Fanny Demers

Price uncertainty, the competitive firm and the dual theory of choice under risk

This paper undertakes an analysis of the competitive firm facing output price uncertainty based on Yaaris dual theory of choice under risk. The axiomatic foundation of Yaaris non-expected utility approach permits the formulation of a preference functional which is linear in profit but non-linear in distribution. Yaaris approach allows seperation of the firms attitude towards risk from its attitude towards wealth and is consistent with experimental evidence on decision-making under uncertainty. In Yaars dual theory the linearity in profit of the preference funcional stems from a constant marginal utility of wealth and is compatible with either risk aversion or risk inclination. This appealing feature of the dual theory allows us (1) to obtain a characterization of output and input decisions of firms which , unlike the von Neumann-Morgenstern theory of the firm, is in comformity with the main results of the theory of the firm under certainty; (2) to find intuitive comparative statistics effects of increases in risk and risk aversion; (3) to define the profit function for a firm with dual theoretic preferences and show how Hotellings lemma can be applied to find the firms output supply and input demand functions.

Cost Uncertainty, Taxation and Irreversible Investment

We examine the impact of learning about the unknown costs of investment on irreversible investment decisions, and show that the presence of learning increases the endogenous cost of adjustment and depresses investment. We demonstrate convergence of the state of information and capital stock to the ergodic set. Once learning is complete, in contrast to the exogenous cost-of-adjustment model, a mean-preserving increase in risk raises the endogenous marginal adjustment cost, reducing investment and the steady-state capital stock.

A privately revealing rational expectations equilibrium for the futures market

Abstract This paper develops a model of the futures market with two types of participants: farmers and speculators. Farmers undertake production decisions and face both output and spot price risk as opposed to speculators who face only spot price risk. Agents have constant absolute risk aversion von Neumann-Morgenstern utility functions and form rational expectations about the future output shock and spot price. We assume that traders specialize in information collection. In our model, the futures price is not a sufficient statistic for the market information. We show that the rational expectations equilibrium (REE) futures price is privately revealing to traders who purchase costly information. This REE is efficient in the sense that in equilibrium traders are in possession of all market information. We demonstrate that traders (a) have an incentive to collect costly information and (b) are better-off by specializing in collecting the information in which they have a comparative advantage (in terms of the quality of the information that they can obtain). Finally, we show that the futures market stabilizes the spot price.

Saving Under Uncertainty: A Bivariate Non-Expected Utility Approach

We adopt the multivariate non-expected utility approach proposed by Yaari [1986] to provide a characterization of the comparative statics effects of greater risk aversion and of mean-preserving increases in risk on saving and borrowing in the presence of income and interest rate risk.We show that in Yaaris model, it is possible to extend the applicability of the Diamond and Stiglitz [1974] and Kihlstrom and Mirman [1974] (DSKM) single-crossing property to establish a relationship between greater risk aversion and saving (or borrowing) on the basis of the individuals ordinal preferences as long as the two risks are independent. We also demonstrate that the comparative statics effects of a joint mean-preserving increase in random income and interest rate on saving and borrowing can be determined by an extension of the DSKM single-crossing property.

Prudence, Demand Uncertainty, Background Risk, and the Law of Supply: A Nonexpected Utility Approach to the Firm ⁄

We identify two motives, prudence and risk aversion, which give rise to precautionary behavior for a quantity- or price-setting monopolist facing demand uncertainty who has dual theoretic preferences. We also analyze a piecewise linear profit function due to a tax on profits that varies with the profit level. We show that the comparative statics of greater risk (mean-preserving spread and mean-utility preserving spread) can be totally or partially determined by the Diamond-Stiglitz and Kihlstrom-Mirman single-crossing property. For example, for a prudent risk-averse quantity-setting dual theoretic monopolist, a mean-preserving spread will have the same impact on output under uncertainty as a fall in the state of demand under certainty. Finally, we find that, in contrast to expected utility, a stochastically larger state of demand (first-order stochastic dominance) will raise output even if background risk is present.