Producer TheoryJonathan Levin and Paul MilgromOctober 20041 Competitive Producer BehaviorSince Marshall, the standard approach to developing a theory of competitive mar-kets is to separate demand behavior (“consumer theory”) from supply behavior(“producer theory”) and then use the notion of market equilibrium to reconciledemand and supply. This note studies producer theory and a separate one studiesconsumer theory.The standard model has the following features. Firms are described by fixedand exogenously given tec hnologies that allow them to conv ert inputs (in simplemodels, these are land, labor, capital and ra w materials) into outputs (products).“Competitive” producers take both input and output prices as given, and choose aproduction plan (a technologically feasible set of inputs and outputs) to maximizeprofits.Before w e get in to the details, let’s remark on a few key features of the model.1. Firms are price takers. This “competitive firm” assumption applies to bothinput and output market s and makes it reasonable to ask questions about(1) what happens to the firm’s ch oices when a price changes and (2) whatcan be inferred about a firm’s technology from its choices at various pricelevels. For output markets, the assumption fits best when each firm hasmany competitors who produce perfectly substitutable products, and a par-allel condition applies to input markets. Of course, even the most casualempiricism suggests that many firms sell differentiated products and have at1least some flexibility in setting prices, and ev en small firms m ay have marketpower in buying local inputs, such as hiring workers who live near a mine orfactory, so the results of the theory need to be applied with care. Even so,the pattern of analysis established in this way is often partially extendableto situations in which firms are not price takers.2. Technology is exogenously given. This assumption is sometimes criticized astoo narrow to be useful in a world of technical change, product innovations,and consumer marketing, but it is more flexible and encompassing than mostcritics acknowledge. The exogenous technology model formally includes thepossibility of investing in technical change, provided these inv estments arethemselves treated as inputs into a production proc ess. Similarly, the modelformally includes advertising and branding that alter consumer’s perceptions,provided that we represent these activities as transforming the output into adifferent product. It allows managerial effort and talent to be inputs as well,if they, too, are treated as simple inputs into production.3. The firm maximizes profits. Since the time of Adam Smith, if not earlier,many observers have emphasized that corporations are characterized by aseparation between ownership (the stockholders) and control (management),and that this separation weakens the incentives of managers to maximizeprofits. The problem of motivating managers to act on behalf of owners hasbeen a main concern for the economics (and la w) of agency theory.4. The Marshallian approach of separat ing the household, where consumptiontakes place, from the firm, in which all production takes place, is intenselycriticized by some economists. An alternative approach treats householdsas bo th consumers and producers. In this alternative view, an essentialfeature of all economic development is the change in household productivebehavior associated with the development of mark ets. As markets develop,households move away from the pattern of producing for themselves onlythe goods they plan to consume toward a pattern in which each householdspecializes, devoting most of its productive efforts to producing one particulargood, which it sells or trades for other goods.2Students sometimes wonder about the role of assumptions such as these, par-ticularly when they are contrary to the facts of the situation. Economists havetaken a range of positions concerning how to think about simplifying assumptions,and there is no consensus about the “correct” view. One extreme position is todeny the relevance of any inference based on such models, because the premisesof the model are false. At the opposite extreme, some practicing economists seemwilling to accept “standard” or “customary” assumptions uncritically. Both ofthese extreme positions are rejected by thoughtful people.All economic modeling abstracts from reality by making simplifying but untrueassumptions. Experience in economics and other fields shows that such assump-tions models can serve useful purposes. One purpose is to support tractable modelsthat isolate and highlight important effects for analysis by suppressing other ef-fects. Another purpose is to serve as a basis for numerical calculations, possibly foruse in estimating magnitudes, deciding economic policies, or designing economicinstitutions. For example, one might want to estimate the effect of a tax policychange on overall investment or hiring.The initial calculations based on a simplifiedmodel might then be adjusted to accoun t for the effects suppressed in the model.For a model to serve these practical purposes, its relevant predictions must bereasonably accurate. The accuracy of predictions can sometimes be checked bytesting using data. Sometimes, the “robustness” of predictions can be evaluatedpartly by theoretical analyses. In no case, however, should models or assumptionsbe regarded as adequate merely because they are “usual” or “standard.” Althoughthis seems to be an obvious point, it needs to be emphasized because the temptationto skip the validation step can be a powerful one. Standard assumptions often makethe theory fall into easy, recognizable patterns, while checking the suitabilit y ofthe assumptions can be much harder. The validation step is not dispensable.2 Production Sets, TechnologyWe start by describing the technological possibilities of the firm. Suppo se there aren commodities in the economy. A production plan is a vector y =(y1, ..., yn) ∈ Rn,where an output will have yk> 0 and an input will hav e yk< 0. If the firm has3nothingtodowithgoodk,thenyk= 0. The production possibilities of the firmare described by a set Y ⊂ Rn,whereanyy ∈ Y is feasible production plan. Figure1 illustrates a production possibility set.6-?¾x1x2·yYFigure 1: A Production Possibility SetThroughout our analysis, we will make the innocent technical assumptions thatY is non-empty (so as to have something