The hypothesis that capital increases at each time in response to an increase in the discount factor is explored for a class of aggregate models of optimal accumulation. When the optimal program is monotonic, capital is shown to increase with an increase in the discount factor. A counterexample in the case of oscillating programs is discussed. An application of the monotone case is given for an adjustment cost model of the firm.

The equivalence between optimal growth solutions and solutions of decentralized models of intertemporal allocation is explored in a one-consumer, heterogeneous capital goods framework. The decentralized economy follows a perfect foresight path. The main result is that the decentralized economy will impose on itself a transversality condition. This yields the interpretation of equilibrium prices as prices consistent with a certainty version of the efficient markets hypothesis. The results rest on the recent contribution by Benveniste and Scheinkman providing sufficient conditions for infinite horizon concave programs to exhibit capital value transversality as a necessary condition for optimality.

Journal Article On the Long-Run Steady State in a Simple Dynamic Model of Equilibrium with Heterogeneous Households Get access Robert A. Becker Robert A. Becker Indiana University, Bloomington Search for other works by this author on: Oxford Academic Google Scholar The Quarterly Journal of Economics, Volume 95, Issue 2, September 1980, Pages 375–382, https://doi.org/10.2307/1885506 Published: 01 September 1980

The authors demonstrate existence of a perfect foresight equilibrium under borrowing constraints in a one-sector model with infinitely-lived heterogeneous agents. The class of admissible preferences includes, but is not limited to, recursive preferences. Existence is proven using a t$2Ctonnement argument under appropriate conditions on preferences and technology. A new measure of discounting, the norm of marginal impatience, is used to determine which technologies are admissible. Depending on the norm of marginal impatience, the admissible technology may either allow for permanent growth or have a maximum sustainable stock.

Core allocations may be defined for infinite horizon capital accumulation models. If agents cannot trust each other in the sense of Gale, then agents may renege on their commitments; their decisions appear time inconsistent. A core allocation is a recursive core allocation provided no coalition can improve upon its consumption stream at any time given its accumulation of assets up to that period. We show for every allocation of consumption in the initial core, one can find a distribution of capital stocks among the agents where no coalition of agents will break the initial core contract at any date. It follows that if the proper distribution of the streams of capital is achieved, then the allocation in the core is also in the recursive core. The latter therefore forges a link between the distribution of wealth (capital), the problem of trust, and time consistent intertemporal contracts