Stationary cardinal utility and optimal growth under uncertainty

In the literature on multiperiod planning under uncertainty, it is generally postulated that preferences may be represented by a von Neumann-Morgenstern utility index that is additive over time. This paper accomplishes two objectives: First, an axiomatic basis is provided for a more general class of non-additive utility indices defined over infinite consumption streams. Second, this class of utility functions is applied to extend existing results (J. Econ. Theory4 (1972), 479–513; J. Econ. Theory11 (1975), 329–339) on the nature of optimal growth under uncertainty. Of particular interest are the existence and stability of a stochastic steady state.     

The nature of the steady state in models of optimal growth under uncertainty

Summary. We study a one-sector stochastic optimal growth model with a representative agent. Utility is logarithmic and the production function is of the Cobb-Douglas form with capital exponent . Production is affected by a multiplicative shock taking one of two values with positive probabilities p and 1-p. It is well known that for this economy, optimal paths converge to a unique steady state, which is an invariant distribution. We are concerned with properties of this distribution. By using the theory of Iterated Function Systems, we are able to characterize such a distribution in terms of singularity versus absolute continuity as parameters and p change. We establish mutual singularity of the invariant distributions as p varies between 0 and 1 whenever . More delicate is the case . Singularity with respect to Lebesgue measure also appears for values such that . For and Peres and Solomyak (1998) have shown that the distribution is a.e. absolutely continuous. Characterization of the invariant distribution in the remaining cases is still an open question. The entire analysis is summarized through a bifurcation diagram, drawn in terms of pairs .Received: 9 April 2002, Revised: 29 October 2002, JEL Classification Numbers: C61, O41.Correspondence to: Tapan MitraThis research was partially supported by CNR (Italy) under the "Short-term mobility" program and by M.U.R.S.T. (Italy) National Group on "Nonlinear Dynamics and Stochastic Models in Economics and Finance" . We are indebted to Rabi Bhattacharya for providing us with the reference to Solomyak's (1995) paper. The present version has benefitted from comments by Mukul Majumdar and two anonymous referees.     

Bankable emission permits under uncertainty and optimal risk-management rules

This article proposes a theory of banking of emission permits under conditions of regulatory uncertainty. Based on a two-period partial equilibrium framework, we examine the effects of increasing risk–in the sense of a mean preserving spread–regarding a future permit allocation at the firm level. We also examine the role of an agency to pool risks by re-allocating permits for a group of firms. Our results are twofold. First, an increase in risk may lead to changes in a firm’s banking strategy, depending on the third partial derivative of its production function with respect to pollution. Second, we define an optimal risk-sharing rule between agents to respond to political decision changes. Our results overall suggest that the bankability of permits may be used as a risk-management tool.     

On industry equilibrium under uncertainty

The paper considers an industry consisting of numerous firms that produce a homogeneous output, the demand for which is a random variable. Each firm belongs to one of K possible types, and each type is characterized by a U-shaped average cost curve. It is shown that: (i) the first-order necessary conditions for efficient investment and output are sufficient; accordingly, the set of competitive equilibria is non-empty and coincides with the set of efficient allocations; (ii) a dynamic process of free entry and exit of firms, guided by expected profits, is quasistable and every limit point is a competitive equilibrium. The paper also defines a sufficient condition for uniqueness of the competitive equilibrium, in which case it is stable.     

The optimal choice of central bank independence and conservatism under uncertainty

This paper examines the optimal monetary delegation arrangement of central bank independence and conservatism in the presence of uncertainty about the central bank’s output objective. We show that full independence is no longer optimal with uncertain central bank preferences, and that optimal delegation involves the choice of both independence and conservatism. Further, we find that the usual trade-off between independence and conservatism no longer necessarily holds. Consequently, high central bank independence may also require a high level of conservatism.     

The optimal control of emissions and renewable resource harvesting under uncertainty

A model of a renewable resource is developed where the growth and quality of the resource are reduced by pollution. Ambient pollution concentrations and the renewable resource stock are modeled as stochastic processes. Conditions for the optimal harvest plan and the optimal emissions rate are derived. The effect of stochastic variations on the optimal management of the resource is analyzed. The steady-state joint probability distribution of the resource and pollution stocks is shown to exist under certain conditions.     

Export taxes versus buffer stocks as optimal export policies under uncertainty

Optimal state-dependent export taxes and costly-to-store buffer stocks are compared in their welfare implications for an exporter possessing monopoly power in the international trade of a volatile commodity. Optimal stochastic control is used to derive the optimal buffer stock rules. It is shown that, if the internal and external fluctuations facing the exporter are large, if the storage costs are low, and if the price elasticity of export supply is small relative to that of export demand, the exporter would gain more from a buffer stock than from a optimal export tax. World welfare is always increased by buffer stocks, as opposed to tariffs; and, under some conditions, the foreign country might also benefit and, hence, not retaliate.     

Managing exotic pests under uncertainty: optimal control actions and bioeconomic investigations

Using a real options framework in continuous time, we examine two problems associated with the management of exotic pests under uncertainty. First, we analyze the optimal timing of investing in a control action. Given fixed control costs, we obtain a closed-form solution for when to control an exotic pest whose density varies randomly. Second, we define an analytical framework for finding the optimal expenditures for obtaining the relevant bioeconomic data. Our numerical results, based on a wide range of bioeconomic parameters, highlight the importance of accounting for uncertainty and irreversibility when developing simple rules to manage exotic pests.     

