On strategic complementarity conditions in Bertrand oligopoly

Summary. For Bertrand duopoly with linear costs, we establish via a single (counter-)example that: (i) A new monotone transformation of the firms' profit functions may lead to the supermodularity of transformed profits when the standard log and identity transformations both fail to do so, and (ii) Topkis's notion of critical sufficient condition for monotonicity of a Bertrand firm's best-reply correspondence cannot be extended to rely only on positive unit costs. Received: January 16, 2001; revised version: March 20, 2002 RID="*" ID="*" This work was completed while the first author was visiting the Institute for Industrial Economics at the University of Copenhagen during Spring 2000. Their financial support and stimulating research environment are gratefully acknowledged. The views expressed here are those of the authors and should not be attributed to the European Commission. Correspondence to: R. Amir     

Existence of a competitive equilibrium in a one sector growth model with heterogeneous agents and irreversible investment

Summary. We prove existence of a competitive equilibrium in a version of a Ramsey (one sector) model in which agents are heterogeneous and gross investment is constrained to be non negative. We do so by converting the infinite-dimensional fixed point problem stated in terms of prices and commodities into a finite-dimensional Negishi problem involving individual weights in a social value function. This method allows us to obtain detailed results concerning the properties of competitive equilibria. Because of the simplicity of the techniques utilized our approach is amenable to be adapted by practitioners in analogous problems often studied in macroeconomics. Received: September 13, 2001; revised version: December 9, 2002 RID="*" ID="*" We are grateful to Tapan Mitra for pointing out errors as well as making very valuable suggestions. Thanks are due to Raouf Boucekkine and Jorge Duran for additional helpful discussions. We also thank an anonymous referee for his/her helpful comments. The second author acknowledges the financial support of the Belgian Ministry of Scientific Research (Grant ARC 99/04-235 “Growth and incentive design”) and of the Belgian Federal Goverment (Grant PAI P5/10, “Equilibrium theory and optimization for public policy and industry regulation”). Correspondence to: C. Le Van     

Private R&;D and Spillovers in European Agriculture

The objective of this paper is to present econometric evidence of the effects of economic incentives, public policies, and institutions on national aggregate private agricultural R&D investments. The main hypothesis we will test in this paper is whether agricultural R&D spillovers represent a disincentive for national private R&D. More specifically, we will test if the spillovers function, which is a determinant of private R&D, follows a quadratic form and if private R&D is determined by the role of incentives and institutions.A previous draft of this paper was presented at the 57th International Atlantic Economic Conference, Lisbon, Portugal, 10–14 March 2004. Comments from participants have been very useful to improve the paper.     

Policy Discrimination with and without Interpersonal Comparisons of Utility

Can the Pareto criterion guide policymakers who do not know the true model of the economy? If policymakers specify ex ante preferences for agents, then Pareto improvements from a distorted status quo are usually possible, and with more commodities than states, one can implement almost every Pareto optimum. Unlike the standard second welfare theorem, planners cannot dictate allocations: agents must trade. Unfortunately ex ante preferences impose interpersonal comparisons. If policymakers merely aim to maximize some social welfare function then optimal policies form an open set; hence small changes in the environment do not necessitate any policy response. Planners with symmetric information about agents can sometimes intervene without making interpersonal comparisons.     

Price discrimination and efficient matching

This paper considers the problem of a monopoly matchmaker that uses a schedule of entrance fees to sort different types of agents on the two sides of a matching market into exclusive meeting places, where agents randomly form pairwise matches. We make the standard assumption that the match value function exhibits complementarities, so that matching types at equal percentiles maximizes total match value and is efficient. We provide necessary conditions and sufficient conditions for the revenue-maximizing sorting to be efficient. These conditions require the match value function, modified to incorporate the incentive cost of eliciting private type information, to exhibit complementarities in types.JEL Clalssification Numbers C7, D4We thank Jonathan Levin, Tracy Lewis, and the seminar audience at University of California at Los Angeles, University of British Columbia, Duke University, and 2003 Econometric Society North American Summer Meeting for comments and suggestions. We are also grateful for helpful suggestions from the referees and the Editor     

Wealth and sustainable development: the role of David Pearce

Green net national product was thought to be one way of measuring sustainable income. However, David Pearce understood that a better measure of sustainable development was to look at what a generation is leaving in form of capital assets to later generations. In this article, his arguments and insights are highlighted against recent theoretical advances.