We investigate the structure of competitive equilibria in an exchange economy parametrized by (i) endowments and (ii) restrictions on market participation. For arbitrary regular endowments, if few consumers are restricted, there are no sunspot equilibria. If endowments are allowed to vary, while restrictions on market participation are fixed, there is a generic set of preferences such that sunspot equilibria exist for a non-empty subset of endowments. Our analysis extends to the general case of an arbitrary number of restricted consumers the results of Cass and Shell for the polar cases in which either (i) no consumers are restricted or (ii) all consumers are restricted.

The purpose of this paper is to investigate in detail the dynamics of a simple model with heterogeneous capital goods under alternative assumptions about expectations formation and saving. Before investment takes place, the entrepreneur has a choice over a large number (to be precise, a continuum) of types of machines; those which require more resources today require less labor per unit of output in the future. But once the machine has been constructed, it cannot be altered. This model raises, moreover, the interesting problem of economic obsolescence: machines may be constructed which subsequently, because of higher wage rates, are no longer profitable to operate. We shall be interested in determining how the dynamic behavior of this economy differs from that of the economy with malleable capital, as analyzed by Solow (1956) and Swan (1956) for the descriptive growth model and by Ramsey (1928) for the optimal growth model. It will be shown that, although there are fundamental differences in short-run behavior, in the long run the economy evolves much like the economy described by the simpler malleable capital models. On the other hand, econometric estimation based on the use of the malleable capital model, such as that of Solow (1957) in estimating the residual, or Arrow, Chenery, Minhas, and Solow (1961) in estimating the elasticity of substitution, may encounter serious biases from the specification error.

This paper examines how, in the presence of individual risk, economic efficiency can be achieved without an unrealistically large number of contingent claims. Market uncertainty is specified in such a way that general types of individual risk and collective risk are properly accounted for and so that, specifically, market clearing is always satisfied ex post as well as ex ante. We show that consistency of beliefs and optimality of allocation can be guaranteed with an appropriate array of pure Arrow securities to spread collective risk and mutual insurance policies to pool individual risk. When there is individual risk common to like groups of individuals, pooling risk by means of mutual insurance permits substantial economizing on market transactions, as compared to those required if dealing instead with the full complement of pure Arrow securities. We show that if there are N households (consisting of H types), each facing the possibility of being in S individual states together with T collective states, then ensuring Pareto optimality requires only H(S-1)T independent mutual insurance policies plus T pure Arrow securities. Our results also help to clarify the question of which missing markets may affect allocational efficiency.