Optimal production of innovations under uncertainty

The paper reports results on a risk-neutral firm's research incentives. When unrelated to the firm's own stake in the program, the risks encourage or discourage risky research spending, depending on the properties of the research technology available. A non-decreasing time path of information builds the idea of an asymmetric probability distribution of the state of knowledge into the model. It follows that the required return on risky investments may actually fall short of the safe return. Since it is the upside risk that dominates, increased controllable risks will increase incentives for risky innovative activity. It is proved, but only in a more restricted framework (with differentiable processes), that the expectational effects involved will strengthen the positive relationship between controllable risks and the expected return.I am greatly indebted to three anonymous referees for helpful suggestions and to the Yrjö Jahnsson Foundation for financial support.     

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 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.     

Choice under complete uncertainty: axiomatic characterizations of some decision rules

Summary. We provide characterizations of four new rules for individual decision-making under complete uncertainty. They are what we call the min-max rule, the max-min rule, the lexicographic min-max rule and the lexicographic max-min rule. These rules provide orderings of the sets of possible outcomes associated with uncertain prospects. They provide significant alternatives to commonly-used rules that focus on worst outcomes or best outcomes only, and lexicographic versions of those rules. Received: August 20, 1998; revised version: November 3, 1999     

Resource allocation in a general equilibrium model of production under uncertainty

The purpose of this paper is to examine the implications of uncertainty for resource allocation, real income, and income distribution in terms of a simple two-sector general equilibrium model of a small country where uncertainty is introduced by assuming that production in one sector occurs in a stochastic environment. Assuming decreasing risk aversion, we show that an increase in uncertainty causes the movement of the resources away from the uncertain sector, a decline in expected real income, and a shift in the distribution of income against the factor employed intensively by the uncertain sector.     

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.     

Cobb-Douglas preferences under uncertainty

This paper axiomatizes Cobb-Douglas preferences under uncertainty. First, we extend the original Trockel (Econ Lett 30:7–10, 1989)’s axiomatic foundation to a general state space framework based on the Strong Homotheticity Axiom, obtaining also the incomplete case a la Bewley (Decis Econ Financ 25:79–110, 2002). We show that this key axiom for the Cobb-Douglas expected utility specification is refuted by Ellsberg’s uncertainty aversion behavioral pattern. Our main result provides a set of meaningful axioms characterizing Cobb-Douglas min-expected utility preferences, an important class of uncertainty averse preferences for studying the consequences of ambiguity in finance and other fields. Finally, we present briefly how to obtain more general representations like the variational case.     

Interim efficient allocations under uncertainty

This paper considers an exchange economy under uncertainty with asymmetric information. Uncertainty is represented by multiple priors and posteriors of agents who have either Bewley's incomplete preferences or Gilboa-Schmeidler's maximin expected utility preferences. The main results characterize interim efficient allocations under uncertainty; that is, they provide conditions on the sets of posteriors, thus implicitly on the way how agents update the sets of priors, for non-existence of a trade which makes all agents better off at any realization of private information. For agents with the incomplete preferences, the condition is necessary and sufficient, but for agents with the maximin expected utility preferences, the condition is sufficient only. A couple of necessary conditions for the latter case are provided.     

Optimal corporate strategy under uncertainty

Within a dynamic setting, optimal corporate strategy management for a multi-division corporation involves restructuring a portfolio of Strategic Business Units (SBUs) periodically so as to maximize the firm's market value. Real option theory has been applied to model and explain managerial flexibility for both project selection and operational decisions. In general, optimal corporate strategy has focused on strategic environments and characteristics of business units rather than on managerial flexibility. In this article, we develop a feasible discrete-time model for optimal corporate strategy that incorporates both endogenous and exogenous factors and is consistent with the value-based criterion for maximizing shareholders’ wealth.     

Peak-load pricing and reliability under uncertainty

This paper develops the welfare foundations of peak-load pricing under uncertainty, building on Brown and Johnson (1969), Crew and Kleindorfer (1976), and Chao (1983). The context is that of a welfare-maximizing public enterprise facing uncertain and nondeferrable demand, and uncertain supply. The paper first describes various elements of outage cost, including rationing costs, disruption costs, and surplus losses due to unsatisfied demand. Exact welfare-optimal results are then derived, in contrast to the earlier approximations by Turvey and Anderson (1977) and Chao (1983). The results are generalized to take account of diverse technologies and multiple planning periods, and their implications for utility pricing and investment in an integrated resource planning context are discussed.     

