Journal Article Some Remarks on Optimal Growth with Intertemporally Dependent Preferences in the Neoclassical Model Get access Mukul Majumdar Mukul Majumdar Cornell University Search for other works by this author on: Oxford Academic Google Scholar The Review of Economic Studies, Volume 42, Issue 1, January 1975, Pages 147–153, https://doi.org/10.2307/2296828 Published: 01 January 1975

The paper studies the problem of optimal intertemporal allocation in an aggregative model with a non-convex technology set and a discounted sum of consumptions as the objective function. The study demonstrates the existence of a threshold initial stock such that the long-run behaviour of optimal programmes depends critically on whether the initial stock is, above or below the threshold. This is in contrast with the standard turnpike theory of convex models in which the long-run behaviour of optimal programmes is independent of the initial stock.

We consider optimal capital accumulation in a nonlinear activity analysis model in which production and primary resource supplies are affected by a stationary stochastic process of exogenous shocks; the optimality criterion is the sum of discounted expected future social utilities. Under various neoclassical conditions on technology and preferences, (i) there exists an optimal policy of investment and consumption expressible as a continuous time-invariant function of the capital stocks and the history of stochastic shocks, and (ii) there is a stationary stochastic process of capital stocks that is consistent with the optimal policy.

This paper formulates the notion of stochastic equilibria as invariant probability distributions consistent with the behavior patterns of individuals and the disequilibrium adjustment mechanism of the economy. Conditions for existence, uniqueness, and stability of such equilibria are examined. WE CONSIDER A CLASS of problems in this paper in which the economic environment is stochastic. We will be concerned primarily with developing an equilibrium concept for general equilibrium models of this type. However the essential ideas can be carried over directly to partial equilibrium applications. The choice of the specific general equilibrium model used results primarily from a desire to facilitate comparisons with earlier work on alternative equilibrium concepts for this model (see Hildenbrand [9] and Majumdar and Bhattacharya [2 and 3]). Randomness can arise from several sources. We will be considering, for concreteness, a simple exchange economy in which the basic data are the preferences and endowments of the economic agents. Either of these can be random. Typically, randomness of endowments can be allowed for by creating contingent markets in which case the Arrow-Debreu deterministic equilibrium suffices. It is conceptually much more difficult to create markets contingent on tastes due to the difficulties of discovering the true taste pattern of an individual, difficulties which do not arise in the case of endowment vectors which can be observed directly. We will be considering an economy without markets for every future contingency and thus there will remain some randomness. This residual uncertainty in the economy necessitates equilibrium concepts other than the Arrow-Debreu system of market clearing prices. 2. NOTATION

Mukul Majumdar, Amartya Sen; A Note on Representing Partial Orderings, The Review of Economic Studies, Volume 43, Issue 3, 1 October 1976, Pages 543–545, https: