[Consider a Bayesian decision problem in which F is the prior distribution over some parameter space T. If —ψ(d, t) is the product of the loss function and the likelihood function, then the Bayesian solution, d_F, maximizes extlesstex-math extgreater$E_\F\(d)= extbackslashint _\T\ extbackslashpsi (d,t)dF(t)$ extless/tex-math extgreater. Suppose \F^n\ is a sequence of distribution functions that approach F^0 in the sup-metric topology. Our main theorem gives conditions under which extlesstex-math extgreater$d_\F extasciicircum \\ extbackslashrightarrow d_\F extasciicircum\0$ extless/tex-math extgreater and extlesstex-math extgreater$E_\F extasciicircum\0\\(d_\F extasciicircum \\) extbackslashrightarrow E_\F extasciicircum\0\\(d_\F extasciicircum\0\\)$ extless/tex-math extgreater.]

Richard E. Kihlstrom, Leonard J. Mirman; Constant, Increasing and Decreasing Risk Aversion with Many Commodities, The Review of Economic Studies, Volume 48, Iss

The model investigated here is an adaptation of the free-entry model introduced in Kihlstrom-Laffont [1979]. In that model the only labor market is one in which employers pay workers an ex ante guaranteed wage. In the model of this paper, there is also a spot market for labor. In the earlier sections of the paper, the existence of the equilibrium is established, and its efficiency is investigated. In this analysis it is assumed that all individuals are identical. In the later sections we drop this assumption and investigate conditions under which employers are more risk-averse than workers.

A great deal of advertising appears to convey no direct credible information about product qualities. Nevertheless, such advertising may indirectly signal quality if there exist market mechanisms that produce a positive relationship between product quality and advertising expenditures. Two models of this phenomenon are presented. In each, advertising signals quality in the short run. The models differ in their treatment of the effect of advertising on long-run sales. In the first, all high-quality firms ultimately establish reputations for high quality whether they advertise or not. This is shown to imply that advertising can signal quality if and only if high-quality production requires investments in specialized assets that increase fixed costs but not marginal costs. In the second model, where nonadvertising firms never acquire a reputation for high quality, advertising might signal quality even if marginal production costs are somewhat lower for low quality. These conclusions closely parallel arguments previously made by Phillip Nelson.

We construct a theory of competitive equilibrium under uncertainty using an entrepreneurial model with historical roots in the work of Knight in the 1920s. Individuals possess labor which they can supply as workers to a competitive labor market or use as entrepreneurs in running a firm. All entrepreneurs have access to the same risky technology and receive all profits from their firms. In the equilibrium, more risk averse individuals become workers while the less risk averse become entrepreneurs. Less risk averse entrepreneurs run larger firms and economy-wide increases in risk aversion reduce the equilibrium wage. A dynamic process of firm entry and exit is stable. The equilibrium is efficient only if all entrepreneurs are risk neutral. Inefficiencies in the number of firms and in the allocation of labor to firms are traced to inefficiencies in the risk allocation caused by institutional constraints on risk trading. In a second best sense which accounts for these constraints, the equilibrium is efficient.

Sanford J. Grossman, Richard E. Kihlstrom, Leonard J. Mirman; A Bayesian Approach to the Production of Information and Learning By Doing, The Review of Economic

[This paper considers the possibility of extending the Arrow-Pratt results on risk aversion to cases in which initial wealth is random. Specifically, we consider a situation in which an individual's wealth is the sum of two independent random variables extbackslashtilde\x\ and ỹ. We define the risk premium π( extbackslashtilde\x\, ỹ) which represents the reduction in mean wealth an individual is willing to accept to eliminate the random variable x̃ while retaining the random variable ỹ. It is shown that if u_1 is uniformly more (Arrow-Pratt) risk averse than u_2 and if either u_1 or u_2 exhibit nonincreasing (Arrow-Pratt) risk aversion, then extlesstex-math extgreater$ extbackslashpi _\2\( extbackslashtilde\x\, extbackslashtilde\y\)$ extless/tex-math extgreater is always smaller than extlesstex-math extgreater$ extbackslashpi _\1\( extbackslashtilde\x\, extbackslashtilde\y\)$ extless/tex-math extgreater. An example is given in which both u_1 and u_2 exhibit increasing risk aversion and in which this result fails.]