t i s t i c s Canada (22 -003) Mushroom Growers Survey (annual) a c a l c u l a t e d , value c a p i t a l / r e g i s t e r e d growing area data f o r B.C. does not include c a p i t a l value of the F.V.M.G.C.A. for reasons of c o n f i d e n t i a l i t y ^calculated, t o t a l production/registered growing area CN/A data not available Mechanized harvesting, used i n some countries which process the bulk of t h e i r production, i s currently not f e a s i b l e for Canadian producers because of t h e i r fresh market orientation. Product which i s mechanically harvested i s only suitable for processing. Processed mushrooms must compete with lower price imports, making that market much les s a t t r a c t i v e than the fresh market. Since only 29 percent of Canadian production i n 1985 was processed, adoption of such technology i s not economically f e a s i b l e . Even i n B.C., where s l i g h t l y more than 50 percent of p r o d u c t i o n i n 1986 was processed, adoption of mechanized harvesting would not be economically f e a s i b l e f o r smaller producers. The additional c a p i t a l investment required for t h i s technology could only be financed by the larger producers, as scale economies are involved. The processed mushroom market i n Canada i s e s s e n t i a l l y a r e s i d u a l market for product which cannot be sold fresh. Competing imports are currently priced at l e v e l s which are low r e l a t i v e to the domestic cost of production f o r fresh and processed mushrooms. For t h i s reason, the continued v i a b i l i t y of the mushroom industry i s very much dependent on sales to the fresh market. 1.10 P r i c i n g Conduct i n the B.C. Mushroom Industry The B.C. Mushroom Marketing Board has the power to set 21 prices at the wholesale l e v e l , but i t s p r i c i n g behaviour i s influenced by two factors: (a) the quantity that must be sold i s not under the association's control and (b) processed mushroom prices are affected by prices of competing imports. The association operates i n the following manner: 1. Mushrooms are graded for fresh and processed q u a l i t i e s at the farm l e v e l and shipped i n bulk containers to the cooperative. 2. Upon receipt, the mushrooms are graded at the packaging plant to ensure uniformity i n grading standards for a l l producers. 3. Fresh q u a l i t y mushrooms are packaged and sold to r e t a i l chain outlets and wholesale d i s t r i b u t o r s at a p r i c e fixed by the B r i t i s h Columbia Mushroom Marketing Board. This p r i c e applies to a l l customers and i s revised once or twice a year, as market conditions change. 4 . Fresh q u a l i t y mushrooms which have not sold on the fresh market are pooled with processing grade product and transferred to the cannery f a c i l i t y or sold to other processors, such as Campbell's. Fresh mushrooms are not storable, as they have a shelf l i f e of only a few days. I t i s the a b i l i t y to process mushrooms which are i n excess of fresh market requirements that enables the association to exercise p r i c e s e t t i n g powers i n the fresh market. 5. Pool prices are established f o r each grade, based on actual quantities sold on the market. Producers receive payment based on the quantities of each grade they have shipped to the association. Thus the quantity that i s produced and shipped of each grade d i f f e r s from what i s ac t u a l l y sold, but a l l producers receive the same price fo r the respective grades because of p r i c e pooling. This e l i m i n a t e s the need to keep track of in d i v i d u a l producer's product as i t i s placed onto the market. 1.11 Recent Developments In recent years, some changes have taken place i n the mushroom industry with respect to the b a r r i e r s to entry, production cutback, and problems with the unity of members i n the a s s o c i a t i o n . Taken together, these events have had a d e s t a b i l i z i n g influence on the industry. 1.11.1 Barriers to Entry i n the B.C. Mushroom Industry The o r i g i n of a u n i f i e d marketing umbrella for producers i n B.C. began with the inception of the F.V.M.G.C.A. i n 1956. However, the mushroom industry i n B.C. was not under supply management control u n t i l 1972. P r i o r to that, producers were able to f r e e l y enter and e x i t the industry. Recent developments pertaining to the extent of supply management i n the mushroom industry have resulted i n a new p o l i c y from the B r i t i s h Columbia Ministry of Agriculture. E f f e c t i v e January 1, 1986, any ind i v i d u a l who applies to produce mushrooms can obtain a permit from the B r i t i s h Columbia Mushroom Marketing Board. No r e s t r i c t i o n s are placed on the square footage of production that may be applied f o r . The change i n p o l i c y was a r e s u l t of complaints from in d i v i d u a l s outside the F.V.M.G.C.A. C r i t i c i s m of the ex i s t i n g system was focussed on the i n a c c e s s i b i l i t y of the industry to ind i v i d u a l s who d i d not belong to the F.V.M.G.C.A. The main thrust of the argument was centered around the i n d i v i d u a l 1 s r i g h t to earn a l i v i n g i n the occupation of his/her choice. The new p o l i c y has not yet affected the actual l e v e l of supply management f o r the B r i t i s h Columbia mushroom industry. While any i n d i v i d u a l has the r i g h t to produce mushrooms, no in d i v i d u a l can gain membership into the F.V.M.G.C.A. without buying out an e x i s t i n g member's shares i n the association. In addition, a l l mushrooms grown i n the B.C. lower mainland area must s t i l l be marketed through the F.V.M.G.C.A. This has important implications, because while non-members have access to the F.V.M.G.C.A. f a c i l i t i e s , they are under the following r e s t r i c t i o n s : 1. Compost, a major input i n the production process i s not supplied to non-members. The association f e e l s that the compost wharf cannot handle any extra capacity without adversely a f f e c t i n g e x i s t i n g members. 2. Growing s u p p l i e s ( p e s t i c i d e s , spawn, etc.) are 24 availa b l e to non-members at a 35 percent surcharge. 3. A 10 percent surcharge on gross d e l i v e r y c r e d i t for non-member product which i s marketed through the association. 4. No quarterly or annual dividend payout to non-members The r e s t r i c t i o n s , apart from being an e f f e c t i v e economic d e t e r r e n t to new entrants, are designed to give members p r e f e r e n t i a l treatment because of t h e i r invested c a p i t a l i n the association. A d d i t i o n a l l y , there i s a desire to promote s t a b i l i t y of prices i n the market, a goal which may be best achieved by maintaining a single s e l l i n g agent for mushrooms. 1.11.2 Production Withdrawal Consumption of fresh mushrooms i n B.C. has been r e l a t i v e l y stable f o r several years. Total production of mushrooms has also been stable, with only moderate increases of les s than 5 percent for the years 1984 to 1986. As t o t a l production of fresh mushrooms exceeds market demand, the surplus has been channeled to the processed market. The processed market, up u n t i l 1985, provided a return s u f f i c i e n t to cover t o t a l costs of production, but i n 1986, the s i t u a t i o n changed dramatically. Prices of imported processed mushrooms declined considerably, mainly due to pr i c e reductions on shipments from mainland China. The pri c e for domestic processed product eroded to l e v e l s below production costs. Some producers, a f t e r a year of strong market prices for both fresh and processed mushrooms and high l e v e l s of p r o f i t i n 1985, were faced with losses i n 1986. In 1987, a decision was made by producers to set up a system of voluntary production withdrawal for a temporary period of s i x months, with an option to reapply for a further s i x months i f market conditions were s t i l l unfavourable. Producers who v o l u n t e e r e d f o r t h i s program r e c e i v e d payment from the F.V.M.G.C.A. of $ 0.25 per square foot of growing area set aside (adequate to cover fixed costs for most producers). A l l producers were to finance t h i s plan, by s e t t i n g money aside from sales. The intent of the plan was to reduce the quantities of mushrooms going into processed grade, while s t i l l supplying as much fresh grade as the market would absorb. While f e a s i b l e as a short run solution, t h i s plan cannot be sustained i n the long run without increasing the sales commission, as the association requires a minimum volume of member patronage to cover costs of operation. Production withdrawal was i n i t i a t e d March 1, 1987. By May, 1987, t o t a l production decreased approximately 20 percent, s i m i l a r to 1983 production l e v e l s . 1.11.3 The Marketing Contract and Problems of Enforcement The continued problems of bootlegging i n the B.C. mushroom industry well a t t e s t to the fact that poor enforcement of a 26 marketing contract r e s u l t s i n abuse of the system, p a r t i c u l a r l y when producer prices are depressed r e l a t i v e to normal years. Bootlegging, or the i l l e g a l sales of mushrooms from the farm, i s a problem which has had a d e s t a b i l i z i n g influence on the industry i n recent years. Growers sign a contract binding themselves to d e l i v e r 100 percent of t h e i r product to the association. However, no system of penalties was i n s t i t u t e d to discourage abuse of the marketing contract. In 1985, several cases of bootlegging were brought to the attention of the Board of Directors of the F.V.M.G.C.A., and subsequently brought to court. In a l l cases, penalty was li m i t e d to damages which the association could prove were incurred as a r e s u l t of i l l e g a l sales. This was f a r from being an e f f e c t i v e deterrent, as monitoring producer bootlegging i s extremely d i f f i c u l t . In 1987, the combination of several factors led to a r i f t i n the association, with several producers choosing not to renew t h e i r annual marketing contracts. Processed mushroom prices had been extremely low the previous year, r e s u l t i n g i n a very low average p r i c e f o r producers i n 1986. In addition, increase i n bootlegging a c t i v i t y and the i n a b i l i t y of the association to e f f e c t i v e l y c o n t r o l i t was the source of much producer d i s s a t i s f a c t i o n . 1.11.4 Factors A f f e c t i n g the V i a b i l i t y of the F.V.M.G.C.A. The f i x i t y of factor inputs i n the f a c i l i t i e s of the F.V.M.G.C.A. makes i t c r u c i a l that the volume of member patronage not be subject to large fluctuations. The F.V.M.G.C.A. obtains revenue, as do many other marketing agencies, through a percentage commission on sales. A minimum l e v e l of patronage i s required i n order to generate s u f f i c i e n t revenue to cover costs. Capital a c q u i s i t i o n s are usually made on the basis of a planned l e v e l of a c t i v i t y . Labour requirements e x h i b i t some downward i n f l e x i b i l i t y as union labour i s employed. The c u r r e n t structure of the F.V.M.G.C.A. makes i t vulnerable to members leaving the association. The marketing contract that a l l members sign i s renewed on an annual basis. In addition, several producers have recently obtained a license to also act as a s e l l i n g agent, e f f e c t i v e October 15, 1988. This court decision makes i t possible f o r other producers to follow s u i t . The decrease i n volume of business as a r e s u l t of bootlegging, members leaving the association, and the ongoing voluntary production withdrawal program, have put the association i n f i n a n c i a l d i f f i c u l t i e s . CHAPTER 2 A MATHEMATICAL MODEL OF THE B.C. MUSHROOM INDUSTRY In t h i s chapter, a mathematical model of demand and supply i n the B.C. mushroom industry i s presented. The model w i l l be used to determine whether the market i s competitive, or whether producers c o l l e c t i v e l y exercise monopoly power. A p a r t i a l equilibrium analysis w i l l be employed. The variables which the model solves for are: market c l e a r i n g p r i c e and quantity of mushrooms, and quantity of inputs used i n the production process. A l l other variables, such as consumer income, pri c e s of other goods, etc., are held constant. Market demand for mushrooms i s modelled by l i n e a r equations i n p r i c e and quantity. Market supply of mushrooms i s modelled by minimizing a producer cost function, subject to a Constant E l a s t i c i t y of Substitution (CES) production technology. The demand model i s presented i n section 1. This i s followed by the supply model i n section 2. Section 3 outlines the modelling of market equilibrium. In section 4, a discussion of welfare measurement using the concept of consumer and producer surplus i s presented. Lastly, i n section 5, an analysis of an a g r i c u l t u r a l quota i s presented. 28 29 2.1 Demand Model The demand f o r mushrooms produced i n B.C. i s divided into four sub-markets according to the d i f f e r e n t categories for consumption: 1. R e t a i l demand for mushrooms consumed fresh i n B.C. 2. Export demand for mushrooms consumed fresh outside of B.C. 3. Derived demand for mushrooms by other processors, such as Campbell•s. 4. Derived demand for mushrooms processed by the F.V.M.G.C.A. and sold i n Canada. Fresh mushroom demand i n B.C. at the r e t a i l l e v e l i s modelled as a l i n e a r function i n pri c e and quantity: (1) X f = c - bP f where Xf = quantity of fresh mushrooms demanded Pf = r e t a i l p r i c e of fresh mushrooms Export demand f o r fresh mushrooms shipped out of B.C. i s assumed to be p e r f e c t l y e l a s t i c at 1986 pri c e s . S i m i l a r l y , mushrooms sold to other processors are also assumed to have p e r f e c t l y e l a s t i c demand at 1986 prices. (2) PI = PI (3) P2 = P2 where PI and P2 are 1986 wholesale prices f o r fresh mushrooms sold outside B.C. and mushrooms sold to 30 processors respectively These assumptions are made i n the i n t e r e s t of simplifying the model, as separate estimation of these two submarkets i s not possible due to data l i m i t a t i o n s . These two markets act as residual markets for fresh mushrooms which cannot be sold i n B.C. Also, these two markets make up les s than 20 percent of t o t a l production i n B.C., so any error introduced by these assumptions should not a f f e c t seriously the r e s u l t s of the model. Derived demand for mushrooms processed by the association i s assumed to be p e r f e c t l y e l a s t i c at 1986 pr i c e l e v e l s : (4) Pp - Pp" where Pp = wholesale p r i c e of mushrooms processed by the F.V.M.G.C.A. That i s , the B.C. mushroom industry i s a pr i c e taker i n the processed mushroom market. The pri c e for mushrooms processed i n B.C. i s assumed to be determined l a r g e l y by pric e s of competing imported processed mushrooms. This assumption i s j u s t i f i e d for two reasons, based on the econometric r e s u l t s presented l a t e r i n chapter 3: 1. Near one to one correspondence between domestic and import p r i c e . 