Tapan Mitra

AGGREGATING INFINITE UTILITY STREAMS WITH INTERGENERATIONAL EQUITY: THE IMPOSSIBILITY OF BEING PARETIAN

It has been known that, in aggregating infinite utility streams, there does not exist any social welfare function, which satisfies the axioms of Pareto, intergenerational equity, and continuity. We show that the impossibility result persists even without imposing the continuity axiom, and in frameworks allowing for more general domains of utilities than those used in the existing literature. Copyright The Econometric Society 2003.

Some Theoretical Results on the Economics of Forestry

The general question of forest management can be stated as follows. Suppose the planner of a piece of forest land obtains utility in any time period from the timber content of trees harvested in that period. If the planner wishes to maximize the discounted sum of such utilities starting from any initial forest, what pattern of planting and harvesting trees should it follow? This paper provides a systematic analysis to answer the above question. In particular, the optimal solution is related to the Faustmann periodic solution and the sustained yield solution, which are prominent in the forestry literature.

On the faustmann solution to the forest management problem

Abstract This paper is concerned with optimal solutions to the forest management problem when future utilities are undiscounted. By examining asymptotic properties of such solutions, we find that (i) if the utility function is linear, then the Faustmann periodic solution is optimal; (ii) if the utility function is increasing and strictly concave, an optimal solution converges to the maximum sustained yield solution, which we characterize as a golden rule. These results may be viewed as a possible resolution to the debate in forestry economics about what constitutes an optimal policy in forest management.

Sustainability and Discounted Utilitarianism in Models of Economic Growth

Discounted utilitarianism treats generations unequally and leads to seemingly unappealing consequences in some models of economic growth. Instead, this paper presents and applies sustainable discounted utilitarianism (SDU). SDU respects the interests of future generations and resolves intergenerational conflicts by imposing on discounted utilitarianism that the evaluation be insensitive to the interests of the present generation if the present is better off than the future. An SDU social welfare function always exists. We provide a convenient sufficient condition to identify SDU optima and apply SDU to two well-known models of economic growth. We also investigate the axiomatic basis for SDU.

Utilitarianism for infinite utility streams: A new welfare criterion and its axiomatic characterization

A definition of a utilitarian social welfare relation (SWR) for infinite utility streams is proposed. Such a relation is characterized in terms of the Pareto, Anonymity and Partial Unit Comparability Axioms. The merits of the utilitarian SWR, relative to the more restrictive SWR induced by the overtaking criterion, are examined.

A Sufficient Condition for Topological Chaos with an Application to a Model of Endogenous Growth

Abstract This paper provides an easily verifiable sufficient condition for topological chaos for unimodal maps which can be satisfied when the well-known Li–Yorke condition is not satisfied. It then shows how this result can be applied to a model of endogenous growth with externalities to establish the existence of chaotic equilibrium growth paths in that framework. Journal of Economic Literature Classification Numbers: C61, D90, O41.

Optimization and chaos

M. Majumdar, T. Mitra: Dynamical Systems: A Tutorial.- T. Mitra: Introduction to Dynamic Optimization Theory.- M. Majumdar, T. Mitra: Periodic and Chaotic Programs of Optimal Intertemporal Allocation in an Aggregative Model with Wealth Effects.- K. Nishimura, M. Yano: Optimal Chaos, Nonlinearity, and Feasibility Conditions.- R. Becker, C. Foias: The Local Bifurcation of Ramsey Equilibrium.- G. Sorger: On the Structure of Ramsey Equilibrium: Cycles, Indeterminacy and Sunspots.- M. Majumdar, T. Mitra: Robust Ergodic Chaos in Discounted Dynamic Optimization Models.- K. Nishimura, M. Yano: Non-Linear Dynamics and Chaos in Optimal Growth: A Constructive Exposition.- K. Nishimura, G. Sorger, M. Yano: Ergodic Chaos in Optimal Growth Models with Low Discount Rates.- G. Sorger: On the Minimum Rate of Impatience for Complicated Optimal Growth Paths.- T. Mitra: An Exact Discount Factor Restriction for Period-Three Cycles in Dynamic Optimization Models.- K. Nishimura, M. Yano: On the Least Upper Bound of Discount Factors that are Compatible with Optimal Period-Three Cycles.- T. Mitra: On the Relationship between Discounting and Entropy of Dynamic Optimization Models.

Periodic and chaotic programs of optimal intertemporal allocation in an aggregative model with wealth effects

SummaryWe examine a discrete-time aggregative model of discounted dynamic optimization where the felicity function depends on both consumption and capital stock. The need for studying such models has been stressed in the theory of optimal growth and also in the economics of natural resources. We identify conditions under which the optimal program is monotone. In our framework, the optimal program can exhibit cyclic behavior for all discount factors close to one. We also present an example to show that our model can exhibit optimal behavior which is chaotic in both topological and ergodic senses.

Dynamic Optimization Under Uncertainty: Non-convex Feasible Set

An editorial note in the Economic Journal (May 1930) reported the death of Frank Ramsey, and his 1928 paper was described as ‘one of the most remarkable contributions to mathematical economics ever made’. In the same issue the editor organized a symposium on increasing returns and the representative firm. This symposium seems to be a natural follow-up of a number of papers published by the Journal during 1926–8, including the well-known article of Allyn Young (1928) that is still available, and duly remembered. The problems of equilibrium of a firm under increasing returns, or more generally, of designing price-guided resource allocation processes to cope with increasing returns, has since been a topic of continuing interest. Ramsey’s contribution was enshrined as a durable piece with a resurgence of interest in intertemporal economics in the fifties. But neither John Keynes, the editor of the Economic Journal who was most appreciative of Ramsey’s talents, neither the subsequent writers on ‘growth theory’ in Cambridge, England (nor, for that matter, those in Cambridge, Massachusetts), have made any precise suggestion towards incorporating increasing returns in a Ramsey-type exercise.

Indefinitely sustained consumption despite exhaustible natural resources

SummaryThis paper analyzes the feasibility of sustaining uniformly positive consumption forever — even when flows of exhaustible resources are an indispensable input. The main result is a characterization of an economys capability for sustaining such consumption — under quite general maintained assumptions on technology — in terms of a single, simple capital-resource substitution condition.