unavailable, the lysine and methionine content of 

 the feed can be augmented with synthetic pro- 

 teins. Kolhonen (1974) described the develop- 

 ment of synthetic methionine and lysine for use 

 in feed formulas. 



Linear programming has been widely adopted 

 by formula feed manufacturers in the United 

 States and western Europe (Kolhonen 1974). 

 Least-cost combinations of feed constituents 

 needed for adequate nutrition are quickly and ac- 

 curately computed for any vector of constituent 

 prices. Thus, the demand for feed ingredients is 

 expected to exhibit great sensitivity to relative 

 prices. In a recent examination of demand for ag- 

 ricultural feed ingredients, Meilke (1974) re- 

 ported that price elasticities are generally >2 in 

 absolute value. It is expected that the demand for 

 fish meal will be elastic also, at least when avail- 

 able quantities allow the feed formula manufac- 

 turers to include between 2 and 8% fish meal in 

 poultry rations. When the supply of fish meal is 

 low enough to jeopardize the maintenance of at 

 least 2% fish meal, the demand may become in- 

 elastic. Thus, one hypothesis to be tested is that 

 the own price elasticity of demand for fish meal 

 falls with increasing price and decreasing quan- 

 tity. 



Markets for fish meal in the United States are, 

 for obvious reasons, concentrated in the poultry- 

 producing regions — California, Arkansas, and 

 states in the Deep South. Domestic production of 

 fish meal occurs mainly in California, the Gulf 

 Coast States, and the South Atlantic States. In 

 some years, however, much of the domestic sup- 

 ply is imported from major foreign producers such 

 as Peru. Foreign meal is a perfect substitute for 

 the domestic product, but the supply of foreign 

 meal has undergone tremendous fluctuations due 

 to variations in fish stocks (especially the Peru- 

 vian anchoveta, Engraulis ringens). Domestic 

 supplies have also been strongly influenced by 

 uncontrolled variations in domestic stocks (espe- 

 cially menhaden Brevoortia tyannus and B. pat- 

 ronus) and by administrative decisions of fishery 

 management agencies (California's anchovy, £;/i- 

 graulis mordax, fishery, e.g., see Pacific Fishery 

 Management Council 1978: 31660-31664). On the 

 supply side of the domestic market, therefore, the 

 major fluctuations are not price induced, but are 

 due to exogeneous factors. On the demand side 

 the poultry industry experienced a steady expan- 

 sion starting in the early 1950's and continuing 

 until about 1970. 



FISHERY BULLETIN: VOL. 78, NO. 2 



DEVELOPMENT OF DEMAND MODEL 



Demand and price analysis has been a cor- 

 nerstone of applied economic research since the 

 1930's (Working 1927; Schultz 1938; Wold and 

 Jureen 1953). Agricultural economists have been 

 particularly active in developing demand models 

 for commodities. Research on demand for fish 

 is of more recent vintage but differs in few im- 

 portant respects from that for agricultural com- 

 modities. For an excellent review of the historical 

 development of demand analysis, see Waugh and 

 Norton (1969). Among the methodological issues 

 addressed in applied demand studies are: 1) spec- 

 ification of the demand model, 2) development of 

 appropriate functional forms, 3) treatment of 

 simultaneity bias in market demand and supply 

 function estimates, and 4) incorporation of 

 dynamic response mechanisms in the demand 

 model. These issues are discussed seriatim. 



Specification 



The specification of a demand model consists of 

 the choice of dependent and independent vari- 

 ables. Annual quantity demanded, as measured 

 by quantity purchased, should be the dependent 

 variable. Purchased quantities are difficult to ob- 

 tain, however, while production, import, and ex- 

 port statistics are well documented. Also, meals 

 derived from different sources differ in protein 

 content and sell at different prices. Both the 

 quantities and the prices must be aggregated 

 such that they represent a reasonably homoge- 

 neous commodity. Fish meal quantities (Table 1, 

 columns 1-6) are converted to a protein equiva- 

 lent basis by multiplying the quantity of each 

 type of meal by the prevailing percentage of pro- 

 tein content. The total available domestic quan- 

 tity, computed by summation of protein equiva- 

 lent fish meals and subtraction of exports, is 

 listed in Table 1, column 7. Similarly, since the 

 prices of the various fish meal types (Table 2, col- 

 umns 1-4) are based on protein content, each 

 price is converted to a protein basis. The aggre- 

 gate price of fish meal introduced as an indepen- 

 dent variable in the demand model is the average 

 price per unit protein for all meal supplied to the 

 U.S. market (Table 2, column 5). Some specifica- 

 tion error may enter the model because domestic 

 supply rather than quantity purchased is used for 

 the dependent variable, but this problem is un- 

 avoidable with available information. 



268 