2. Quantity variable not s i g n i f i c a n t l y d i f f e r e n t from zero i n the pri c e dependent regression equation. That i s , the domestic l e v e l of processed mushroom production has no s t a t i s t i c a l l y measurable e f f e c t on the p r i c e l e v e l of processed mushrooms. A diagramatic representation of the B.C. mushroom industry i s presented i n Figures 2.1 to 2.4 below: X w h o l e s a l e X farm Quantity (lbs) X w h o l e s a l e X farm Quantity (lbs) Figure 2.1 B.C. Fresh Market Demand Figure 2.2 Fresh Market Demand (out of B.C.) X w h o l e s a l e X farm Quantity (lbs) X w h n l p s a l e X farm Quantity (lbs) Figure 2.3 Derived Demand by Other Processors Figure 2.4 Derived Demand for B.C. Processed Fresh and processed mushrooms are produced as a j o i n t product. The fresh mushrooms are s p l i t into two components, sales within B.C. and sales outside of B.C. (5) X f = aX (6) X f l = klX where: X = t o t a l production of mushrooms i n B.C., fresh and processed Xf = quantity of fresh mushrooms marketed as fresh i n B.C. a = proportion of X which i s marketed as fresh within B.C. X f l = quantity of fresh mushrooms marketed as fresh outside of B.C. k l = proportion of X which i s marketed as fresh outside of B.C. Processed mushrooms are also s p l i t into two components, mushrooms shipped to other processors and mushrooms processed at the F.V.M.G.C.A. (7) Xp2 = k2X (8) Xp = (l-a-kl-k2)X where Xp2 = quantity of processed mushrooms shipped to other processors k2 = proportion of X which i s shipped to other processors Xp = quantity of processed mushrooms canned by the F.V.M.G.C.A. The industry average p r i c e received by producers i s a weighted combination of the prices obtained i n the four separate markets, adjusted for the wholesale-retail margin and marketing costs: (9) P = a[(Pf-M)(1-CF)] + k l [ P l ( l - C F l ) ] + k2[P2(l-CP)] + (l-a-kl-k2)[P p(1-CP)] where M = Retail-Wholesale margin CF = Commission (as a f r a c t i o n of one) on fresh mushrooms sold i n B.C. CF1 = Commission on fresh mushrooms sold outside of B.C. CP = Commission on mushrooms d e s t i n e d f o r processing From (1), the pr i c e Pf can be expressed as follows (10) P f = (c-X f)/b = (c-aX)/b Substituting (10) into (9) and rearranging terms gives (11) P = (ac/b-aM)(1-CF) + k l [ P l ( l - C F l ) ] + [k2P2 + (l-a-kl-k2-)P p](1-CP) + a 2/b(l-CF)X The t o t a l revenue function (TR) i s obtained by multiplying the pr i c e function with t o t a l quantity sold X: (12) TR = dX - f X 2 where d = (ac/b-aM)(1-CF) + kl[PI(1-CF1)] + [k2P2+(l-a-kl-k2)P p](1-CP) f = a 2/b(l-CF) F i n a l l y , marginal revenue (MR) i s obtained by d i f f e r e n t i a t i n g 34 t o t a l revenue with respect to quantity X: (13) MR = 6TR/6X = d - 2fX 2.2 Supply Model On the supply side, production i s assumed to be "reasonably" modelled using a CES technology (Arrow et a l . ) . The production function i s : (14) X = G(DK + (1-D)L)" V/P where X = t o t a l production K = l e v e l of fixed inputs L = l e v e l of variable inputs D = d i s t r i b u t i o n parameter G = sc a l i n g factor v = returns to scale parameter p = substitution parameter Fixed inputs are mainly composed of buildings and equipment. Variable inputs include a l l inputs which are purchased f o r use i n the production process and whose l e v e l s of u t i l i z a t i o n may be varied as economic conditions change. The c o e f f i c i e n t G i s a scal i n g factor which varies according to the units i n which output and inputs are measured. Returns to scale i s captured by the parameter v. An increase i n both inputs by a factor 9 would r e s u l t i n an increase i n output of G v. Therefore, the production function exhibits increasing returns to scale technology when v > 1, decreasing returns to scale when v < 1, and constant returns to scale when v = 1. The c o e f f i c i e n t p i s a substitution parameter. In fact, the CES production function encompasses a whole family of production functions, depending on the value of p. This i s apparent from the derivation of the e l a s t i c i t y of substitution (Walters, p.286) between inputs K and L: (15) b = e l a s t i c i t y of substitution = l/(l+p) The higher the value of p, the lower the e l a s t i c i t y of subs t i t u t i o n . The value of p cannot be less than -1. As p approaches -1, the e l a s t i c i t y of subs t i t u t i o n tends to i n f i n i t y . At the other extreme, as p approaches i n f i n i t y , the e l a s t i c i t y of s u b s i t i t u t i o n approaches zero, as i n the case of fixed c o e f f i c i e n t s , or Leontief technology. When p = 0, the e l a s t i c i t y of s u b s t i t u t i o n i s 1 giving r i s e to a Cobb Douglas technology. The d i s t r i b u t i o n parameter D, together with the substitution parameter p determines the d i s t r i b u t i o n of income between factors. To see t h i s , the solution f o r a competitive equilibrium where the marginal rate of substitution i s equal to the r a t i o of factor p r i c e s gives r e s u l t s i n the following expression (Arrow et a l , p.233), (16) WL/RK = D/(1-D)*(K/L)P When the subs t i t u t i o n parameter i s equal to 0, (unit e l a s t i c i t y of s u b s t i t i o n between inputs), the d i s t r i b u t i o n of income between K and L does not vary with the factor r a t i o K/L. The greater the deviation of p from zero, the greater the impact factor r a t i o s have on the d i s t r i b u t i o n of income. The u n i t p r i c e of inputs i s assumed to be constant with respect to quantity of inputs purchased. Total cost i s : (17) C = RK + WL where R = unit cost of fixed input W = unit cost of variable input The cost function can be minimized subject to the production function (14). The d e t a i l s are presented i n Appendix A. The r e s u l t i s a minimum cost function, with cost of inputs, G, D, and quantity of inputs as parameters. This i s i n fac t a supply function. (18) C-hat = G - V v x l / v e ( P + l ) / P where e = D ( V (P+l))R(P / (P+l)) + ( i - D ) ( V ( P+l)) W ( P / ( P + 1 ) ) F i n a l l y , marginal cost (MC) i s obtained by d i f f e r e n t i a t i n g the cost function with respect to output X. (19) MC = 6C-hat/6X = G - V v / v e ( P + l ) / P x ( l - v ) / v 2.3 Modelling Market Equilibrium The welfare e f f e c t s of two market s i t u a t i o n s can be examined. At one extreme, monopolistic market behavior i s modelled by se t t i n g industry production at the l e v e l where marginal revenue (equation (13)) i s equal to marginal cost of pro d u c t i o n (equation (19)). The other extreme, perfect competition, i s modelled by set t i n g market p r i c e (equation (11)) equal to marginal cost of production. The competitive p r i c i n g decision works well when dealing with returns to scale less than or equal to unity. However, no competitive p r i c i n g decision e x i s t s f o r an increasing returns to scale industry i f production occurs i n the region where marginal cost i s below average cost. In such a s i t u a t i o n , there i s incentive to produce the marginal uni t when p r i c e i s greater than marginal cost, even though such production i s i n the region where pr i c e i s l e s s than average cost. A competitive market would therefore r e s u l t i n e x i t of some firms from the industry as producers, t r y i n g to equate p r i c e with marginal cost, incur losses. I f increasing returns to scale characterized production for a l l relevant ranges of production, the eventual market outcome would be a s i n g l e firm. Such a firm would then be able to exercise monopoly power i n the market. However, i f increasing returns to scale e x i s t only for a c e r t a i n portion of the supply curve, then a competitive equilibrium may e x i s t at some point near the region where returns to scale are neutral. This p o s s i b i l i t y i s explored i n the mathematical model by s e t t i n g p r i c e equal to average cost when increasing returns to scale are involved. R e s t r i c t i o n s on the supply of mushrooms, through the use of production area quotas, are incorporated into the model by solving for a solution subject to a constant f i x e d l e v e l of fixed input, K (see Appendix A) . The l e v e l of fixed input K i s an appropriate measure of the quantity of resources whose l e v e l of 38 usage i s d i s t o r t e d due to the existence of the quotas on area of production. 2.4 The Concept of Consumer Surplus Discussion of the welfare implications of supply management t y p i c a l l y make use of the concept of economic surplus. In Figure 2.1, l i n e a r demand D and supply S functions are shown. Price o s D Quantity Figure 2.5 Welfare E f f e c t s of Supply Control Source: Barichello (1985) The consumer surplus i s defined as the area P'cP. This area i s the extra revenue that a p e r f e c t l y discriminating monopolist could extract by s e l l i n g to i n d i v i d u a l consumers at sequentially lower p r i c e s . In a competitive market, consumers buy a l l units at one market c l e a r i n g p r i c e . Therefore, the area under the demand curve and above the p r i c e l i n e can be argued to be a consumer surplus. S i m i l a r l y , area PcO i s a producer surplus i n the sense that the producers receive the same p r i c e P f o r every unit produced, but the costs of production l i e below the supply curve S. R e s t r i c t i o n of production to the quantity Q gives r i s e to : 1) loss i n consumer surplus PacP i i ) loss i n producer surplus bed . . . . ^\ 111) gain i n producer surplus PabP The net e f f e c t i s a welfare loss of area adc, which i s the so c a l l e d "deadweight t r i a n g l e l o s s " . Producers gain from imposition of the quota i f the gain PabP more than o f f s e t s the loss bed. 2.5 F i n a n c i a l Analysis of Production Quota The ownership of quota w i l l have a value attached to i t as supply r e s t r i c t i o n r e s u l t s i n greater than normal p r o f i t s on a l l units of production. Producers who already have a quota a l l o c a t i o n but wish to increase production would obtain benefits of magnitude 'ad' on marginal units of output. Assuming that the quota can be defined i n terms of production, i f a competitive market f o r quota which i s sold on an incremental basis ex i s t s , producers would be w i l l i n g to pay a p r i c e up to the expected net present value (NPV) of pr i c e "ad" f o r each addi t i o n a l unit of quota. The marginal benefits of quota ownership would be r e f l e c t e d i n the market pr i c e for quota. I f the market equilibrium i s competitive, there i s on average no excess p r o f i t to be obtained at the margin, as production continues up to the l e v e l where marginal cost i s equal to p r i c e . Therefore, no value w i l l be associated with marginal units of production quota, unless the prospective buyer has a lower marginal cost than the industry average. Such a s i t u a t i o n would be remedied i n a well functioning market f o r quota which allows the higher marginal cost producer to s e l l part of his quota to a lower marginal cost producer. The quota market would reduce marginal rents towards zero. However, quota can s t i l l take on a value i n a competitive market, as ownership of quota i s e s s e n t i a l l y a license to produce. That i s , there are inframarginal rents associated with quota ownership which can be approximated by the difference between t o t a l revenue and t o t a l cost of production ( p r o f i t ) . Therefore, the market pr i c e for quota which i s sold to a new entrant into the industry would be related to the benefits of entry into the industry. The valuation of quota as the benefit from marginal units of production i n a supply r e s t r i c t e d market i s separate and d i s t i n c t from the valuation of quota as a production l i c e n s e i n an otherwise competitive market. I t i s important to d i s t i n g u i s h the marginal rents of the former from the inframarginal rents of the l a t t e r . The market p r i c e for quota can be analysed i n the same fashion as a f i n a n c i a l asset which provides a flow of returns over time. The following discussion i s a b r i e f summary of the d e t a i l e d a n a l y t i c a l method that Barichello (1984) employs i n his analysis of marketing quota i n the B r i t i s h Columbia dairy industry. The net present value of an asset i s defined by the following formula, (1) P q = 2 F t / ( l + r t ) t where Pg = net present value of quota = quota p r i c e Ft = benefit at time t from one uni t of asset r-£ = discount rate at time t N = expected l i f e of the asset As presented, the equation requires d e t a i l e d information which i s seldom available to the analyst/farmer contemplating a quota purchase decision. A useful s i m p l i f i c a t i o n of the equation would be to assume a constant l e v e l over time of both the discount rate and the benefits of quota. The equation becomes (2) P q = 2 F / U + r j t The quota investment can now be treated as an annuity, which can be solved f o r any one of Pg, F, r, or N when the other three are known. A producer would solve for P Q , given h i s knowledge of 42 the other varia b l e s . In a market where quota i s rented, the magnitude of variable F i s d i r e c t l y related to the rental rate of quota. Where there i s no market f o r quota r e n t a l , the magnitude of the benefit can be approximated by the si z e of "ad" i n Figure 1. However, there may be additional benefits to quota ownership which are not captured by the measures mentioned above. One source of benefit can be found i n the tax system. Producers are permitted to deduct from income an allowance for depreciation of quota, even though quota does not depreciate and i n fa c t usually appreciates i n value. Although t h i s tax advantage i s p a r t i a l l y recaptured upon resale of the quota through taxation of c a p i t a l gains, the net r e s u l t i s the equivalent of an i n t e r e s t free loan which grows i n s i z e as depreciation i s claimed u n t i l the quota i s sold. Another source of benefit i s the p o s s i b i l i t y of future c a p i t a l gains. This may a r i s e from the i n s t i t u t i o n a l rules and regulations which e x i s t i n the industry. An example would be the s i t u a t i o n i n which the industry l e v e l of quota i s increased i n order to accomodate demand growth. The new quota may be shared among e x i s t i n g members. Since the increase i n quota l e v e l s i s a r e s u l t of demand growth, there i s no decrease i n the value of e x i s t i n g quota, and therefore any additional quota can be treated as a c a p i t a l gain r e s u l t i n g from ownership of the o r i g i n a l quota. Quota pri c e s may also appreciate as a r e s u l t of technological advances which decrease the cost of production, thus increasing the value of benefits i f producer prices are not adjusted downwards. The expectation of c a p i t a l gains may be incorporated into the valuation of quota by subtracting from the discount rate a v a r i a b l e g, the expected rate of growth of i n the p r i c e of the quota. The discount rate r i s the opportunity rate of i n t e r e s t that a producer can expect to earn on the next best a l t e r n a t i v e investment. This rate may be adjusted to r e f l e c t the perceived r i s k of owning quota. Returns to a g r i c u l t u r a l production can vary greatly from year to year as a r e s u l t of b i o l o g i c a l factors beyond the producer's control, such as y i e l d s , disease, weather, etc. Input pr i c e s are variable, as are output p r i c e s . Also, the rules and regulations which govern the industry may be modified by new government regulations. Consumer groups may lobby for lower pr i c e s and p a r t i a l or f u l l dismantling of the quota system. These and other r i s k s which would r e s u l t i n loss of benefits from ownership of quota can be i m p l i c i t l y included i n the valuation of quota by adjusting upwards the discount rate r. A l t e r n a t i v e l y , the time horizon N for expected l i f e of the quota may be shortened. This corresponds to the notion of a "payback period", the number of time periods neccessary for the benefits of an asset to equal the market p r i c e of the asset. A r i s k i e r asset would command a shorter payback period than another asset with the same pr i c e but with a more c e r t a i n rate of return. To summarize the methodology, the f i n a l form of the expression f o r the net present value of quota i s (4) P q* = S F / U+r-gjt 44 where P q* = P q adjusted for tax benefits g = expected rate of appreciation of quota p r i c e CHAPTER 3 CONSUMER DEMAND THEORY, ECONOMETRIC MODELLING AND ESTIMATION This chapter focuses on the methodology for obtaining the parameters needed for the demand section of the mathematical model presented i n Chapter 2. F i r s t , a b r i e f overview of consumer demand theory i s presented i n section 1. Section 2 presents the formulation of econometric equations to estimate the demand f o r mushrooms produced i n B.C. In section 3, the res u l t s of the econometric equations are presented. Lastly, i n section 4, a cost of production model i s s p e c i f i e d . 