Inter-basin water transfers under uncertainty: Storage capacity and optimal guaranteed deliveries

This paper deals with water transfers between jurisdictions not claiming riparian rights to the same water source, and taking place through straightforward sales. Taking into account the uncertain nature of water surpluses, we investigate, within a partial equilibrium framework, the implications of a third party's provision of storing facilities upon the potential supplier's decision whether, and to what extent, it is worthwhile to guarantee a constant amount of water exports. The analysis suggests that there exists a minimum storage capacity below which the potential supplier will never find it profitable to divert a constant amount of water outside his boundaries; the greater the uncertainty about future surpluses and/or internal costs due to even occasional water shortages resulting from the water export commitment, the higher the required minimum storage capacity will be. Above this minimum, an increase in the capacity would be better for the surplus agent, but in a situation in which water surplus is expected to decrease over time, increases in storage capacity would make him willing to guarantee a smaller amount of water deliveries.This work has been carried out under the auspices of the European Science Foundation's research program Sharing fresh water resources in the Mediterranean region: An economic perspective. Previous versions have been presented at ESF workshops held at the Universities of Haifa, Padova and Crete. Financial support from MURST (funds 40% — 1992) is gratefully acknowledged. We wish to thank Nunzio Cappuccio, Haluk Akdogan, Karl Mäler, Mordechai Shechter, Naomi Zeitouni, and two anonimous referees for helpful comments. The usual disclaimer applies.     

Consequences of irreversibilities on optimal intertemporal CO2 emission policies under uncertainty

This paper investigates how irreversibilities affect the optimal intertemporal accumulation of greenhouse gases in the atmosphere under uncertainty. More precisely, the evolution of the future temperature is assumed to follow an Itô-process with the drift provided by greenhouse gas emissions. This paper considers two different kinds of irreversibilities: of emissions (i.e., CO₂ once dissolved into the air cannot be collected later) and of stopping. These issues are investigated first (in the tradition of the real option literature) as pure stopping problems and then allowing for a continuous choice of emissions. Implications for global warming are: an irreversible stopping of greenhouse gas emissions is never optimal in a continuous framework and yields in the real option framework a less conservationist stopping rule in which uncertainty increases the stopping threshold (i.e. works against conservation).     

On the theory of east-west trade under uncertainty

Taking the final stage of the existing socialist economy as the labormanaged economy, this paper establishes a model of East-West trade between a capitalist economy and a labor-managed economy, both of which face asymmetric technological uncertainty. The model reflects the facts that the securities markets for firms' ownership shares exist only in the capitalist economy and that the firm's objective function in the capitalist economy is different from that in the labor-managed economy. It also considers the existence of international forward markets for commodities as international risk-sharing arrangements. Thus, the paper shows that all the basic theorems in traditional trade theory (Factor Price Equalization, Heckscher-Ohlin, Stolper-Samuelson and Rybczynski) carry over to the uncertain environments characterized by different types of economies.This is the final version of the paper, the first draft of which was presented at the 1987 annual meeting of the Japanese Association of International Economics. An earlier version has recently appeared in my book,Competition, Monopoly and International Trade Under Uncertainty (written in Japanese, Tokyo: Asian Economic New Press 1989). I wish to thank professors H. E. Leland, S. Fujino, H. Eguchi, M. Ohyama, K. Otaka, M. Ogawa, T. Ohsawa, K. Fukao, M. Nishijima and two anonymous referees for their helpful comments. Any remaining errors, however, are my responsibility.     

On the investment sensitivity of debt under uncertainty

We investigate the impact of debt on a panel of U.S. manufacturing firms' capital investment behavior as the underlying firm-specific and market-level uncertainty changes. Our estimates show that the influence of leverage on capital investment may be stimulating or mitigating depending on the effects of uncertainty.     

On the theory of monopolistic competition under demand uncertainty

Establishing a model of a monopolistically competitive industry in which risk-averse Cournot firms act under demand uncertainty and in which the output of individual firms and the number of firms in the industry are both endogenously determined by free entry and exit, this paper attempts to investigate the effects of demand uncertainty on the market equilibrium of a monopolistically competitive industry. It is assumed, for calculus simplification, that the firms are identical in the sense that they have the same monopolistic power and the same production technology. The paper presents some interesting and useful comparative statics results which are contrary to those proposed in the existing papers.This is a revised version of my paper which was firstly presented to the annual meeting of the Japanese Association of International Economics held in 1988 and then included partially in my book published in 1989. I am indebted to professors D. Bös, S. Fujino, M. Ohyama, M. Nishijima, to the members of the Public Economics Research Seminar in Bonn, and to two anonymous referees for their helpful discussions and useful suggestions. Any remaining errors, however, are my responsibility.     

The optimal minimum wage with regulatory uncertainty

For two different regulatory standards, we examine the optimal minimum wage in a competitive labor market when the government is uncertain about supply and demand. Solutions are related to underlying supply and demand conditions, and to the extent of uncertainty and of rationing efficiency. With expected earnings maximization, greater uncertainty widens the range of parameter values for which a minimum wage should be set. With expected worker surplus maximization and sufficiently efficient rationing, a minimum wage should always be set. However, in both cases regulatory uncertainty may require a low minimum wage that may not bind in equilibrium.