Nonconvex Production Technology and Price Discrimination

A modern firm often employs multiple production technologies based on distinct engineering principles, causing non-convexities in the firm's unit cost as a function of product quality. Extending the model of Mussa and Rosen (1978), this paper investigates how a monopolist's product line design may crucially depend on the non-convexities in the unit cost function. We show that the firm does not offer those qualities where the unit cost exceeds its convex envelope. Consequently, there are "gaps" in its optimal quality choice. When the firm is only permitted to offer a limited number of quality levels (due to possible fixed costs associated with offering each quality), the optimal location of quality levels still lies within those regions of the quality domain where the unit cost function coincides with its convex envelope. We further show that the firm's profit is a supermodular function of its quality levels, and characterize a necessary condition for the optimal quality locationPrice Discrimination, Product Line Design, Nonconvex Production

Bayesian Analysis and Model Revision for kâth Order Markov Chains with Unknown k.

mass 1 concentrated on the true process, provided that the prior probability measure has full support and the true process is irreducible. Second, I extend this result to the case in which k is unbounded (but finite), which requires that the Bayesian decisionmaker (DM) construct a prior on an infinite-dimensional parameter space. Finally, in an alternative approach to this case, I suppose that the DM considers a succession of models corresponding to larger and larger values of k. Each time the DM revises his model he extends his prior probability measure to the new - and larger - parameter space in a way that is "consistent" with the previous prior, and recomputes his posterior probability measures. I show that, roughly speaking, if the DM does not revise his model âtoo frequently,â then he will be increasingly confident that the current posterior is increasingly concentrated on the true process. I motivate the procedure of model revision by considerations of bounded rationality.Information Systems Working Papers Serie

Profit Maximization with Bankruptcy and Variable Scale

In a diffusion model of an enterprise with variable scale, sufficient conditions are given for the maximization of expected profit (expected total discounted withdrawals) to lead to eventual bankruptcy with probability one. The optimal withdrawal policy is an "overflow policy," in which the withdrawal rate is equal to zero if the asset level is below a "barrier," and equal to the maximum rate if the asset level is greater than or equal to the barrier. The optimal policy for the control of the drift (yield) and volatility (risk) of the earnings process is derived as the solution of a differential equation, and a formula is given for the corresponding value function. The optimality of the constructed policy is demonstrated using the standard "Bellman Conditions."Information Systems Working Papers Serie

Bounded Rationality, Indeterminacy, and the Theory of the Firm

Information Systems Working Papers Serie

Viscous Demand

In many markets, demand adjusts slowly to changes in prices, i.e., demand is "viscous." For such a market, the time path of a firm's prices acquires added significance, compared with the case of instantaneous demand response. In this paper I explore some problems in strategic dynamic pricing of a service, in the presence of viscous demand, for simple models of a monopoly and a duopoly.Information Systems Working Papers Serie

Notes on Implementing Sustainable Development

"Sustainable Development" refers to a set of issues relating to two general questions: (1) Are the presently prevailing technologies and lifestyles of economic development so destructive of the earth's natural resources and environment that the current pace of development cannot be maintained? (2) If so, what combinations of technology, life-style, and rate of growth are sustainable in the 'long-run,' and what mechanisms of cooperation and incentives can be devised to implement them? After providing some introductory background material for newcomers to the subject, and concluding that the answer to the first question is "yes." I sketch some challenges to economic theory implied by the second question. In particular, I argue that, for transnational issues like global warming, the 'standard' approaches of mechanism design theory are inadequate in the absence of a world government or equivalent institution for enforcing cooperative agreements. On the other hand, the typical large multiplicity of noncooperative equilibria of such global dynamic "games" creates a role for analysts to discover (invent?) equilibria that are superior to the status-quo equilibrium, if indeed the current situation can reasonably be interpreted as a (dynamic) equilibrium. I explore this idea in the context of an oversimplified model of the "Global Warming Game."Information Systems Working Papers Serie