3.1 Consumer Demand Theory A h i s t o r y of the development of consumer demand theory can be found i n Hassan and Johnson (Hassan and Johnson, pp. 2-4) . Much of the organization and content for the discussion to follow i s borrowed from Hassan and Johnson, and Deaton and Muellbauer. I t i s intended to be a b r i e f discussion of some of the issues i n demand theory as they pertain to t h i s study. 45 46 3.1.1 C l a s s i c a l Consumer Demand Theory The cornerstone of the c l a s s i c a l theory of consumer demand i s the u t i l i t y function, (1) u = u(q) where u i s the u t i l i t y or s a t i s f a c t i o n derived from consumption of goods q = [qj_], an n-element column vector of quantities of various commodities. Res t r i c t i o n s on the curvature properties of the u t i l i t y function, namely that i t i s s t r i c t l y increasing, s t r i c t l y quasi-concave, and twice continuously d i f f e r e n t i a b l e , r e s u l t i n a well indifference curve. These r e s t r i c t i o n s are necessary i n order to assure consistency of choice by the consumer. A set of s i x axioms of choice can be formulated (Deaton and Muelbauer 1980, pp. 26-30), the acceptance of which i s equivalent to the existance of the u t i l i t y function. Quantity of q2 Quantity of q l Figure 3.1 Indifference Curve for the U t i l i t y Function (1) 47 Consumer demand i s subject to a l i n e a r budget constraint, (2) p'q = m where p = [pjj i s an n-element column vector of pri c e s , and p'q i s the vector product of p transpose and q. Using the method of Lagrange, the u t i l i t y function (1) can be maximized subject to the budget constraint (2), (3) L(q,/i) = u(q) - /i(p'q - m) Where n i s the Lagrangian m u l t i p l i e r , which has an int e r p r e t a t i o n as the marginal u t i l i t y of the constraint, income. The f i r s t order conditions for a maximum are: (4a) u-L - up = 0 (4b) p'q - m = 0 Where i s the p a r t i a l derivative of u t i l i t y u with respect to q. The set of f i r s t order conditions provides n+l equations i n 2n+2 var i a b l e s . From t h i s , a unique set of equations can be solved i n terms of prices and income. The sol u t i o n comprises a set of "demand equations", (5) q i = q i ( P i , . . . , P n , m ) i = l , . . . , n (6) ix = M(PI# • • • ,Pn'm) Assumning the existance of a set of demand functions (5), the f a c t that they s a t i s f y the budget constraint (2) places a r e s t r i c t i o n on the functions q-̂ , (7) 2 Piqi(p,m) = m This i s commonly referred to as the "adding up r e s t r i c t i o n " . Another implication of the budget constraint concerns the e f f e c t 48 of o v e r a l l p r i c e l e v e l on demand. For any p o s i t i v e number 6, and for a l l i from 1 to n, (8) qi(ep,em) = qi(p,m) Homogeneity of degree zero implies an absence of "money i l l u s i o n " . I f a l l prices and income are twice as high, o v e r a l l demand remains unchanged, because only the absolute p r i c e l e v e l has changed, not the r e l a t i v e p r i c e l e v e l . This i s of course a weak assumption, but i t i s not t r i v i a l , as examples may be found of goods which have an appeal because of t h e i r absolute p r i c e l e v e l . High p r o f i l e luxury items, such as diamonds and other jewelry are an example. Manipulation of the f i r s t order conditions (4) y i e l d further r e s t r i c t i o n s on the set of demand equations. These are presented i n Table 3.1 below. Table 3.1 Restrictions on the System of Demand Equations R e s t r i c t i o n Name Engel Aggregation Cournot Aggregation WJ (n^ - n-j) Symmetry Relation Homogeneity Condition Source: Hassan and Johnson (1976), p.11 Table 1 The Engel aggregation condition states that the weighted sum of income e l a s t i c i t i e s with weights ŵ  = Piqi/m (expenditure proportion of tota l ) i s unity. Cournot aggregation expresses the S Wj[Oi = 1 S w-jeij = - WJ e i j = Wj/Wi * e i j - S e i j = -r>i weighted sum of p r i c e e l a s t i c i t i e s e^j i n column j as the negative of expenditure proportion on commodity j . The symmetry r e l a t i o n implies that the matrix of cross-price e l a s t i c i t i e s i s symmetrical. Lastly, the homogeneity condition i s a re-statement of (8), i n terms of e l a s t i c i t i e s . In summary, the c l a s s i c a l theory of consumer demand provides a complete set of demand equations which are obtained from maximization of a consumer u t i l i t y function subject to a budget constraint. The demand functions r e l a t e quantities consumed to a l l commodity prices and income. Given n commodities, there are n d i r e c t p r i c e e l a s t i c i t i e s , n 2-n cross-price e l a s t i c i t i e s , and n income e l a s t i c i t i e s , for a t o t a l of n2+n parameters that need to be estimated at the same time. By imposing the r e s t r i c t i o n s which are outlined i n Table 3.1 and the budget constraint, the number of parameters can be reduced. The symmetry r e l a t i o n allows a reduction of h(n2-n) parameters. Cournot and Engel aggregation further reduce t h i s number by n-1, to ^(n 2+n)-l remaining independent parameters. This number of parameters i s s t i l l too large to allow d i r e c t estimation of a complete demand equations. 3.1.2 Extension of the C l a s s i c a l Theory of Consumer Demand In order to estimate the parameters of the set of demand equations, further r e s t r i c t i o n s are required. Many studies, including t h i s , make ad hoc assumptions by omitting c e r t a i n variables i n the demand functions. The unfortunate drawback of t h i s method i s that the bias introduced by these r e s t r i c t i o n s needs to be evaluated i n order to assess the v a l i d i t y of the r e s u l t s . As a solution to the unrestricted equations cannot be computed, there i s , i n general, no basis from which to assess the bias of additional r e s t r i c t i o n s . The r e s u l t s are therefore dependent on the r e s t r i c t i o n s which are applied. The a l t e r n a t i v e to ad hoc estimation i s a systematic re- working of the c l a s s i c a l theory of consumer demand. What i s needed are more r e s t r i c t i o n s on the basic t h e o r e t i c a l groundwork; that i s , more r e s t r i c t i v e behavioral assumptions. Much of current research e f f o r t s i n demand theory i s centered about a more s p e c i a l i z e d u t i l i t y function. One widely used assumption i s the notion of s e p a r a b i l i t y . Many published r e s u l t s (e.g., Hassan and Johnson) employ some form of s e p a r a b i l i t y assumption, and i t i s useful to compare t h e i r findings against the simpler, ad hoc s p e c i f i c a t i o n s which w i l l be employed i n t h i s study. 3.1.3 Single Equation Demand Estimation Econometric estimation of single equation demand i s widely used i n the l i t e r a t u r e . From the discussion i n the previous sections of t h i s chapter, i t i s c l e a r that s i n g l e equation estimation i m p l i c i t l y contains some strong assumptions on the underlying theory of consumer behavior. As an example, the following demand equation i s often used, (9) q i = a + bm + 2 e i j P j + u i i = l , . . . , n where u^ i s a disturbance term. Some assumptions which are implied by (9) are: 1. The j summation index does not include a l l commodities, even within the same group (e.g., a l l vegetables). The l i m i t k-[ means that the res t of the n-k^ parameters are forced to be zero. While the r e s u l t i n g bias may be zero for unrelated goods (e.g., vegetables and cars), the bias may not be t r i v i a l f or goods which are close substitutes or complements. 2. Price i s the dependent variable, and a l l the other r i g h t hand side variables are exogenous. In the market, equilibrium i s generally determined simultaneously i n pr i c e and quantity. Other behavioral equations may need to be estimated simultaneously, as not a l l the variables on the r i g h t hand side are completely exogenous to pr i c e . This i s the problem of simultaneous equation bias. Functional form also implies some form of r e s t r i c t i o n on consumer behaviour. For example, the double log form, popular i n the l i t e r a t u r e , v i o l a t e s the Engel aggregation c r i t e r i o n . I f Engel aggregation i s applied to a system of equations employing the double log functional form, a l l income e l a s t i c i t i e s are forced to equal one (Yoshihara, p.261). In general, single equation estimation imposes r e s t r i c t i o n s 52 on the function estimated. In addition, not a l l the r e s t r i c t i o n s (Table 1) which are available from economic theory are employed. However, time and data l i m i t a t i o n s often d i c t a t e s i n g l e equation methods. Single equation estimates are useful i f the bias introduced i s not too large. 3.2 The Demand for Mushrooms i n B.C. The demand f o r mushrooms produced i n B.C. can be conveniently s p l i t into two components, fresh and processed. The bulk of fresh mushroom consumption i n B.C. i s centered i n the heavily populated areas of Greater Vancouver and the Fraser Valley region (lower mainland). The r e l a t i v e l y short shelf l i f e of fresh mushrooms l i m i t s marketing of B.C. mushrooms i n other regions of Canada. In contrast, B.C. processed mushrooms are marketed i n every province of Canada. 3.2.1 Demand for Fresh Mushrooms The F.V.M.G.C.A. i s the sole s e l l i n g agent for B.C. produced mushrooms. As the l o c a l fresh product accounts for more than 90 percent of B.C. consumption, the F.V.M.G.C.A. i s a pr i c e setter. Therefore, p r i c e i s an exogenous variable and the dependant var i a b l e for fresh mushroom demand i s the quantity consumed. From the discussion i n the previous section on consumer demand theory, the other determinants of demand include prices of 53 substitutes, complements, and income. The demand f o r fresh mushrooms i n B.C. i s formulated as follows: (1) CONSUMP = f(PIFV, CPIB, RINCO, RAD, TREND, DUMMY) where CONSUMP = per capita consumption (lbs/capita/month) of fresh mushrooms i n B.C. PIFV = r e a l p r i c e index of fresh mushrooms at the r e t a i l l e v e l minus r e a l p r i c e index for vegetables CPIB = r e a l consumer p r i c e index of beef f o r Canada (1981=100) RINCO = re a l labour income for B.C. ($/month) RAD = r e a l advertising expenditures, media and prom o t i o n ($/capita/month) f o r f r e s h mushrooms TREND = time trend, Jan.1983=1...Sept. 1986=57 DUMMY = dummy variables denoting seasonality i n each month of the year (except December) Data on these variables were available on a monthly basis from January 1982 to September 1986. Values for CPIB, RINCO, and RAD have been adjusted by the consumer p r i c e index f o r a l l goods i n Vancouver, 1981=100, to obtain r e a l values. The variable PIFV was constructed as follows. The pr i c e f o r mushrooms was constructed into an index with base year 1981, and deflated by the consumer pr i c e index for a l l goods. A fresh vegetable p r i c e index f o r Vancouver, 1981=100 was also deflated by the consumer 54 pr i c e index f o r a l l goods. The difference was then taken between the mushroom r e a l p r i c e index and the vegetable r e a l p r i c e index. Appendix B contains a l i s t i n g of some of the variables used 4. A p r i o r i , the standard assumptions based on economic theory state that the c o e f f i c i e n t for: 1. Own Price i s negative. Mushrooms are assumed to be normal good. In addition, fresh mushrooms are thought to be a substitute f or fresh vegetables. As the pri c e difference between mushrooms and other fresh vegetables increases, the quantity demanded decreases. 2. CPIB i s negative. Mushrooms are believed to be complement to beef. 3. RINCO i s p o s i t i v e . Mushrooms are a superior good. As income increases, more i s availa b l e f o r expenditure on goods which the consumer desires more of. 4. RAD i s p o s i t i v e . Advertising mushrooms i s expected to increase consumption. In a recent B.C. consumer survey commissioned by the F.V.M.G.C.A. (Marketrend) , i t was found that the two major uses for fresh mushrooms are as an accompaniment to meat dishes, p a r t i c u l a r l y steak, and with salads. The var i a b l e CPIB i s included i n the demand equation as a proxy for steak p r i c e s . The usage of mushrooms i n salads i s captured i n the variable PIFV, the difference between price indices for fresh mushrooms and a l l 4The data on some of the variables i s c o n f i d e n t i a l , and therefore cannot be l i s t e d . 