Journal Article Optimum Growth in an Aggregative Model of Capital Accumulation Get access David Cass David Cass Yale University Search for other works by this author on: Oxford Academic Google Scholar The Review of Economic Studies, Volume 32, Issue 3, July 1965, Pages 233–240, https://doi.org/10.2307/2295827 Published: 01 July 1965

This is primarily an expository paper, presenting many of the concepts and results of modern capital theory in the context of analyzing Wicksell's classical model of natural aging processes. The only novel result is a demonstration that efficient allocation over time in the Wicksellian model implies that real (though not value) aggregation can be utilized to reduce it, for all practical purposes, to the well-known one-sector neoclassical model.

Can extrinsic uncertainty ("animal spirits," "market psychology," "sunspots,"...) play a significant role in rational expectations equilibrium models? We establish that extrinsic uncertainty cannot matter in the static Arrow-Debreu economy with complete markets. But we also establish that extrinsic uncertainty can matter in the overlapping-generations economy with complete markets but where market participation is limited to those consumers alive when the markets are open. Equilibrium allocations in which extrinsic uncertainty plays no role are Pareto optimal in the traditional sense. Equilibrium allocations in which extrinsic uncertainty does play a role are Pareto optimal in a (weaker) sense which is appropriate to dynamic analysis.

This paper generalizes Samuelson's well-known analysis concerning the use of fiat or outside money to support Pareto-optimal allocations in an overlapping- generations framework. While maintaining an elementary demographic structure butexpanding the list of available commodities in each period, we establish the following result: If there is a fixed supply of fiat money, and individuals are also permitted to issue bonds or inside money, then there always exists at least one stationary equilibrium yielding a Pareto-optimal allocation.

This paper presents an analysis of the structure of competitive equilibrium in a smooth, exchange economy where there are incomplete markets in financial instruments whose overall payoffs (both prices and yields) are fixed in units of account. The main result establishes that such market incompleteness generates a comparable degree of allocation indeterminateness. It is also shown how this real indeterminacy may increase when prices and yields are treated as variables rather than parameters.

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.

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.