Once the concept of equilibrium has been defined, it might seem natural to apply the standard procedure of Arrow-Debreu theory, first analyzing existence and then the optimality of equilibrium. However, the normal procedure is reversed: the normative properties of marginal cost pricing equilibrium are analyzed first. It is not surprising that a concept of equilibrium motivated by efficiency conditions can lead to inefficient equilibria; for the first order conditions are necessary conditions which in the absence of convexity are not sufficient. What is perhaps more surprising is that there exist economies (that is, characteristics and a rule for distributing income) for which none of the marginal cost pricing equilibria are efficient. Thus, in a non-convex economy, considerations of equity (income distribution) and efficiency cannot be kept separate. In view of this, it is important to give conditions under which marginal cost pricing equilibria are known to be efficient. This chapter also considers the elasticity condition for efficiency for a single output and the elasticity condition for efficiency for many outputs.
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