55 fresh vegetables. Advertising i s included i n the model, as there i s presently an extensive on-going promotion campaign. On average, for the years between 1982 and 1986, greater than $1,000,000 each year has been a l l l o c a t e d f o r promotion of fresh mushrooms produced i n B.C. The name brand "Money's Mushrooms" receives regular exposure i n newspapers ads, magazines a r t i c l e s , radio spots, and t.v. comercials. The advertising variable i s actual monthly expenditures on advertising for fresh mushrooms. This variable i s not necessarily i n d i c a t i v e of the actual amount of advertising that occured i n any given month. For example, t e l e v i s i o n commercial costs are often paid immediately, but the commercials may run f o r several months afterwards. Despite t h i s major l i m i t a t i o n , i t i s the best available measure of advertising expenditure. An income variable i s included, i n order to t e s t the hypothesis that increases i n disposable income r e s u l t i n higher consumption of fresh mushrooms. No data were avail a b l e for disposable income fo r B.C. on a monthly or quarterly basis. The v a r i a b l e RINCO, labour income, was chosen as a proxy for disposable income. Monthly dummy variables are used to capture any seasonal component(s) which i s not explained by the other variables i n the model. In p a r t i c u l a r , inspection of monthly fresh mushroom sales data reveals a marked decline i n quantities sold i n the months of February, September and October of each year. No plausible explanation i s available f o r decline i n September and October, so a dummy var i a b l e i s used fo r both months. The decline i n quantity sold i n the month of February can l i k e l y be attributed to fewer days i n that month. A trend variable i s included to capture any pattern of change i n consumption which i s not explained by the other independent variables included i n the model. Time and d a t a l i m i t a t i o n s n e c e s s i t a t e d e x c l u s i o n r e s t r i c t i o n s with resp e c t to complement and s u b s t i t u t e r e l a t i o n s h i p s which are not explored i n the demand model. The most obvious exclusion, processed mushroom pri c e s , was made necessary by data l i m i t a t i o n s . Processed mushroom prices were only a v a i l a b l e at the wholesale l e v e l . Processed mushrooms are a storable commodity, therefore wholesale prices i n any given month are not a r e l i a b l e i n d i c a t i o n of r e t a i l p r i c e s i n that month. Also, processed mushroom prices for imports into B.C. were not a v a i l a b l e on a monthly basis. Further, p r i c e of l o c a l processed mushrooms was only available for 44 observations, 13 fewer than were av a i l a b l e for other variables i n fresh demand. The decision was made to exclude processed prices i n the fresh demand model. 3.2.2 Advertising and Demand The r o l e that advertising plays i n the demand function i s one that deserves special attention. Advertising e f f e c t s are d i f f i c u l t to model for several reasons. 57 The appropriate unit with which to quantify advertising i s not c l e a r . The type of media employed, such as radio, t.v., or newspaper c e r t a i n l y has a bearing on the effectiveness of the advertising expenditure. However, the researcher r a r e l y has access to s u f f i c i e n t information on these variables to attempt l e a s t squares regression. Usually, data l i m i t a t i o n s d i c t a t e using expenditure d o l l a r s as a measure, but t h i s i s , at best, only an approximation. Another problem l i e s i n the differences that e x i s t i n the response of i n d i v i d u a l s to advertising. Different people not only respond d i f f e r e n t l y to advertising, but a p a r t i c u l a r person may also respond d i f f e r e n t l y to r e p e t i t i o n of the same stimulus depending on other factors which are too complex to model. L a s t l y , even i n the absence of the above problems, advertising e f f e c t s are d i f f i c u l t to model because they are thought to p e r s i s t longer than the current time period. Two important issues a r i s e : (a) what i s the magnitude of the e f f e c t , (b) how does t h i s change over time. In the discussion that follows, a l l variables other than advertising are omitted for ease of exposition. The " d i r e c t lag" model i s the simplest way of estimating advertising effectiveness over time. Lagged advertising values are included i n the equation as independent va r i a b l e s : (1) Yt = a o + s b j x t - j + e t where: y^ = demand at time t x-t-_j = advertising expenditures at time t - j 58 e-t = spherical disturbance term ( i d e n t i c a l l y d i s t r i b u t e d , with mean 0 and variance a 2 ) . S p e c i f i c a t i o n of the lag length n requires a subjective decision by the researcher. I f the lag length chosen i s shorter than the true lag length, truncation bias would r e s u l t . I f n i s longer than the true lag length, t e s t s of the s i g n i f i c a n c e of a d d i t i o n a l lagged values may be used. The above procedure r e s u l t s i n e f f i c i e n t , unbiased estimates of the c o e f f i c i e n t s when the standard assumptions of ordinary l e a s t squares r e g r e s s i o n are v a l i d (Johnson, pp. 168-71). However, t h i s i s seldom the case and i n practice, the assumption of independence among the exogenous variables i s often v i o l a t e d . S p e c i f i c a l l y , lagged advertising variables are often found to be highly c o l l i n e a r (the problem of m u l t i c o l l i n e a r i t y ) . The r e s u l t i n g estimates become i n e f f i c i e n t (large standard e r r o r s ) , but are s t i l l unbiased asymptotically. A n o t h e r approach uses a weighted moving average representation for advertising. Past values are s p e c i f i e d as a stock or "goodwill" variable. Studies that have used t h i s method include Nerlove and Waugh, and Kinnucan. Again, a subjective decision must be made about the length of the lag, and as well, an appropriate weighting scheme must be chosen. The l i m i t a t i o n of t h i s approach i s t h a t the d u r a t i o n of a d v e r t i s i n g effectiveness cannot be r e l i a b l y derived from the r e s u l t s . S i g n i f i c a n t estimates of the parameters may be obtained even i f the actual duration i s shorter than the moving average because of 59 aggregation (Clarke, p.346). The d i s t r i b u t e d lag family of models are used widely for estimating advertising effectiveness. In p a r t i c u l a r , the Koyck model (Koyck) i s very useful. I t circumvents the problem of m u l t i c o l l i n e a r i t y by imposing a structure on the manner i n which past values of advertising outlays a f f e c t demand. This r e s u l t s i n a reduction i n the number of parameters that need to be estimated. The model i s derived from (1) and assumptions that: 1. n i s i n f i n i t e 2. the c o e f f i c i e n t bt declines exponentially with parameter such that 0 < 9 < 1 and bj = ©bj_! Equation (1) reduces to: (2) yt = a Q + 9 y t _ 1 + b Q x t + v t v t = e t - e t - l The parameter 9 represents the decaying e f f e c t of advertising over time. The reduced form (2) can also be derived from a hypothesis of adaptive expectations (Johnson, p.348). A re l a t e d model i s the p a r t i a l adjustment model. The reduced form i s the same as (2) , but with a much simpler structure f o r the error term. The p a r t i a l adjustment model i s derived from a d i f f e r e n t hypothesis of r a t i o n a l behaviour (Johnson, p.349). The carryover e f f e c t (represented by the lag dependent variable) , i s not a l l due to advertising as i n the Koyck model. In t h i s case, the i n e r t i a i s at t r i b u t e d to demand i n time t changing very l i t t l e from demand i n time t-1. The int e r p r e t a t i o n of 9 would therefore include other variables such 60 as p r i c e , product l o y a l t y , etc. The p a r t i a l adjustment process may be s p e c i f i e d as (3) y t " y t - i = ©(Yt* " Yt-l) + u t That i s , the difference between current period demand and the previous period i s a f r a c t i o n 9 of the difference between optimal, desired current period demand y^* and previous period demand. In contrast to the adaptive expectations and p a r t i a l adjustment models, which are derived from models with an expectations mechanism, a t h i r d type of d i s t r i b u t e d lag model can be postulated which i s driven s o l e l y by an autoregressive error. The cumulative e f f e c t s model (Griliches) has assumptions: i) Yt = a o + a x t + u t i i ) u t = eu t_! + e t i i i ) 0 < G < 1 Combining these assumptions r e s u l t s i n : (4) y t = a Q + ax t + eax^^. + c y t ^ + e t Noting that (4) i s very s i m i l a r to (2), Clarke (p.352) suggests a te s t equation: (5) y t = A Q + Ax t + Bxt.! + Cyt - x + v t v t = e t - Det.i The r e s u l t s can be categorized as follows: Adaptive Expectations (Koyck) P a r t i a l Adjustment Cumulative E f f e c t s B=0 B=0 B=-AC C=D D=0 D=0 61 A discussion of the r e s u l t s obtained from regression analysis of the three d i f f e r e n t models above i s presented i n section 3 of t h i s chapter. 3.2.3 Demand f o r Processed Mushrooms Processed mushrooms produced i n B.C. are sold i n every province i n Canada. More than 50 percent of l o c a l l y produced mushrooms are processed. Unlike the fresh market, the demand for processed mushrooms includes a s i g n i f i c a n t quantity of imports from P a c i f i c Rim countries. The market p r i c e i s influenced by t o t a l quantities (import and domestic) a v a i l a b l e . The qu a l i t y of l o c a l product i s distinguishable from imports, allowing a small p r i c e premium f o r Money's name brand. Processed market demand i s not modelled i n the same manner as the fresh market. The endogenous variable i n the processed market i s p r i c e , which i s determined i n the market. This i s i n contrast to p r i c e formation for fresh grade, where p r i c e i s set by the s e l l e r . In addition, inventory management i s possible i n the processed market, an option which i s not av a i l a b l e i n the fresh market. The market for B.C. processed mushrooms i n Canada i s modelled as a pr i c e function, with variables as described above. An appropriate model using p r i c e as the dependent variable ( I n t r i l i g a t o r , p.224) i s as follows: (7) CPRICED = f(CCONSBC, CPRICEI, PINV, RPDI) where 62 CPRICED = r e a l p r i c e of B.C. canned product ($/lb) at the wholesale l e v e l CCONSBC = Canadian consumption of B.C. product (lb/capita/month) CPRICEI = r e a l p r i c e of imported product ($/lb) at the wholesale l e v e l PINV = processed inventories of B.C. product RPDI = Canadian r e a l per capita disposable income The variables are available on a monthly basis from January 1983 to September 1986. Price for processed mushrooms was adjusted by the Consumer Price Index f o r Processed Foods i n Canada (1981=100) to obtain r e a l values. RPDI was adjusted by the Consumer Price Index for A l l Items i n Canada (1981=100). A Canadian p r i c e function i s estimated, instead of a B.C. price f u n c t i o n , because data for B.C. consumption of processed mushrooms was not available. Appendix B contains a l i s t of some of the variables used 5. A p r i o r i , the expected sign of the c o e f f i c i e n t f o r : 1. CCONSBC i s negative. Processed mushrooms are a normal good. 2. CPRICEI i s p o s i t i v e . A higher imported p r i c e permits a 5The data on some of the variables i s c o n f i d e n t i a l , and therefore cannot be l i s t e d . higher B.C. p r i c e . 3. PINV i s negative. Large inventories have a depressing e f f e c t on p r i c e . That i s , i n order to reduce inventories, p r i c e must also be lowered, a l l else being constant. 4. RPDI i s p o s i t i v e . Processed mushrooms are a superior good. As i n the previous discussion of exclusion r e s t r i c t i o n s i n the fresh mushroom demand model, an obvious substitute variable, fresh mushroom price, was excluded due to data l i m i t a t i o n s . Wholesale fresh mushroom prices were not avail a b l e on a monthly basis. Also, prices of processed mushrooms for other regions of Canada were not available on a monthly basis. An inventory variable i s included as the l o c a l producers' a s s o c i a t i o n i s a c t i v e l y engaged i n inventory management. Inventory l e v e l s comprise a s i g n i f i c a n t l e v e l of t o t a l processed quantities. In 1986, a year with very weak processed prices i n the market, monthly inventory l e v e l s were on average as high as monthly sales of processed mushrooms. Import processed prices are included as the import share of domestic sales i s very high. In 1985, 73 percent of the Canadian processed market was offshore product. Imported mushrooms are believed to be a very close substitute f o r domestic processed mushrooms. 64 3.3 Econometric Estimation and Results of Demand for Mushrooms In the following discussion of r e s u l t s , a l l of the regressions were obtained using the regression package SHAZAM (White). The equations were estimated using a l i n e a r functional form. A p r i o r i , economic theory does not indicate which functional form i s the most appropriate. 3.3.1 Fresh Demand Equations The various lag models discussed i n the previous section on demand were estimated. In Table 3.2, the r e s u l t s for a simple model without lag variables, and the P a r t i a l Adjustment model are presented. The r e s u l t s for the t e s t equation (5), the Cumulative E f f e c t s , and Koyck Model are presented i n the Table 3.3. In Table 3.2, the r e s u l t s for a simple model without any allowances f o r the dynamic, inter-period e f f e c t s of advertising are presented. This estimate w i l l be biased but i t i s provided as a base case from which to compare the r e s u l t s of the other models. The independent variables explain 73.7 percent of the v a r i a t i o n i n the dependent model. A l l the independent variables, except r e a l income (RINCO), are s t a t i s t i c a l l y s i g n i f i c a n t at a 90 percent l e v e l . The t e s t of the n u l l hypthesis: H 0: RINCO i s s t a t i s t i c a l l y d i f f e r e n t from zero was rejected at the 5 percent c r i t i c a l l e v e l ( t c a i c < t c r i t = 2.02). 65 The Stock (Partial) Adjustment model i s also presented i n Table 3.2 . The o v e r a l l f i t of t h i s model i s only marginaly better than the simple model. The usual t e s t f o r s e r i a l c o r r e l a t i o n i n the residuals, the Durbin-Watson s t a t i s t i c , cannot be used as i t i s biased i n a lagged dependent model. An a l t e r n a t e t e s t , the Durbin-h s t a t i s t i c , shows no s e r i a l c o r r e l a t i o n i n the residuals. However, the c r u c i a l v a r i a b l e for t h i s model, lagged consumption (LCONS) i s not s t a t i s t i c a l l y s i g n i f i c a n t at the 95 percent l e v e l . The P a r t i a l Adjustment model i s therefore rejected. The r e s u l t s for t e s t equation (5) without any correction for s e r i a l c o r r e l a t i o n i n the residuals are presented i n the f i r s t column of Table 3.3 . As Durbin's h s t a t i s t i c cannot be ca l c u l t a t e d for t h i s p a r t i c u l a r regression, there i s no t e s t a v a i l a b l e f o r the presence of autocorrelation. As both variables c r u c i a l to the Cumulative E f f e c t s model, lagged consumption (LCONS) and lagged advertising (LRAD) are not s t a t i s t i c a l l y s i g n i f i c a n t , the equation i s re-run with an assumption of f i r s t order s e r i a l c o r r e l a t i o n (column 2 i n Table 3.3). The estimated autocorrelation parameter RHO i s s t a t i s t i c a l l y s i g n i f i c a n t ( t - s t a t = -4.31), implying the o r i g i n a l equation did indeed have f i r s t order s e r i a l c o r r e l a t i o n i n the residuals. This r e s u l t does not support the Current Ef f e c t s model, which predicts the value of RHO to be zero (D=0 i n equation (5)). Also, the lagged advertising v a r i a b l e LRAD i s s t i l l s t a t i s t i c a l l y not s i g n i f i c a n t l y d i f f e r e n t from zero. The Cumulative E f f e c t s model i s therefore rejected. 