Decomposition of Milk Supply Response into Technology and Price-Induced Effects Don P. Blayney and Ron C. Mittelhammer An economically relevant aggregate production function and an aggregate profit function are used to decompose milk supply response into technology and price effects. Decomposing milk supply response in this way provides insights into dairy industry efficiency and its impact on the effectiveness of price support programs as well as the extent to which aggregate milk production will expand despite prices motivating supply curtailment. An empirical analysis of supply response decomposition for the state of Washington is presented. Expected market price effects were obtained but were overwhelmed by technology effects resulting in milk output expansion when price signals motivated supply reduction. Key words: aggregate supply response, dairy, duality, technology and price effects. The U.S. dairy industry has experienced a chronic oversupply of raw milk. Contributing factors in- clude technological advances ranging over bulk milk tanks, automatic detachers, modern waste- handling equipment, automated feeding sys- tems, and better management of the milk cow through DHI (dairy herd improvement) pro- grams and closer monitoring of feeding. Chang- ing levels of input and output prices also are in- volved. In this paper an economically relevant aggre- gate production function (ERAPF) for an indus- try is applied to decompose milk supply re- sponse into technology and price-induced responses. The method allows a quantitative as- sessment of the degree to which milk supply changes can be attributed to pure technological advance as opposed to responses by producers to changing price levels. Decomposing supply changes in this way can provide insight into the effectiveness of research and extension efforts aimed at improving efficiency in the dairy in- dustry as well as the extent to which such efforts undermine or enhance government price support programs designed to stabilize milk supply through market price intervention. This empir- Don P. Blayney is an economist with Economic Research Service, U.S. Department of Agriculture; Ron C. Mittelhammer is a pro- fessor of agricultural economics at Washington State University. The authors thank the Journal reviewers for their helpful and constructive comments and suggestions. ical method is also useful in evaluating the ex- tent to which milk producers will continue to expand aggregate production despite downward trends in output price and increasing input prices. Theoretical Considerations The notion of an aggregate profit function ap- pears within the context of the general equilib- rium literature (e.g., Debreu, Varian). The ag- gregate profit function is defmed for given output and input prices and a given aggregate produc- tion relation. We examine the applicability of Hotelling's lemma to an aggregate profit func- tion in an industry where profit-maximizing firms produce a single product and take prices as given. In order to define the aggregate profit func- tion, consider the problem of maximizing the aggregate profit that can be generated by dis- tributing production of output across the firms in the industry, as m m (1) 1T(P, w) = max P 2: qj - 2: c/w, q), q! ..... qm i- I I where P is the output price, w is the vector of input prices, qj is the output of the jth firm, and c/ w, %) is the cost function of the jth firm. The cost functions CIO, ... , emO are assumed to satisfy all the usual regularity conditions, in- cluding second-order continuous differentiabil- Copyright 1990 American Agricultural Economics Association