Do Managers Use Their Information Efficiently
It is often true that a manager's opinions about events relevant to production are valued but are not fully known by others. This note suggests that in such circumstances there may be a problem with production. Consider a competitive equilibrium in a standard Arrow-Debreu model of an economy. In such an equilibrium production decisions are guided by prices and, in particular, by contingent commodity prices (which in fact may be implicit in stock market prices). Moreover, in such an equilibrium the managers of production processes play a strictly passive role since complete instructions for production are implicit in the criterion of profit maximization.' However, if the probabilistic beliefs of the managers are valued but are not fully known by the other agents in the economy, then it seems that these agents might well prefer to have the managers play an active role in making production decisions. In other words, it seems that profit maximization with respect to contingent commodity prices may encourage managers to act contrary to what would be the best wish of others, and consequently that the absence of markets in certain contingent commodities might not be undesirable.2 Our discussion of this issue will make reference to a simple example. An economy with many identical individuals and few identical managers uses seed to produce wheat which may be grown in two regions, A and B. Managers decide where to plant the seed. The wheat harvest is uncertainit is either positive or zero-depending on which of the two possible states of nature, a and ,B, occurs. This is described in Table 1, where si is the amount of seed planted in region i and f is the usual type of production function (f' > 0, f < 0). Let us suppose for simplicity that consumers alone determine prices in competitive equilibrium, that is, the few managers have only a negligible impact on the prices. Assume initially that consumers have fixed beliefs, independent of those which the managers might have. Specifically, assume that consumers believe the state a will occur with probability a. Then, since a competitive equilibrium in which there are markets for contingent wheat is Pareto efficient, it must in this case maximize expected utility of consumers. Consequently, if each consumer's endowment consists of one unit of seed and his von Neumann-Morgenstern concave utility function U(.) depends only on consumption of wheat, the problem solved by the market is to maximize expected utility:
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