66 Table 3.2 Econometric Estimates of Fresh Mushroom Demand Linear and Stock Adjustment Models LINEAR STOCK MODEL ADJUSTMENT LCONS 0.149 (1.22) RAD 4.32E-01 0.438 (2.22)** (2.25)** RINCO 1.43E-06 1.50E-05 (0.01) (2.26)** MVINDEX -9.40E-04 -8.17E-04 (-2.47)** (-2.09)** CPIB -1.96E-03 -1.82E-03 (-1.93)* (-1.78)* TREND1 1.59E-03 1.33E-03 (7.28)** (4.34)** FE -2.69E-02 -2.83E-02 (-2.69)** (-2.82)** SE -4.29E-02 -4.09E-02 (-3.9)** (-3.7)** OC -4.25E-02 -3.66E-02 (-3.5)** (-2.81)** CONSTANT 0.445 0.382 (3.4)** (2.74)** Durbin-Watson 1.73 2.01 Durbin-h N/A -0.19 R-Square Adj 0.737 0.740 NOTE: t - s t a t i s t i c s i n brackets ** s i g n i f i c a n t at 95 % * s i g n i f i c a n t at 90 % Table 3.3 Econometric Estimates of Fresh Mushroom Demand Cumulative E f f e c t s and Koyck Lag Models CUMULATIVE EFFECTS KOYCK LAG OLS AUTO OLS AUTO LCONS 0.117 0.457 0.127 0.455 (0.87) (4.08)** (0.99) (4.24) RAD 0.282 0.420 0.312 0.410 (1.17) (2.18)** (1.46) (2.72) LRAD 6.42E-05 -1.51E-05 (0.28) (-0.08) RINCO 1.68E-04 1.35E-04 1. 70E-04 1.34E-04 (1.03) (1.16) (1.06) (1.16) LRINCO -2.93E-04 -1.62E-04 -3. 00E-04 -1.60E-04 (-1.63) (-1.15) ( -1.70)* (-1.15) MVINDEX -1.21E-03 -1.59E-03 -1. 18E-03 -1.60E-03 (-2.26)** (-3.52)** ( -2.27)** (-3.77) LMVINDEX 5.03E-04 1.44E-03 5. 11E-04 1.44E-03 (0.98) (3.59)** (1.00) (3.61) CPIB -1.68E-03 -1.95E-03 -1. 65E-03 -1.97E-03 (-1.19) (-1.62) ( -1.19) (-1.68) LCPIB 3.33E-04 1.32E-03 3. 00E-04 1.34E-03 (0.24) (1.09) (0.22) (1.14) TREND1 1.29E-03 6.94E-04 1. 27E-03 6.99E-04 (3.96)** (3.02)** (4.03)** (3.2) FE -2.66E-02 -2.36E-02 -2. 74E-02 -2.33E-02 (-2.54)** (-2.77)** ( -2.75)** (-3.00) SE -4.77E-02 -4.57E-02 -4. 85E-02 -4.53E-02 (-3.58)** (-3.85)** ( -3.78)** (-4.20) OC -3.56E-02 -3.08E-02 -3. 58E-01 -3.08E-02 (-2.71)** (-2.68)** (-2.76)** (-2.68) CONSTANT 0.449 0.225 0.450 0.224 (2.66)** (1.96)* (2.70)** (1.96) RHO -0.551 -0.550 (-4.31) (-4.35) Durbin-Watson 2.17 1.85 2.18 1.85 Durbin-h N/A 0.94 -2.59 0.85 R-Square Adj 0.742 0.771 0.748 0.776 NOTE: t - s t a t i s t i c s i n brackets ** s i g n i f i c a n t at 95 % * s i g n i f i c a n t at 90 % 68 The r e s u l t s for the Koyck model, with a correction f o r f i r s t order s e r i a l c o r r e l a t i o n of the residuals, indicate that i t f i t s the data best, explaining 77.6 percent of the v a r i a t i o n i n the dependent va r i a b l e . The Koyck model i s not rejected, as the c o e f f i c i e n t of the lag dependent variable, LCONS, i s not s i g n i f i c a n t l y d i f f e r e n t from the s e r i a l c o r r e l a t i o n parameter RHO (D i n t e s t equation (4). The 95 percent confidence i n t e r v a l s for LCONS and RHO are calculated below: COEF. STD. ERR. CONFIDENCE INTERVAL LCONS 0.455 0.107 +/" 0.216 RHO 0.550 0.127 +/~ 0.256 Both variables are within each other's confidence i n t e r v a l . A l l other variables show the a p r i o r i expected signs. As the Koyck model f i t s the data much better than the other models, the res t of the discussion w i l l focus on the Koyck model. A l l the variables, except labour income (RINCO) were s t a t i s t i c a l l y s i g n i f i c a n t at at le a s t the 90 percent l e v e l . Since labour income was included i n the model as a proxy for disposable income (not available for B.C. on monthly or quarterly b a s i s ) , i t s poor performance may be due to labour income being a poor approximation to disposable income. The regression was also run with Canadian disposable income, but the r e s u l t s were also not s i g n i f i c a n t for the income vari a b l e . I t i s possible that i n the short run, income has l i t t l e e f f e c t on consumption of fresh 69 mushrooms. The exclusion of an important variable which i s a substitute for fresh mushrooms, processed mushroom pri c e s , was necessitated by data l i m i t a t i o n s as discussed e a r l i e r . However, the regressions were estimated with the i n c l u s i o n of an additional v a r i a b l e ; wholesale processed prices as a proxy f o r r e t a i l processed mushroom prices. The wholesale processed mushroom p r i c e may not be a good proxy for the r e t a i l processed p r i c e i n any given month, since inventory management forms an i n t e g r a l part of that market. The econometric r e s u l t s confirmed t h i s suspicion, as the r e s u l t s implied that processed mushrooms are a complement to fresh mushrooms. This i s highly counter- i n t u i t i v e , so these r e s u l t s were not used. Clarke (Clarke, p.348) notes that the Koyck model has an implied duration i n t e r v a l which can be calculated using the formula: 1* = log(l-p) / l o g ( l ) where 1* = duration i n t e r v a l p = cumulative proportion of t o t a l impact 1 = c o e f f i c i e n t of the lagged dependent variable For the Koyck model estimated i n Table 1, the implied duration i n t e r v a l for p = 0.9 i s 2.92. That i s , for advertising to exert 90 percent of i t s influence on demand requires on average 2.9 months. 70 3.3.2 Demand E l a s t i c i t i e s f or Fresh Mushrooms E l a s t i c i t i e s calculated from the Koyck model for the appropriate independent variables are presented i n Table 3.4 below: Table 3.4 Demand E l a s t i c i t i e s f or Fresh Mushrooms Calculated at the Means VARIABLE SHORT RUN LONG RUN ELASTICITY ELASTICITY RINCO 0.28 0.51 OWN PRICE -0.56 -1.03 CPIB -0.53 -0.97 RAD 0.036 0.066 Income e l a s t i c i t y of demand i s s u b s t a n t i a l l y l e s s than one, implying that mushrooms are a normal, but i n f e r i o r good. This r e s u l t i s consistent with a p r i o r i expectations, as the demand for the majority of foods i s income i n e l a s t i c . By way of comparison, an Agriculture Canada study (Hassan and Johnson) employing a f u l l system of demand equations for foods obtained an estimate f o r income e l a s t i c i t y f o r fresh vegetables of 0.09. The estimate f o r the income e l a s t i c i t y of demand should be treated with caution, as the income variable was not s t a t i s t i c a l l y s i g n i f i c a n t i n the demand equation. In the short run, p r i c e e l a s t i c i t y of demand f o r fresh mushrooms i s less than one i n absolute value. Hassan and Johnson's estimate f o r d i r e c t p r i c e e l a s t i c i t y of fresh vegetables i s -0.2420. Both estimates are p r i c e i n e l a s t i c , although the own p r i c e e l a s t i c i t y obtained for fresh mushrooms i n t h i s study i s higher (in absolute value) than the e l a s t i c i t y estimate f o r a l l fresh vegetables i n the Hassan and Johnson study. Again, t h i s i s i n t u i t i v e l y p l ausible, as one would expect that the aggregated category can to be l e s s p r i c e responsive than any i n d i v i d u a l item within that category. This i s due to the p o s s i b i l i t i e s that e x i s t f o r s u b s t i t u t i o n between commodities within the same group. The long run estimate f o r own price e l a s t i c i t y i s j u s t s l i g h t l y over one i n absolute value. The beef CPI e l a s t i c i t y was negative, as expected for a good which i s postulated to be a complement for fresh mushrooms. The fact that beef CPI cross e l a s t i c i t y to fresh mushrooms i s i n e l a s t i c i s also consistent with a p r i o r i expectations. However, Hassan and Johnson's estimate (Hassan and Johnson, table 15 p.42) f o r cross p r i c e e l a s t i c i t y of t o t a l fresh vegetable demand with respect to beef p r i c e was only 0.01689. The corresponding estimates for other meats were a l l le s s than 0.06. The value obtained i n t h i s study was -0.53, considerably larger (in absolute value) than the above mentioned estimate by Hassan and Johnson f o r beef cross p r i c e e l a s t i c i t y with respect to vegetable consumption. Fresh mushrooms are used i n many other dishes, such as salads, pizza, soups, etc. Therefore, beef prices are expected to have a much smaller e f f e c t than estimated i n t h i s study. Beef prices must be behaving as a proxy for some other(s) v a r i a b l e which has not been included i n the regression. Advertising e l a s t i c i y i s quite low. That i s , advertising expenditures appear to have very l i t t l e e f f e c t on the l e v e l of consumption of fresh mushrooms. The low demand responsiveness to advertising expenditures may be due to the var i a b l e not being a suitable measure of the actual l e v e l s of advertising a c t i v i t y . A l t e r n a t i v e l y , consumers may simply be unresponsive to advertising i n the short run. The current high l e v e l of consumption of fresh mushrooms i n B.C. may instead be attributed to widespread a v a i l a b i l i t y of product and stable p r i c e s . 3.3.3 Processed Demand Equations The market for processed mushrooms produced i n B.C. was modelled as a pri c e dependant equation. The r e s u l t s are presented below: Table 3.5 Price Dependent Demand Model VARIABLE COEFFICIENT CCONSBC -1.01 CPRICEI (-1.56) 1.14 PINV (6.22)** 1.88 E-05 (-1.12) RPDI 1.01 E-04 (2.40)** CONSTANT -0.863 (-1.82)* D-W R~2 ADJ. 1.55 0.496 ** s i g n i f i c a n t at 95% * s i g n i f i c a n t at 90% The o v e r a l l f i t of t h i s regression was not high, with only 49.6 percent of the v a r i a t i o n i n processed p r i c e explained by the independent vari a b l e s . A l l c o e f f i c i e n t s have the a p r i o r i expected signs. However, import p r i c e (CPRICEI) and income (RPDI) were the only v a r i a b l e s which were s t a t i s t i c a l l y s i g n i f i c a n t at the 95 percent confidence l e v e l (see t - s t a t i s t i c s , Table 3.5). The inventory variable, PINV, was not s i g n i f i c a n t l y d i f f e r e n t from zero at the 90 percent l e v e l . The quantity va r i a b l e , CCONSBC, was also not s i g n i f i c a n t l y d i f f e r e n t from zero at the 90 percent l e v e l . The main conclusion that can be drawn from the r e s u l t s i s the strong r e l a t i o n s h i p between import p r i c e and domestic pr i c e . The c o e f f i c i e n t for CPRICEI i s 1.14; very close to one. That i s , the wholesale p r i c e of l o c a l processed mushrooms moves with the import wholesale p r i c e on an almost one f o r one basis. This implies that changes i n the import processed p r i c e determine to a large extent the corresponding change i n the p r i c e l e v e l for l o c a l , B.C. product. 3.3.4 E l a s t i c i t y of Price F l e x i b i l i t y for Processed Mushrooms The in t e r p r e t a t i o n of e l a s t i c i t i e s f o r processed mushrooms needs to be discussed. In a p r i c e dependent equation, the calculated e l a s t i c i t i e s are i n fact e l a s t i c i t i e s of price f l e x i b i l i t y . That i s , the dependent variable being p r i c e , not q u a n t i t i t y , means that calculated e l a s t i c i t i e s measure the 74 percentage change i n pri c e that i s caused by a one percent change i n dependent variable, for example q u a n t i t i t y . This i s the inverse of the usual d e f i n i t i o n of pr i c e e l a s t i c i t y i f c e r t a i n r e s t r i c t i o n s are s a t i s f i e d (Houck p. 792), namely that the matrix of cross e l a s t i c i t i e s f o r substitutes i s zero. When t h i s condition i s not s a t i s f i e d , the absolute value of the inverse of the pri c e f l e x i b i l i t y of demand i s a lower l i m i t on the absolute value of the actual, unobserved pr i c e e l a s t i c i t y of demand. A l l of t h i s i s not to imply that the e l a s t i c i t y of price f l e x i b i l i t y i s not a useful s t a t i s t i c , only that i t i s a non- standard measure and therefore requires care to ensure that the correct i n t e r p r e t a t i o n i s used. The c o e f f i c i e n t s of pr i c e f l e x i b i l i t i e s f o r the processed mushroom p r i c e dependent demand function are presented i n Table 3.6. Table 3.6 C o e f f i c i e n t s of Price F l e x i b i l i t i e s f o r Processed Demand Function, Calculated at the Means Variable C o e f f i c i e n t of Price F l e x i b i l i t y CCONSBC -0.06742 CPRICEI 0.8898 PINV -0.02545 RPDI 1.376 The c o e f f i c i e n t of pr i c e f l e x i b i l i t y f o r CCONSBC, the qu a n t i t i t y of l o c a l product demanded, i s quite low (-0.06742). This supports the i n i t i a l assumption of an exogenously determined p r i c e . The q u a n t i t i t y of l o c a l supply has very l i t t l e e f f e c t on i t s own p r i c e , as a close substitute, import processed mushroom i s a v a i l a b l e . The c o e f f i c i e n t of pr i c e f l e x i b i l i t y f o r import processed mushroom p r i c e i s close to unity (0.89). A one percent change i n import p r i c e r e s u l t s i n a 0.89 percent change i n domestic p r i c e . This also confirms the dominant e f f e c t that import p r i c e has on domestic p r i c e . 3.4 Cost of Production Model In t h i s section, a cost of production model f o r a mushroom farm i n B.C. i s presented. The r e s u l t s w i l l be used as parameters for the Constant E l a s t i c i t y of Substitution Production Function i n the mathematical model of the B.C. mushroom industry (Chapter 2) . Total costs are grouped into two broad categories- f i x e d costs (R) and variable costs (W) . The model i s based on data for the years 1983 to 1986. A Balance Sheet and Capital Cost Schedule i s included for 1986. Mushroom farms i n B.C. vary i n s i z e , from small operations which r e l y e n t i r e l y on family labour, to larger farms which employ several labourers. To simplify the analysis, the notion of a "representative farm" i s used as the basis f o r a cost of production model. 76 3.4.1 Assumptions The cost of production f o r B.C. mushroom farms was examined i n d e t a i l by b u i l d i n g a cost model on the spreadsheet package, Lotus 1-2-3. For the year 1986, the following assumptions are employed i n the model 6: 1) The s i z e of operation, i n terms of square footage of production area, i s 30,000 square feet, which i s divided into 12 growing rooms of 2,500 square feet each. This i s approximately the average s i z e of a production uni t i n B.C.7 2) 4.75 cycles (crops) are employed per year per growing room. This figure i s obtained from a b i o l o g i c a l growing cycle of 77 days which i s currently employed by the majority of producers. 3) Y i e l d per growing cycle i s calculated from the average y i e l d f o r a l l producers i n B.C. In 1986, the average y i e l d was 3.53 pounds of mushrooms per square foot per crop. 6Some of the data i s obtained from the f i n a n c i a l records of i n d i v i u d a l producers. For reasons of c o n f i d e n t i a l i t y , no data sources are quoted. 7Average area per producer calculated as t o t a l B.C. square footage divided by number of producers. 