The relation of optima and market equilibria with externalities
Three main theorems provide the basis for welfare economics. These indicate sufficient conditions under which (a) there exists a competitive equilibrium, (b) competitive equilibria are Pareto-optimal, and (c) Paretooptima are supportable by competitive equilibria. One condition found in all three is that the economic environment be decomposable. That is, the admissible actions and preferences of any agent should be independent of the actions of the other agents. Furthermore, demonstration of the existence of indecomposabilities, usually called externalities, has generally been considered sufficient evidence of “market failure” and of the need for remedies. One such remedy is that the externalities be “internalized.” That is, agents who have an impact on each other should get together and make a joint decision. This indicates that there are informational, as well as technological, reasons for market failure due to externalities. In this paper, the impact of externalities on conclusions (b) and (c), above, is investigated. It is shown that, even if externalities exist, the information structure may be such that (b) and (c) still hold. Delaying definitions until later, we show that (b) holds with externalities in the production sector if information is extensive enough, and (c) holds with externalities in production and consumption if information is limited enough. It is the relation between apparently possible actions and actually possible actions which provides the basis for these results. These concepts are defined in Section 3, and their implications for consumer and producer behavior in a competitive economy are explored in Sections 4 and 5. The rest of the paper is devoted to indicating the impact, on (b) and (c), of externalities. In the next section, a description of the economic environment is presented which includes most of the notations used in the rest of the paper.