Intertemporal price cap regulation under uncertainty

This paper examines the intertemporal price cap regulation of a firm that has market power. Under uncertainty, the unconstrained firm 'waits longer' before investing or adding to capacity and as a corollary, enjoys higher prices over time than would be observed in an equivalent competitive industry. In the certainty case, the imposition of an inter-temporal price cap can be used to realise the competitive market solution; by contrast, under uncertainty, it cannot. Even if the price cap is optimally chosen, under uncertainty, the monopoly firm will generally (a) under-invest and (b) impose quantity rationing on its customers.     

Preferences for environmental quality under uncertainty

Although the expected effects of environmental policies and interventions are rarely known with certainty, stated preference surveys rarely elicit preferences over uncertain environmental outcomes. This article presents empirical results challenging the view that ignoring such uncertainty during preference elicitation is of no consequence so long as people only care about final environmental states. We show that measured preferences for final environmental states, water quality in this case, depend on whether people choose between final states or between lotteries over final states. In contrast to the typical finding for monetary lotteries, we find significant under-weighting of low probability events related to water quality.     

Optimal fishery harvesting rules under uncertainty

This paper derives the optimal fishery harvest policy in a real-option model with a stochastic logistic growth process, harvest-sensitive output price, and both fixed and variable harvesting costs. The policy specifies the harvest trigger and harvest size, while outputs from the model include the value of the fishery and the risk of extinction. The optimal policy is illustrated with data from the Pacific Halibut Fishery. For this particular case, the optimal policy recommends harvesting when the fish stock rises to about three-quarters the environmental carrying capacity, and the amount harvested should be approximately a quarter of the prevailing stock. This harvesting policy maximizes the value of the fishery, and importantly, the resulting risk of extinction is negligible. We also carry out some sensitivity analysis to see how the optimal policy (and the resulting fishery value and risk of extinction) change when the input parameters are varied, particularly the ecological parameters intrinsic growth rate and volatility of the stock, and also the economic parameters that have been ignored in previous papers (price sensitivity and fixed cost). If the optimal policy is followed, the risk of extinction will be negligible, except for very low growth rate and high volatility.     

Irreversible exit decisions under mean-reverting uncertainty

Although many economic variables of interest exhibit a tendency to revert to long-run levels, mean reverting processes are rarely used in investment and disinvestment models in the literature. Previous work by Sarkar (J Econ Dyn Control 28(2):377–396, 2003), that focuses on irreversible entry decisions, showed that mean reversion has three effects on investment: (a) the “variance effect” (mean reversion reduces the long-run uncertainty and thus brings closer the critical investment level), (b) the “realized price effect” (the lower variance resulting from mean reversion makes it less likely to reach extreme high or low price levels, thereby reducing the likelihood of reaching the investment trigger) and (c) the “risk discounting effect” (mean reversion lowers the required rate of return, which affects both the project value and the value of the real option to invest). Metcalf and Hassett (J Econ Dyn Control 19(8):1471–1488, 1995) and Sarkar (J Econ Dyn Control 28(2):377–396, 2003) showed that (a) and (b) work in opposite directions, essentially canceling each other out, however the effect of (c) depends on parameter values, making the overall effect (a–c) of mean reversion on entry decisions ambiguous and parameter-dependent. In this paper, we show that as far as irreversible exit decisions are concerned, the effect of mean reversion is negative: Mean reversion unambiguously lowers the rate of irreversible disinvestment/exit for reasonable parameter values, since the mean reversion in this case only affects the value of the real option to exit and not the value resulting from (real) option exercise.     

Sequential location under one-sided demand uncertainty

In entering a new market, firms face demand uncertainty. We depart from the usual Hotelling duopoly model with sequential entry. We allow firms to locate outside of the city and assume that market conditions are common knowledge. We then introduce one-sided demand uncertainty. We find that demand uncertainty can be seen as a differentiation force when faced by the first entrant and as an agglomeration force when faced by the second entrant. Finally, the second firm’s imperfect information implies higher welfare losses.     

Providing global public goods under uncertainty

We study how uncertainty and risk aversion affect international agreements to supply global public goods. We consider a benchmark model with homogeneous countries and linear payoffs. When countries directly contribute to a public good, uncertainty tends to lower signatories' efforts but may increase participation. Despite risk aversion, uncertainty may improve welfare. In contrast, when countries try to reduce a global public bad, uncertainty tends to increase signatories' efforts and decrease participation. In that case, an ex-ante reduction of uncertainty may have a large positive multiplier effect on welfare.