77 4) Labour requirements are broken down into operator and hired labour. The operator i s assumed to work 10 hours a day, 5 days a week, for an annual t o t a l of 2,600 hours. Operator wage i s $12 an hour, plus a WCB rate (Workers' Compensation Board) of 3 per cent. Hired labour requirements are 592 hours per cycle, for an annual t o t a l of 2808 hours based on complete turnover of one growing room per week. The cost of hired labour i s $8 an hour, plus 4 percent f o r benefits and 3 per cent for WCB. The rates used for benefits and WCB are those required by the B.C. labour code. 5) Energy requirements are broken down into four categories: i . N a t u r a l gas and e l e c t r i c i t y f o r heating and a i r conditioning costs $0.22 per square foot per cycle. i i . Truck and panel van require 7800 l i t r e s of fu e l per year. i i i . Tractor and bobcat require 8350 l i t r e s of fu e l per year. i v . O i l and l u b r i c a t i o n for a l l farm vehicles i s 15 percent of f u e l cost. 6) Harvesting cost i s $0.18 per pound of mushroom, plus 4 per cent benefits and 3 per cent WCB. 7) Quantities and cost of materials used are as outlined i n the Cost of Production Model. I t should be noted that the 78 quantities used are based on what i s believed to be the average f o r the industry as whole. An i n d i v i d u a l operation may be using more or l e s s . 8) . Interest on operating c a p i t a l i s calculated using the Chartered Bank Rate for prime business loans. The time period used i s h a l f of a growing cycle, to r e f l e c t the fact that not a l l costs are incurred at the beginning of the cycle, but are i n fact d i s t r i b u t e d throughout the cycle. 9) Property taxes are $3,000 a year. 10) Insurance costs $3,300 a year. 11) Accounting, l e g a l , and o f f i c e expenses are $4,100 a year. 12) The r e a l rate of in t e r e s t i s applied to c a p i t a l costs to obtain the opportunity cost of c a p i t a l . The rate used i s 5 percent. 13) D e p r e c i a t i o n can be calculated using two al t e r n a t i v e methods: st r a i g h t l i n e and de c l i n i n g balance. For tax purposes, the de c l i n i n g balance method i s required, but t h i s method places the most weight on the f i r s t few years, and i s therefore not very suitable for looking at costs using a single year time frame. The de c l i n i n g balance method gives 79 equal weight to a l l years and i s therefore a more appropriate measure of depreciation i n t h i s case. 14) The r e n t a l rate of land i s used as the cost of land. For a 5 acre farm i n the Fraser Valley, the r e n t a l rate i s $140 per acre per year. 15) The market return f o r growers i s $0,838 a pound, as calculated from monthly statements from the Fraser Valley Mushroom Grower's Cooperative Association f o r the year 1986. 16) The c a p i t a l cost schedule i n the model i s obtained by estimating the c a p i t a l equipment needs of a representative farm. Repair and maintenance i s calculated as 5 percent of c a p i t a l cost for truck, t r a c t o r and van and other equipment. For buildings i t i s 2 percent of c a p i t a l cost. 80 3.4.2 The Cost of P r o d u c t i o n Model A n a l y s i s o f Mushroom P r o d u c t i o n Costs i n B.C. (1983-1986): A R e p r e s e n t a t i v e O p e r a t i o n i n the F r a s e r V a l l e y 1983 1984 1985 1986 Farm C h a r a c t e r i s t i c s Number of B u i l d i n g s 12 12 12 12 rooms Square Footage 2500 2500 2500 2500 ft/room C y c l e s per Year 4.32 4.32 4.40 4.75 c y c l e s / y e a r Average Y i e l d 3.48 3.52 3.57 3.53 l b s / f t 2 Labour Requirements Operator Hours 2600 2600 2600 2600 hours/year Hourly Rate 9.50 10.00 12.00 12.00 $/hour WCB Rate 3 3 3 3 % H i r e d Labour Hours 2554 2554 2601 2808 hours/year H o u r l y Rate 6.50 7.00 7.50 8.00 $/hour WCB Rate 3 3 3 3 % B e n e f i t s 4 4 4 4 % T o t a l Labour Costs Operator (+WCB) 0.196 0.207 0.243 0.226 $ / f t 2 / c y c l e H i r e d 0.128 0.138 0.148 0.158 $ / f t 2 / c y c l e WCB & B e n e f i t s 0.01 0. 01 0.01 0.01 % Energy Requirements Gas and E l e c t r i c i t y 27216 27648 28600 31350 $/year Truck and Panel Van 7094 7094 7225 7800 l i t r e s / y e a r T r a c t o r 7593 7593 7734 8349 l i t r e s / y e a r O i l and Lube Rate 15 15 15 15 % F u e l Cost 0.35 0.36 0.37 0.38 $ / l i t r e H a r v e s t i n g Cost Harvest Rate 0.16 0.17 0.18 0.18 $/lb WCB Rate 3.00 3.00 3.00 3 . 00 % B e n e f i t s 4.00 4 . 00 4.00 4.00 % T o t a l Harvested 451008 456192 471240 503025 l b s / y e a r T o t a l Harvest Cost 0.5958 0.6403 0.6876 0.6799 $ / f t 2 / c y c l e M a t e r i a l s Spawn Cost Cases Used 29.00 30.00 31.00 32.75 $/case 12 12 12 12 c a s e s / c y c l e 81 Supplement Cost 32. 00 33. 00 34. 00 34. 50 $/bag Bags Used 4 4 4 4 c a s e s / c y c l e Chemical Cost 4000. 00 5000. 00 6000. 00 6000. 00 $/year Compost Cost 27. 21 29. 79 29. 97 30. 00 $/yard Yards Used 55 55 55 55 y a r d s / c y c l e C a s ing S o i l Cost 20. 50 21. 00 21. 50 22. 00 $/yard Yards Used 12 12 12 12 y a r d s / c y c l e Bed P l a s t i c Cost 48. 00 49. 00 49. 50 50. 00 $ / r o l l R o l l s Used 0. 33 0. 33 0. 33 0. 33 r o l l s / c y c l e Bed N e t t i n g Cost 1732. 00 1732. 00 1732. 00 1732. 00 $ / r o l l R o l l s Used 8. 25 8. 25 8. 25 8. 25 r o l l s Replacement Freq. 10 10 10 10 ye a r s I n t e r e s t on Op e r a t i n g C a p i t a l C h a r t e r e d Bank 11. 17 12. 06 10. 58 10. 50 % D i v i d e d by 4. 32 4. 32 4. 40 4. 75 c y c l e s / y e a r 2 2 2 2 f o r average P r o p e r t y Taxes 2850. 00 2900. 00 3000. 00 3000. 00 $/year Insurance 2800. 00 2800. 00 2800. 00 3300. 00 $/year R e p a i r & Maintenance B u i l d i n g Rate 5 5 5 5 % Truck, T r a c t o r , e t c . 2 2 2 2 % L e g a l & Accounting 1800. 00 1900. 00 2000. 00 2100. 00 $/year O f f i c e 2000. 00 2000. 00 2000. 00 2000. 00 $/year I n t e r e s t on Investment Real I n t e r e s t Rate 5 % Land Cost Cost p e r a c r e Number Acres 145.00 150.00 140.00 140.00 $/acre 5 5 5 5 a c r e s Market Return Average Farm P r i c e 0.8105 0.8689 0.9142 0.8378 $/lb 82 Cost o f P r o d u c t i o n Summary D o l l a r B a s i s 1983 1984 1985 1986 C u l t u r a l Costs 0.553 0.584 0.599 0.610 $/lb No n v a r i a b l e Cash Costs 0.059 0.059 0.057 0.055 $/lb T o t a l Cash Costs 0.611 0.644 0.656 0.665 $/lb Non-cash Costs o p e r a t o r l a b o u r 0.056 0.059 0.068 0.064 $/lb S u b t o t a l 0.668 0.703 0.724 0.729 $/lb Return t o Investment 0.035 0.035 0.033 0.031 $/lb D e p r e c i a t i o n 0.053 0.053 0.048 0.045 $/lb T o t a l Non-cash Costs 0.145 0.146 0.150 0.140 $/lb Cost o f P r o d u c t i o n 0.756 0.790 0.806 0.805 $/lb Grower Return 0.811 0.869 0.914 0.838 $/lb Net Returns t o R i s k and 0.054 0.079 0.108 0.033 $/lb Management 24477 36034 51115 16451 $/year Cost o f P r o d u c t i o n Summary Percentage B a s i s 1983 1984 1985 1986 C u l t u r a l Costs 73.11 73.99 74.37 75.82 No n v a r i a b l e Cash Costs 7.75 7.52 7.08 6.78 T o t a l Cash Costs 80.86 81.51 81.44 82.60 Non-cash Costs o p e r a t o r l a b o u r 7.46 7.43 8.46 7.94 S u b t o t a l 88.32 88.94 89.91 90.54 Return t o Investment 4.62 4.37 4.15 3.89 D e p r e c i a t i o n 7.06 6.69 5.94 5.57 T o t a l Non-cash Costs 19.14 18.49 18.56 17.40 100.00 100.00 100.00 100.00 83 Cost of Production 1986 Cultural Costs Hired Labour WCB Premium & Benefits Heating and A i r Conditioning Vehicle Fuel & Lubrication Materials Harvesting Total Cultural Costs $ / s q . f t . / Y e a r $/pound 0.158 0.011 0.220 0.050 1.037 0.680 2.155 0.045 0.003 0.062 0.014 0.294 0.193 0.610 Nonvariable Cash Costs Interest on Operating Capital Taxes Insurance Legal & Accounting O f f i c e Expenses Repair & Maintenance Land Rental 0.024 0.021 0.023 0.015 0.014 0.086 0. 010 0.007 0.006 0.007 0.004 0.004 0.024 0. 003 Total Nonvariable Cash Costs 0.193 Total Cash Costs 2.348 0.055 0.665 Non-Cash Costs Operator Labour Return to Investment Depreciation 0.226 0.111 0.158 0.064 0.031 0.045 Total Noncash Costs 0.494 2.842 0.140 0.805 Cost of Production Grower Return 2.842 per square foot 0.805 $ per pound 0.838 $ per pound Net Returns to Risk and Management 0.033 $ per pound 16451 $ per year 84 Capital Cost Schedule, 1986 Buildings Cost Class Deprec. Interest L i f e Mushroom Houses 200000 6 13333 10000 Cooler 5000 8 333 250 E l e c t r i c a l Hookup 8000 8 533 400 Equipment A i r Handling Equip. 40000 Bed F i l l i n g Machine 10000 CO 2 Meter 1500 Front End Loader 10000 Fuel Tanks 400 Manure Conveyor 3 000 P a l l e t Jack 300 Pesticide Spray Equip. 300 Ph Meter 100 Picking Equipment 600 Pick-Up Truck 5000 Portable A i r Cond. 4000 Portable Lighting 100 Power Tools 1500 Small Tools 1500 Spawn Machine 2 000 Steam B o i l e r 10000 Table Scales 400 Tamping Machine 2000 Thermometers 432 Truck 7000 Watering Equipment 900 Welding Equipment 500 Wheelbarrows 600 Total Equipment Total Build., Equip. 315132 Coop Shares 30000 Total 345132 8 4000 2000 10 8 1000 500 10 8 150 75 10 10 667 500 15 8 20 20 20 8 300 150 10 8 0 15 5 8 0 15 5 8 10 5 10 12 0 30 5 10 333 250 15 8 400 200 10 8 0 5 5 8 150 75 10 12 150 75 10 8 0 100 5 8 667 500 15 8 0 20 5 8 0 100 5 8 0 22 5 10 467 350 15 12 0 45 5 8 50 25 10 8 0 30 5 22563 15757 1500 _ 85 3.4.3 Results of the Cost of Production Model The cost of producing a pound of mushrooms i n 1986 was $0,808, while the grower return was $0,838. The p r o f i t for producing 503,025 lbs was $16,451. Total cost of production was d i s t r i b u t e d with 16 percent fi x e d cost, and 84 percent variable cost. Fixed cost (R) was $1.69 per square foot of growing area. Variable cost (W) was $8.70 per square foot of growing area. These values for R and W w i l l be used as parameters fo r the cost function derived i n Chapter 2. The minimization of t h i s cost function, subject to a CES production function, r e s u l t s i n an expression which relates cost of production to output l e v e l , and prices of inputs. This i s the supply function. CHAPTER 4 RESULTS OF THE MATHEMATICAL MODEL OF THE BRITISH COLUMBIA MUSHROOM INDUSTRY In t h i s chapter, the mathematical model f o r the B.C. mushroom industry, described i n chapter 2, i s msed to determine whether the market behaves i n a competitive or monopolistic manner. The parameters required for the demand section of the model are obtained from econometric estimation of the demand functions presented i n chapter 3. Results of the cost of production function i n chapter 3 are used i n the supply section of the mathematical model. In section 1, actual industry data from the year 1986 i s entered into the mathematical model, using the al t e r n a t i v e assumptions of monopoly and perfect competition i n the market. In section 2, the analysis i s extended to include the years 1983 to 1985. Based on the re s u l t s obtained for market behavior i n sections 1 and 2, an analysis of quota values i s then presented i n section 3. 86 87 4.1 Monopoly versus Competitive P r i c i n g , 1986 The r e s u l t s for market equilibrium predicted by the mathematical model of the B.C. mushroom industry are presented i n Tables 4.1 to 4.4 . Actual data from the calendar year 1986 are used to c a l i b r a t e the model. A l l prices are expressed i n constant 1981 d o l l a r s . The assumptions used to generate the re s u l t s are: 1. a range of 0.8 to 1.05 f o r the returns to scale technology i n the production function and 2. a low e l a s t i c i t y of substitution between the two factors of production, namely b=0.5, implying p=l. 3. a l l other variables which a f f e c t demand, such as income, p r i c e of complements, etc., are fix e d at t h e i r mean values f o r the year of int e r e s t , 1986. In terms of the econometric equations, the e f f e c t s of a l l the independant variables except p r i c e were combined into a constant intercept term. In Table 4.1, some data for 1986 i s presented. The data for average p r i c e and quantity produced are actual values f o r 1986. The quantity of L, variable input, i s an estimate of the average for the industry i n 1986, as calculated i n the cost of production model i n Chapter 2. In Table 4.2, the re s u l t s for the monopoly p r i c i n g model with a quota r e s t r i c t i o n i s presented. The square footage of production area i s r e s t r i c t e d to equal the actual quota l e v e l i n 88 the industry. Po s i t i v e p r o f i t s are earned, as the monopoly p r i c i n g model equates marginal revenue with marginal cost. The r e s u l t s are not consistent with the data. Production l e v e l s are only about 55 percent of actual production i n 1986. For example, i n the case of constant returns to scale (v=l) , predicted output was approximately 19 m i l l i o n pounds, as compared to actual output of 34.8 m i l l i o n pounds i n 1986. The predicted demand f o r var i a b l e input was also only about 52 percent of actual. Given a very low e l a s t i c i t y of su b s t i t u t i o n between fixe d and va r i a b l e input, the implication i s f o r substantial i d l e capacity. The r e s u l t s for a competitive market equilibrium with a quota r e s t r a i n t are presented i n Table 4.3. The predicted production l e v e l s are consistent with the actual market data. The v a r i a t i o n between predicted and actual i s only about f i v e percent. Where returns to scale are les s than and equal to one, p o s i t i v e p r o f i t s are earned. The competitive p r i c i n g model equates p r i c e with marginal cost, and given an upward sloping marginal cost curve, p r o f i t s w i l l be p o s i t i v e provided the equilibrium p r i c e l i e s above the t o t a l cost curve at the equilibrium quantity. Where returns to scale are greater than one, p r i c e i s equated to average cost, and therefore p r o f i t s are zero. Table 4.1 Market Quantity, Price, Input Levels, 1986 89 TOTAL PRODUCED (lbs) 34800000 AVERAGE PRICE ($/lb) 0.64 K (square feet/farm) 30000 L ($/farm) 261103 Table 4.2 Monopoly P r i c i n g Model, with Quota Constraint, 1986 v=.8 V=. 9 V=l v=1.05 TOTAL PRODUCED (lbs) 18800637 18947331 19152192 19269768 AVERAGE PRICE ($/lb) 1.16 1.16 1.15 1.14 COST ($/lb) 0.59 0.63 0.66 0.67 REVENUE-COST ($/farm) 156057 145458 136235 132076 K (square feet/farm) 30000 30000 30000 30000 L ($/farm) 111762 123531 134354 139414 Table 4.3 Competitive P r i c i n g Model, with Quota Constraint, 1986 v=.8 v=.9 v=l v=1.05 TOTAL PRODUCED (lbs) 31822179 33513921 35192553 35417631 AVERAGE PRICE ($/lb) 0.73 0.68 0.63 0.62 COST ($/lb) 0.61 0.62 0.62 0.62 REVENUE-COST ($/farm) 58588 30490 3268 0 K (square feet/farm) 30000 30000 30000 30000 L ($/farm) 233835 253358 269396 270962 Table 4.4 Competitive P r i c i n g Model, no Quota Constraint, 1986 v=.8 v=.9 V=l V=1.05 TOTAL PRODUCED (lbs) 31153431 33322653 35391480 35421288 AVERAGE PRICE ($/lb) 0.76 0.69 0.62 0.62 COST ($/lb) 0.61 0.62 0.62 0.62 REVENUE-COST ($/farm) 69143 33573 0 0 K (square feet/farm) 26615 29065 30968 30946 L ($/farm) 231639 252971 269528 269336 Note: A l l values are i n 1981 r e a l d o l l a r s Table 4.5 Industry Welfare E f f e c t s of Moving from Competitive to Monopoly Pri c i n g , with Current Quota, 1986 v=.8 v=. 