Knowledge that Transforms

We develop a model in which a monopolist uses differences across consumers in their valuation of time to imperfectly price discriminate. Though it is customary to analyse price discrimination problems by the calculus of variations after postulating a continuum of types, we assume a finite number of types and exploit the geometry and duality of the contract set and the structure of the programming specification. We analyse in detail the qualitative properties of the model's solution and show by construction that our results exhaust the implications of the model for equilibrium contract pairs. We show that imperfect discrimination is not bounded in welfare terms between perfect discrimination and single-price monopoly and that the deadweight loss, consumer surplus and output comparisons between single-price monopoly and imperfect discrimination are ambiguous.

Past work on aggregation of production functions has focused on aggregation over firms where technology is embodied in fixed capital. This paper shows that much of the stringency of the necessary conditions for aggregation resides in the nature of aggregation over firms and not in the immobility of capital. Roughly, when capital is mobile, aggregation is permitted for any group of factors under the union of the conditions which otherwise applied to aggregation of fixed or aggregation of movable factors, respectively. No truly new conditions appear. The results are also interpreted in terms of output aggregation.

We prove the existence of approximate equilibria in exchange economies, giving bounds on the excess demand in terms of the number of traders and norms of the endowments, but independent of the preferences.

We develop a model in which each firm chooses a hiring standard as well as a wage schedule and an application fee, we then characterize the set of Nash equilibria, and establish necessary and sufficient conditions for the existence of equilibrium. If the distribution of productivities within each ability type is Gaussian, workers who pass the test will be paid more than the value of their marginal product, while workers who fail the test will receive a wage, net of the application fee, below the value of their marginal product.

The problem of integrating back from an incomplete set of demand functions to a utility function is considered. Conditions permitting local integrability are analogous to those which arise in local integrability theorems for complete systems. But the analysis of the global integrability of incomplete systems differs markedly from that of complete systems.

If the representative consumer of a country is risk averse then the choice of trade controls must take account of their effects on the fluctuations of domestic real income. If the world price of the importable is uncertain and risk aversion is high then the optimal policy for achieving a ceiling on expected imports involves a reduction in imports and a rise in the domestic price as the world price falls. Moreover, a quota is superior to a tariff in achieving the ceiling. Under domestic uncertainty, a tariff is superior to a quota but it could be optimal to reduce the domestic price as imports increase.

The point of this paper is that inventory adjustment attenuates downward pressure on price when realized demand is low because firms accumulate inventory hold-overs, speculating that demand will be stronger in the succeeding period. When realized demand is high the firm draws down its inventories until a "stock-out" occurs and price rises to clear the market.

The effect of conventional and final-offer compulsory arbitration on negotiated settlements is characterized, using Nash's variable-threats bargaining solution, with particular attention to the interaction between arbitral risk and bargainers' risk preferences. When there is no arbitral risk, both schemes are shown to have the same effect on negotiated settlements under very general conditions, even when bargaining is over several issues. Whether or not there is arbitral risk, negotiated settlements favour a bargainer more if his opponent is more risk-averse. On the other hand, increases in arbitral risk need not improve the position of the less risk-averse bargainer. As a by-product of the analysis, Kihlstrom, Roth and Schmeidler's risk-sensitivity results for the Nash and Raiffa-Kalai-Smorodinsky solutions are generalized from fixed-threats to variable-threats bargaining.

It is frequent practice to model an industry or economy as if it were a single agent solving a single optimization problem. A model of firm behavior which has had extensive use as an aggregative model is the adjustment cost model of investment. We assume there are a number of competitive firms in an industry that choose investment paths to maximize their present value; the technologies of the firms exhibit capital stock adjustment costs. For general concave technologies of the firms, there is no aggregate concave technology that can represent the technological possibilities available to the industry. We find conditions on the technologies of the firms that are necessary and sufficient for the existence of an aggregate technology that can consistently model the industry's behavior and discuss their empirical implications.

A consumer faces list prices for commodities, but can buy one at a discount. Discounts vary randomly between sellers. The number of quotations sought depends on list prices, search costs and wealth. This function is homogeneous of degree zero, and, provided some sufficient conditions are satisfied, is; increasing in wealth; decreasing in search cost; independent of the list price of the discounted commodity if indirect utility is multiplicatively separable; increasing in the list price if the commodity is a necessity; increasing in the list price of substitutes. Slutsky's equation is generalized to include search.