9 v=l Loss i n Consumer Surplus Loss i n Producer Surplus Gain i n Producer Surplus Net Gain Producer Surplus Deadweight Loss 10760816 12472866 14225680 1263231 1073386 849884 7994307 9010870 10027740 6731075 7937483 9177856 4029740 4535382 5047823 Note: a l l values are i n r e a l 1981 d o l l a r s An i n t e r e s t i n g r e s u l t i s the predicted magnitude of p r o f i t s which the industry would enjoy i f a monopoly p r i c i n g market could be sustained. The relevant measures of consumer and producer surplus are presented i n table 4.5. The derived demand for mushrooms at the farm-gate l e v e l i s used. This i s obtained by deducting from r e t a i l demand the retail-wholesale margin, and the percentage commission that the association charges for marketing member production, i n order to a r r i v e at the p r i c e schedule that producers face. For a value of v=l, annual producer surplus would increase by approximately 9 m i l l i o n d o l l a r s (1981 d o l l a r s ) . Consumers would be adversely affected with higher p r i c e s . The loss i n consumer surplus of approximately 14 m i l l i o n d o l l a r s a year would be quite substantial. The net r e s u l t would be a s o c i a l net loss of 5 m i l l i o n d o l l a r s annually. The resultant p r i c e s are predicted to be about 100 percent higher than current l e v e l s . In order to sustain these prices, higher t a r i f f s would be required for fresh mushroom imports from the U.S. Movement of fresh mushrooms from other provinces, such as Alberta, would also have to be r e s t r i c t e d , as the higher prices would make i t p r o f i t a b l e to ship into the B.C. market. This r e s u l t , that the fresh mushroom industry i n B.C. i s not regulated i n such a way as to extract more than competitive pri c e s from consumers, i s not surp r i s i n g given the nature of the supply r e s t r i c t i n g mechanism employed. The r e s t r i c t i o n i s on the square footage of production area, and not on output. Moreover, the r e s t r i c t i o n i s not binding on output, as producers are s t i l l able to supply s u f f i c i e n t quantities of mushrooms into the market to a r r i v e at a competive market c l e a r i n g equilibrium. The quota does, however, s h i f t the r e l a t i v e r a t i o of fixed to v a r i a b l e input. Given a low e l a s t i c i t y of substitution between fix e d and variable inputs, the s h i f t i n the r a t i o of fixe d to va r i a b l e inputs has an upper bound. This change i n r a t i o can r e s u l t i n a higher cost of production, depending on the degree of s u b s t i t u t a b i l i t y between the inputs. Even with an assumption of constant returns to scale i n the production function, when the quota r e s t r i c t i o n on fixed input i s binding, the average cost of production i s not completely independent of production l e v e l . In Table 4.4, for v=l, the cost of producing mushrooms i s $ 0.62 per pound without the quota r e s t r i c t i o n . The cost of production with quota r e s t r i c t i o n , i n Table 4.3, i s also $ 0.62 per pound. The r a t i o of fixed and variable inputs are close to the r a t i o that would be obtained i n a competitive market for both 92 inputs. This implies that the r e s t r i c t i o n on quota i s not binding on production, given the assumptions i n the model. The above conclusions are robust to changes i n the basic assumptions employed i n the production function technology. The parameters of i n t e r e s t are the substitution parameter p, and the returns to scale parameter v. The s u b s t i t u t i o n parameter, i n i t i a l l y set at one, was varied from a range of one h a l f to two. Factor demands i n the models without the quota r e s t r i c t i o n are not affected at a l l . In the models with a quota r e s t r i c t i o n , the e f f e c t on factor demands i s very small, as the quota r e s t r i c t i o n i s not binding. The r e s u l t s of the model are not very s e n s i t i v e to changes i n the value of the s u b s t i t u t i o n paramameter, i n d i c a t i n g that the factor r a t i o s are not very f a r from where they would be i n a competitive equilibrium. The returns to scale parameter v was varied from a range of 0.8 to 1.05. The value of v has a p o t e n t i a l l y large impact on the r e s u l t s of the mathematical model, as i t d i r e c t l y a f f e c t s the marginal cost of production, and therefore the i n t e r s e c t i o n of supply and demand. However, the main conclusion, that the market i s i n a competitive equilibrium, i s stable for the p l a u s i b l e range of v from 0.8 to 1.05 . Personal discussion with knowledgeable sources i n the industry leads the author to place the most l i k e l y value of v at about one, for constant returns to scale. 4.2 Monopoly versus Competitive P r i c i n g , 1983 to 1986 The r e s u l t s i n section 1 support a model of competitive p r i c i n g behavior i n the B.C. mushroom industry f o r the year 1986. In t h i s section, data for the years 1983 to 1985 are also applied to the model i n order to assess industry market behavior i n previous years. For the reasons outlined before i n section 1 of t h i s chapter, the assumptions used i n the model are: 1. constant returns to scale (v=l), and 2. a low e l a s t i c i t y of substitution (p=l). The model i s used to generate average producer prices and t o t a l industry supply. In Figure 4.1, monopoly and competitive pri c e s f o r the years 1983 to 1986 are expressed as a percentage of the actual p r i c e s . For a l l years, the p r i c i n g model that f i t s the data best i s the model of perfect competition. In Figure 4.2 the corresponding industry supplies for the two p r i c i n g models are presented as a percentage of actual industry supply. The competitive model provides the best f i t for market behavior i n the B.C. mushroom industry. Figure 4 .1 "Optimal" Prices as a Percentage of Actual Prices 1 2 0 " 1983 1984 1985 1986 Figure 4 - 2 "Optimal Quantities as a Percentage of Actual Quantities 95 4.3 The Payback Period for Quota Given the r e s u l t s of the mathematical model, analysis of the value of quota i n the B.C. mushroom industry must be based on the inframarginal rents of quota ownership. The market s i t u a t i o n for quotas i n the B.C. mushroom industry supports t h i s conclusion. The majority of quota sales involve transfers of the en t i r e farm. The market i s very t h i n for incremental units quota to add to an ex i s t i n g operation. A l l the elements needed to analyse the p r i c e of quota are now avai l a b l e . Assuming quota i s purchased at the 1986 average p r i c e of four d o l l a r s per square foot, the number of years required for quota benefits to sum to the purchase p r i c e can be calculated. This i s known as the payback period. A d i r e c t estimate of the annual benefits of quota ownership i s not avail a b l e , as no market for the rent a l of quota i n the B.C. mushroom industry e x i s t s . As a proxy, from the cost of production model (chapter 3), the average net returns to r i s k and management ( t o t a l revenue minus t o t a l cost) f o r the years 1983 to 1986 i s $ 1.07 per square foot of quota. This value w i l l be used as the annual benefits a r i s i n g from the purchase of quota. A choice for the opportunity i n t e r e s t rate i s avail a b l e from Jenkins' estimate of the private r e a l cost of c a p i t a l facing farmers i n Canada for the decade from the mid-1960's to mid- 1970's, f i v e percent. In addition, because of the poten t i a l r i s k s of p a r t i a l or complete loss of quota rents discussed 96 e a r l i e r , a three percent r i s k premium i s added to the intere s t rate, for a t o t a l of eight percent. The expected rate of quota appreciation i s d i f f i c u l t to determine, as no quota p r i c e series of a reasonable sample size are a v a i l a b l e . However, an estimate can be obtained from prices prevalent i n the period from 1983 to 1986. Using four annual observations (3, 3.5, 4, 4 for the years 1983 to 1986 res p e c t i v e l y ) , the calculated average annual rate of quota appreciation was 7.7 percent. Very l i t t l e quota appreciation occured i n 1985-1986. Problems with the unity of members i n the industry very l i k e l y had an impact on the trading value of quota i n these two years. Assuming recent quota p r i c e performance has greater weight than past performance, a compromise rate of f i v e percent w i l l be assumed. Quota purchase merits a spe c i a l tax advantage. An E l i g i b l e C a p ital Account i s created, made up of one ha l f the cost of quota purchase. An annual deduction from taxable income of up to 10 percent of the balance i n t h i s account may be made for as long as there i s a p o s i t i v e balance. Upon eventual resale of the quota, i f h a l f the proceeds of the sale exceeds the remaining balance i n the E l i g i b l e Capital Account, the difference (half the c a p i t a l gains), i s added to taxable income. The marginal tax rate w i l l be assumed to be 50 percent. Using equation (4) i n chapter 2, the calculated payback period i s four years. The r e s u l t i s reasonably robust to changes i n the values of the parameters used i n the cal c u l a t i o n s . 97 For example, using an opportunity i n t e r e s t rate of 10 percent and an expected rate of c a p i t a l appreciation of zero percent (cf 8 and 5 respectively) gives a payback period of f i v e years. This r e l a t i v e l y short payback period can be interpreted i n one of two ways. I t may be a signal that investment i n quota i s very p r o f i t a b l e . A l t e r n a t i v e l y , quota purchase may be perceived by producers as a high r i s k investment which requires a very short payback period. Given the recent i n s t a b i l i t y i n the B.C. mushroom industry, i t seems l i k e l y that quota purchase i s associated with a high l e v e l of r i s k . CHAPTER 5 SUMMARY, CONCLUSIONS AND POLICY IMPLICATIONS In t h i s chapter, the study i s summarized, and conclusions are drawn with s p e c i f i c emphasis on the p o l i c y implications of t h i s study. The f i r s t section i s a summary of the major findings i n t h i s study. This i s followed by a b r i e f discussion of some issues which have a large bearing on the future prospects of the B.C. mushroom industry. Po l i c y implications as they r e l a t e to the r e s u l t s of t h i s study are examined. 5.1 Summary and Conclusions The mushroom industry i n B.C. i s the only mushroom producing region i n Canada which markets and d i s t r i b u t e s through a central s e l l i n g agency. In addition, industry output i s regulated through the use of production area quotas. The major objective of t h i s study i s to determine whether the mushroom market i n B.C. behaves i n a competitive manner, or i f producers c o l l e c t i v e l y exercise monopoly power. In order to do achieve t h i s objective, a mathematical model of the B.C. mushroom industry i s constructed, using a p a r t i a l equilibrium 98 9 9 analysis. The major s t r u c t u r a l relationships are defined i n terms of demand and supply parameters. The parameters which a f f e c t demand are estimated with econometric equations. Supply response i s modelled by minimizing a l i n e a r cost function, subject to a Constant E l a s t i c i t y of Substitution production function. Quota on production area i s modelled by solving the cost minimization problem subject to a constant l e v e l of fixed input. The l e v e l of fixe d input i s assumed to be an appropriate measure of the quantity of resources whose l e v e l of usage i s d i s t o r t e d due to the existance of quotas on the area of production. The r e s u l t s of t h i s study show unambiguously that the mushroom industry i n B r i t i s h Columbia operates i n a competitive manner. That i s , producers do not c o l l e c t i v e l y exert market power i n order to extract higher than competitive prices for output. In addition, analysis of the quota r e s t r i c t i o n on production area indicates that the quota i s not binding on production. Therefore, given the production technology, no s o c i e t a l welfare gains can be r e a l i z e d by increasing the t o t a l a l l o c a t i o n of quota i n the B.C. mushroom industry. A key feature of the industry i s the j o i n t product r e l a t i o n s h i p between fresh and processed mushrooms. Mushrooms which are of s u f f i c i e n t l y f i n e q u a l i t y for the fresh market are produced as a j o i n t product with mushrooms whose lower qu a l i t y necessitate sales into the processed market. There i s a minimum proportion of t o t a l production that producers must s e l l to the 100 processed market. Producers c o l l e c t i v e l y have some degree of control over the market for fresh mushrooms. They determine the fresh market p r i c e , which i n turn determines the quantity which i s sold fresh. The r a t i o of fresh to processed i s under the control of producers, subject to a minimum proportion of t o t a l production which must be sold as processed. Producers are able to do t h i s since mushrooms which are not sold fresh are sold as processed into a market which can absorb a l l production at the p r i c e of imported processed mushrooms. The processed market i s dominated by imports from P a c i f i c Rim countries such as Taiwan, Korea, and China. The returns which producers obtain from the fresh market are higher than from the processed market. From the cost of production model i n Chapter 4, i n 1986 the t o t a l costs of production were higher than the prices that producers received for mushrooms i n the processed market. Therefore, the lower pri c e s , r e l a t i v e to t o t a l cost of production, that producers received i n the processed market were o f f s e t by higher prices i n the fresh market. 5.2 P o l i c y Implications The r e s u l t s obtained i n t h i s study have several implications for future p o l i c y i n the B.C. mushroom industry. At present, i t would appear that the current structure of the industry i s i n the 101 process of some dramatic changes. One c a t a l y s t of change, the problem of lower p r i c e d import processed mushrooms, i s longstanding, and not under the d i r e c t control of the B.C. industry. This i s discussed i n the f i r s t part of t h i s section. A much more serious issue concerns the breakdown of the cooperative s p i r i t which fostered the beginnings of the industry as i t e x i s t s today. This i s discussed i n the second part of t h i s section. 5.2.1 The Problem of Processed Mushroom Imports Processed mushroom imports have been perceived as a problem by the Canadian mushroom industry since the l a t e 1960s. The matter was brought to the attention of the Canadian Government i n 1969 (Skrow) . In 1973, the matter was referred to the A n t i - Dumping Tribunal. The findings of a subsequent study by the Anti-Dumping Tribunal, summarized i n the f i n a l paragraph of the report, were that "preserved mushrooms, as defined f o r the purposes of t h i s inquiry, are l i k e l y to be imported into Canada at such pri c e s , i n such quantities, and under such conditions as to threaten serious injury to Canadian producers of l i k e or d i r e c t l y competitive goods." In October 1979, the t a r i f f on imports of processed mushrooms into Canada was increased from 12.5 percent to 20 102 percent. However, t h i s measure was not s u f f i c i e n t to curb the growth of imports. In 1973, the import share of the Canadian processed market was 46 percent. In 1979, the import share reached a high point of 84 percent, d e c l i n i n g to 73 percent by 1985. Import processed mushrooms have penetrated the Canadian market through low p r i c e s . As a r e s u l t of high import share i n the processed market, the processed mushroom market i s not p r o f i t a b l e f o r domestic producers. The p r i c e domestic producers receive for processed grade mushrooms i s often below the t o t a l cost of production. In B.C., the transfer p r i c e to producers for processed mushrooms was on average approximately 20 percent below the t o t a l cost of production for the years 1982-1986. Domestic producers need to process a c e r t a i n proportion of t h e i r output because of the j o i n t product r e l a t i o n s h i p that e x i s t s between fresh and processed grade mushrooms. Therefore, i n the long run, domestic producers must subsidize lower returns i n the processed market with higher returns from the fresh market. For a l l producers acting c o l l e c t i v e l y , there e x i s t s a r a t i o f o r sales of fresh to processed mushrooms which r e s u l t s i n zero p r o f i t s . In a competitive market, where each producer perceives his/her own action to have a very small e f f e c t , short run competition amongst producers i n the fresh market has the p o t e n t i a l to be s u f f i c i e n t l y disrupting to force e x i t of some producers. The competitive solution of marginal cost equals 103 p r i c e would not be stable. Individually, producers would have an incentive to s e l l a r a t i o of fresh to processed which i s h i g h e r than the zero p r o f i t r a t i o f o r a l l producers c o l l e c t i v e l y . This would occur because each producer believes that his/her own behavior has no e f f e c t on fresh market pr i c e s . From the re s u l t s of t h i s study, i t appears that B.C. producers have some control over p r i c i n g i n the fresh market, but l i t t l e control over p r i c i n g i n the processed market, which i s dominated by the p r i c e of competing imports. Further, the pri c e of processed mushrooms i s low r e l a t i v e to t o t a l costs of production. A case can therefore be made for the formation of a central marketing agency for mushroom producers i n B.C. s o l e l y on the basis of increased industry s t a b i l i t y . The B.C. mushroom industry i s an example of the benefits that producers can enjoy by marketing through a ce n t r a l s e l l i n g agency. Members benefit from scale economies for purchase of input, and processing/marketing of output. More importantly, they can c o l l e c t i v e l y set pr i c e i n the fresh mushroom market such that the average p r i c e received for output (processed and fresh) i s equated to marginal cost. The r e s u l t s of the mathematical model of the B.C. mushroom industry support t h i s hypothesis. The industry, through the cen t r a l s e l l i n g agency, exercises i t s p r i c e s e t t i n g power i n the fresh mushroom market i n order to obtain for members an average p r i c e that at l e a s t covers the cost of production. Were t h i s not the case, the association would be i n serious jeopardy of 104 d i s s o l v i n g i t s membership. The mathematical model with competitive assumptions of marginal cost equated to average p r i c e generates r e s u l t s which are consistent with the actual industry data. 5.2.2 Producer Unity I t i s concluded that the B.C. mushroom industry operates within a competitive market. Producers c o l l e c t i v e l y market through a central s e l l i n g agency, the Fraser Valley Mushroom Growers 1 Co-operative Association, and achieve economies of scale i n input purchase, marketing and d i s t r i b u t i o n . However, the r e s u l t s discussed above are dependent upon the assumption that members of the producer association are able to act c o l l e c t i v e l y . Recent i n s t a b i l i t y within the industry point to some areas where changes i n the rules and regulations of the association would i n j e c t more s t a b i l i t y into the industry. The marketing contract needs to be enforced r i g i d l y , with penalties that e f f e c t i v e l y discourage producers from breaching the contract. S p e c i f i c a l l y , producers must be e f f e c t i v e l y discouraged from i l l e g a l off-farm sales, as t h i s reduces the average pool p r i c e that producers receive through the marketing association. The large c a p i t a l investment i n the processing f a c i l i t i e s of the F.V.M.G.C.A. necessitates a long term f i n a n c i a l commitment from member producers, as a minimum volume of a c t i v i t y i s 105 required to cover costs of operation. The annualy renewable marketing contract that the association currently uses needs to be lengthened i n order to provide the association with more f i n a n c i a l s t a b i l i t y . F i n a l l y , given the fixed f i n a n c i a l obligations of the association, i t s future v i a b i l i t y i s threatened by the recent change i n marketing p o l i c y which allows the formation of other marketing agencies. 106 BIBILIOGRAPHY Arrow, Kenneth J . , Chenery, H.B., and Solow, R.M. "Capital-Labour Substitution and Economic E f f i c i e n c y " Rev. of Econ. and S t a t i s t . 3(1961):225-249 Barichello, Richard R. "Assessing Supply Management as a Policy Tool." Paper presented at Lectureship Series, Tuscon, Arizona. November 1984 Bar i c h e l l o , Richard R. "Analysing an A g r i c u l t u r a l Marketing Quota" University of B r i t i s h Columbia Discussion Paper No. 84-06 August 1984 Clarke, Darral G. 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Cornell University Publication, A.E. Res. 83-13 February 1983 107 Koyck, L. M. Distributed Lags and Investment Analysis North-Holland Publishing Company, Amsterdam, 1954. Marktrend Marketing Research Inc. "Money's Mushrooms Usage and Attitude Study" A p r i l 1987 Ministry of Agriculture and Food Natural Products Marketing (B.C.) Act Order i n Council No. 2265 J u l y 26, 1966 B.C. Registry 153/66 Nerlove, M. and Waugh, F.V. "Advertising Without Supply Control: Some Implications of a Study of the Advertising of Oranges," J . of Farm Econ. 4(1961):813-837 Song, Dae H. and Halberg, M.C. "Measuring Producer's Advantage from C l a s s i f i e d P r i c i n g of Milk", Amer. J . Agr. Econ. 1(1982):l-7 Skrow, E. "Submission to The Inter-Departmental Committee" Canadian Mushroom Growers' Association (1969) Walters, A. A. An Introduction to Econometrics W.W. Norton & Company Inc., New York, 1970. White, Ken J . , "A General Computer Program for Econometric Methods. Shazam," Econometrica 1(1978):239-240 Yoshihara, K., "Demand Functions: An Application to the Japananese Expenditure Pattern", Econometrica 2(1969):257-274 108 APPENDIX A. Mathematical P r o o f s P r o d u c t i o n F u n c t i o n , two Inputs X = G[DK"P + (1-D)L"P]" V/P Cost F u n c t i o n min C = RK + WL S . t . X " P / V = G ~ P / V [ D K " P + (1-D)L"P] C = RK + WL + M [ X " P / V " G"P/ V(DK"P + ( 1 - D ) L " P ) ] F i r s t Order C o n d i t i o n s (1) 6C/6K = R + / x p D K ' P ' ^ P / v (2) 6C/6L = W + M P ( 1 - D ) L " P _ 1 G " P / V s e t (1) and (2) equal t o zero f o r s t a t i o n a r y p o i n t d i v i d e (1) by (2) and rearrange R _ _D K " P " 1 W 1 =D L m u l t i p l y both s i d e s by K/L RK = _D K " P " 1 WL 1 =D L add one t o both s i d e s RK + WL D K ~ P X 1 - D 1 L " P WL 1-D L (1-D)L"P s u b s t i t u t e f o r : C = RK + WL X - P / V G " P / V = DK"P + ( l - D ) L - P C = X " P / V G P / V WL 7 l = D ) " L " P / V s o l v e f o r L X1 =D1L"P = x : P / v G P / v "L C L = ( l - D ) 1 / ( P + l ) w - 1 / ( P + l ) x P / ( v ( P + 1 ) ) c 1 / ( P + l ) G - P / ( v ( P + 1 ) ) t h e r e f o r e 109 WL = ( I - D ) V ( P + I ) W P / ( P + 1 ) X P / ( V ( P + 1 ) ) C 1 / ( P + I ) G - P / ( V ( P + 1 ) ) by symmetry RK = D 1 / ( P + I ) R P / ( P + I ) X P / ( V ( P + I ) ) C 1 / ( P + I ) G - P / ( V ( P + 1 ) ) since C = WL + RK C = G - P / ( v ( P + 1 ) ) x P / ( v ( P + 1 ) ) c 1 / ( P + l ) e where e = [D 1/(P+l) RP/(P+l) + ( i - D ) V ( P + l ) W P / ( P + 1 ) ] Marginal Cost MC = = §-l/ve(p+l)/pX(l-v)/v 6X v Factor Demands Using Duality: SC/6R = K and 6C/6W = L where K and L are factor demands | | = X E + i l x l / v e ( p + l ) / p - l E _ - D l / ( p + l ) R p / ( p - r l ) - i G - i / v 6R p P+l therefore K = D V (p+l) x l / v e l / p R - l / (p+l) G - l / v s i m i l a r l y L = ( l - D ) V (P+l) xVVel/Pw-l/(p+l) G - l / v Production Function with Fixed Input K X = G[DK~P + (1-D)L~P]" V/P Cost Function C = RK + WL from production function _ X"P/ V - G"P/VDK-P "VP L G=P/^7l=5j' therefore C — RK + w ?:P/^-_G:P/VDK-P -VP C - RK + W G-P7V(i_ D) Marginal Cost MC = W(-l) X-P/ V - G"P/ VDK-P -VP-1 ( - E X X - P / V " 1 p~ ~~G=PT^Jl-b) V G =P/ V(1=D)" = W G P / V X ~ ( ( P + V ) / V ) X"P/ V - G-P/ VDK"P ~ ( ( P + 1 ) / P V(l-D)" G =P / v ( l-57 APPENDIX B. Data Tables Table BI Fresh Mushroom Price, Sales, Imports R e t a i l Sales Quantity Value Price i n B.C. of Imports of Imports Vancouver into Canada into Canada $ per l b lbs i n '000s lbs $ i n '000s 1982 1 1.69 749214 5499036 3417 2 1.69 724956 4043778 2741 3 1.69 749426 7431864 4793 4 1.70 774432 4597504 3018 5 1.75 790052 7197937 4646 6 1.69 775354 4884894 3131 7 1.69 781142 5391459 3677 8 1.69 732595 3607714 2304 9 1.75 689296 4427916 2868 10 1.67 711640 3378613 2286 11 1.70 834771 3925093 2406 12 1.80 863033 3953569 2326 1983 1 1.77 920091 6000778 3836 2 1.76 805992 4574604 2929 3 1.78 962000 3623327 2243 4 1.80 844000 4759995 2861 5 1.82 886000 4720051 2884 6 1.81 900000 4418376 2847 7 1.88 827000 3786658 2352 8 1.93 833000 2922026 1889 9 1.91 803000 5263896 3185 10 1.99 802000 2967187 1889 11 1.97 977894 4020227 2485 12 1.93 971288 2337496 1453 1984 1 1.97 977000 3277549 2058 2 1.90 926000 2966127 2057 3 1.90 1016000 4003528 2602 4 2.02 1027000 3729220 2472 5 2.20 953000 4936078 3456 6 2.18 897000 5574986 3771 7 2.18 859000 4385135 2977 8 2.13 899000 6860586 4694 9 2.13 745000 4097563 3055 10 2.13 744000 1911504 1385 11 2.13 861000 2912666 2078 12 2.13 939000 2523062 1741 Table Bl Fresh Mushroom Price, Sales, Imports -Continued R e t a i l Sales Quantity Value Price i n B.C. of Imports of Imports Vancouver into Canada into Canada $ per l b '000 lbs lbs '000 $ 1985 1 2.13 922000 3832703 2395 2 2.15 894000 4577244 3205 3 2.13 1042000 5034151 3284 4 2.16 988000 5110207 3363 5 2.20 1129000 5360360 3388 6 2.20 1005000 4791109 2992 7 2.20 1010000 8060318 4902 8 2.18 972000 5431033 3313 9 2.16 851000 7018034 4126 10 2.10 965000 4809269 2837 11 2.10 955000 3447621 2114 12 2.10 1087000 5074305 2966 1986 1 2.10 1158000 4720254 2733 2 2.08 971000 3237844 1822 3 2.06 1102000 3361232 1927 4 2.05 1123000 5004586 2756 5 2.05 1095000 5493098 3233 6 2.04 1054000 4789698 2748 7 2.10 1144000 4540471 2554 8 2.05 927000 4525188 2417 9 2.06 980000 3808195 1927 Source: F r u i t and Vegetable and Honey Crop and Market Report Agriculture Canada, various issues Manager's Report F.V.M.G.C.A., various issues S t a t i s t i c s Canada Catalogue 65-007 113 Table B2 Consumer Price Indices A l l Items Fresh Veg. Process Veg. A l l Items Beef Vancouver Vancouver Canada Canada Canada 1981=100 1981=100 1981=100 1981=100 1981=100 1982 1 106.40 104.80 109.00 105.40 92.70 2 107.10 113.80 109.60 106.70 91.60 3 107.80 104.10 113.20 108.00 95.40 4 108.50 111.80 115.40 108.60 96.50 5 110.00 111.10 117.70 110.10 104.50 6 110.70 117.00 118.80 111.20 109.00 7 111.20 106.10 120.10 111.80 106.90 8 112.10 94.40 122.70 . 112.30 103.10 9 112.50 83.20 123.00 112.90 100.20 10 113.00 84.90 122.60 113.60 96.60 11 113.50 91.50 124.10 114.40 97.70 12 113.20 96.50 124.80 114.40 98.20 1983 1 113.60 95.50 126.10 114.10 95.30 2 114.20 95.50 127.40 114.60 97.20 3 115.00 101.60 125.70 115.80 95.20 4 115.60 100.90 125.70 115.80 100.00 5 115.60 107.20 125.10 116.10 104.90 6 116.30 111.00 125.50 117.40 104.80 7 117.60 106.70 126.70 117.90 101.20 8 117.90 95.90 126.40 118.50 100.30 9 118.10 93.90 127.70 118.50 99.60 10 118.30 99.60 127.50 119.20 101.90 11 118.40 102.50 128.00 119.20 100.00 12 118.50 104.90 128.90 119.60 101.30 1984 1 119.00 118.60 128.50 120.20 102.50 2 119.70 128.00 131.10 120.90 105.90 3 120.10 128.50 131.60 121.20 107.30 4 120.50 127.30 130.40 121.50 108.40 5 120.90 121.00 131.00 121.70 106.50 6 120.80 117.20 131.90 122.20 107.40 7 122.00 114.10 132.20 122.90 106.30 8 122.30 119.40 131.50 122.90 106.80 9 122.50 103.60 131.20 123.00 106.00 10 122.50 103.30 128.60 123.20 107.10 11 122.90 109.10 129.20 124.00 105.10 12 122.80 104.20 129.80 124.10 111.20 Table B2 Consumer Price Indices -Continued 114 A l l Items Fresh Veg. Process Veg. A l l Items Beef Vancouver Vancouver Canada Canada Canada 1981=100 1981=100 1981=100 1981=100 1981=100 1985 1 123.20 111.70 131.50 124.60 108.20 2 123.50 115.80 131.80 125.40 111.40 3 123.30 111.50 133.30 125.70 110.30 4 124.40 118.50 131.70 126.20 113.60 5 124.90 110.70 133.40 126.50 109.80 6 125.10 113.90 134.40 127.20 110.50 7 125.60 113.90 133.40 127.60 110.80 8 125.80 103.80 133.60 127.80 108.50 9 126.20 96.10 132.80 128.00 106.10 10 126.50 96.10 131.70 128.40 105.60 11 126.60 103.70 132.00 128.90 108.20 12 126.70 117.60 131.60 129.50 110.00 1986 1 127.30 123.80 133.30 130.10 112.40 2 127.40 112.70 134.60 130.60 108.60 3 128.00 106.70 133.30 130.90 110.00 4 128.10 117.30 133.60 131.10 106.50 5 129.00 124.30 134.20 131.70 108.90 6 129.30 126.90 136.70 131.90 108.90 7 130.00 119.50 135.60 132.90 109.20 8 130.30 111.30 137.40 133.30 109.90 9 130.30 106.60 137.10 133.30 113.40 Sources: S t a t i s t i c s Canada Catalogue 62-010 Table B3 Income and Population Labour Disposable Population Population Income Income B.C. Canada B.C. Canada '000,000 $ '000,000 $ •000 •000 1982 1 2134.2 260616.0 2778.8 24534.3 2 2141.7 261752.0 2781.6 24556.8 3 2186.0 263060.0 2784.3 24579.3 4 2190.6 264368.0 2787.2 24605.6 5 2206.6 265676.0 2790.1 24631.8 6 2240.7 265573.3 2794.6 24656.3 7 2093.2 265470.7 2797.3 24678.6 8 1951.1 265368.0 2800.0 24700.9 9 2168.1 265070.7 2802.7 24723.2 10 2181.9 264773.3 2804.5 24743.0 11 2154.0 264476.0 2806.3 24762.8 12 2079.6 265853.3 2808.1 24782.6 1983 1 2180.0 267230.7 2810.4 24801.5 2 2102.9 268608.0 2812.6 24820.5 3 2165.0 274286.7 2814.9 24839.4 4 2170.0 279965.3 2820.5 24862.0 5 2250.6 285644.0 2826.0 24884.5 6 2299.5 285261.3 2824.4 24904.6 7 2171.4 284878.7 2827.9 24924.5 8 2161.7 284496.0 2831.4 24944.4 9 2297.9 284978.7 2834.9 24964.3 10 2238.5 285461.3 2837.5 24983.3 11 2147.9 285944.0 2840.1 25002.4 12 2142.9 290394.7 2842.7 25021.4 1984 1 2133.9 294845.3 2845.3 25040.1 2 2094.3 299296.0 2848.0 25058.9 3 2097.5 300352.0 2850.6 25077.6 4 2193.7 301408.0 2854.3 25100.9 5 2293.2 302464.0 2857.9 25124.1 6 2343.5 305612.0 2860.4 25145.2 7 2227.2 308760.0 2863.4 25166.6 8 2231.2 311908.0 2866.4 25188.0 9 2334.1 313726.7 2869.4 25209.4 10 2343.7 315545.3 2871.4 25227.5 11 2323.9 317364.0 2873.3 25245.7 12 2290.3 319542.7 2875.3 25263.8 Table B3 Income and Population -Continued Labour Disposable Population Population Income Income B.C. Canada a B.C. Canada $ i n '000,00 '000,000 •000 '000 1985 1 2284.1 321721.3 2877.2 25282.3 2 2257.0 323900.0 2879.1 25300.8 3 2304.6 323750.7 2881.0 25319.3 4 2316.4 323601.3 2882.9 25339.6 5 2401.6 323452.0 2884.7 25359.8 6 2465.9 325264.0 2886.5 25380.0 7 2368.7 327076.0 2888.4 25402.1 8 2408.6 328888.0 2890.4 25424.1 9 2499.9 331516.0 2892.3 25446.2 10 2472.1 334144.0 2894.2 25464.5 11 2427.0 336772.0 2896.0 25482.9 12 2393.6 337921.3 2897.9 25501.2 1986 1 2371.9 339070.7 2898.9 25517.9 2 2346.7 340220.0 2900.0 25534.5 3 2386.4 340274.7 2901.0 25551.2 4 2429.1 340329.3 2903.5 25571.2 5 2494.2 340384.0 2905.9 25591.1 6 2540.1 342369.3 2908.8 25611.9 7 2439.8 344354.7 2911.8 25633.0 8 2390.7 346340.0 2914.9 25654.1 9 2495.4 348325.3 2917.9 25675.2 Source: S t a t i s t i c s Canada Catalogue 72-005 S t a t i s t i c s Canada Catalogue 13-001 Canadian S t a t i s t i c a l Review Catalogue 91-001 aGenerated from quarterly data by l i n e a r i n t e r p o l a t i o n

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