Larry S. Karp

Taxes and Quotas for a Stock Pollutant with Multiplicative Uncertainty

We compare taxes and quotas when firms and the regulator have asymmetric information about abatement costs. Damages are caused by a stock pollutant. Uncertainty enters multiplicatively, i.e. it affects the slope rather than the intercept of abatement costs. We calibrate the model using cost and damage estimates of greenhouse gases. As with additive uncertainty, taxes dominate quotas. The advantage of taxes is much greater with mulitiplicative, compared to additive uncertainty.

Dynamic Oligopoly in the Rice Export Market

A linear-quadratic dynamic oligopoly model is used to estimate the competitiveness of the rice export market. The model nests various market structures using either open-loop or feedback strategies. The estimated feedback model implies a less competitive market structure than the estimated open-loop model. The rice export market is oligopolistic, but it is closer to competitive than collusive. Copyright 1989 by MIT Press.

Non-constant Discounting in Continuous Time

This note derives the dynamic programming equation (DPE) to a differentiable Markov Perfect equilibrium in a problem with non-constant discounting and general functional forms. We begin with a discrete stage model and take the limit as the length of the stage goes to 0 to obtain the DPE corresponding to the continuous time problem. We characterize the multiplicity of equilibria under non-constant discounting and discuss the relation between a given equilibrium of that model and the unique equilibrium of a related problem with constant discounting. We calculate the bounds of the set of candidate steady states and we Pareto rank the equilibria.

A Dynamic Model of Oligopoly in the Coffee Export Market

A linear-quadratic, dynamic feedback oligopoly model that nests various market structures is used to estimate the degree of competitiveness and the adjustment paths of the two largest coffee exporters, Brazil and Colombia. Their estimated behavior is relatively competitive. This subgame perfect dynamic model is-compared to a standard static oligopoly model and the open-loop model (the dynamic generalization of the standard static model). Both classical and Bayesian tests of open-loop and feedback dynamic models are reported.

Social Welfare in a Common Property Oligopoly

Output in a Markov Nash-Cournot equilibrium to a noncooperative differential game in which m oligopolists extract a common property nonrenewable resource is bounded by the output of m-firm and (m - 1)-firm static oligopolies. The author discusses the welfare effects of the number of firms and of the divergence between private and social discount rates. He compares extraction under the Markov and open-loop equilibria and then offers an explanation for the possibility that the resource is exhausted instantaneously in a continuous time game. This explanation does not depend on the fact that the period of commitment is infinitesimal. Copyright 1992 by Economics Department of the University of Pennsylvania and the Osaka University Institute of Social and Economic Research Association.

Optimal tariffs on exhaustible resources

We characterize the Markov perfect equilibria of two games in which oligopsonistic importers of an exhaustible resource confront competitive suppliers who have rational expectations. The games differ only in the timing of moves, or the speed with which participants can adjust their plans. The optimal tariff when sellers move first (are less flexible) differs considerably from that in which buyers move first, and sellers retain more control over intertemporal arbitrage opportunities. If the initial stock is small, buyers suffer a disadvantage from being the first-mover; this is reversed if the stock is large.

Taxes Versus Quotas for a Stock Pollutant

We compare the effects of taxes and quotas for an environmental problem in which the regulator and polluter have asymmetric information about abatement costs, and the environmental damage depends on the stock of pollution. We thus extend, to a dynamic framework, previous studies in which environmental damages depend on the flow of pollution. As with the static analysis, an increase in the slope of the marginal abatement cost curve, or a decrease in the slope of the marginal damage curve, favors taxes. In addition, in the dynamic model, an increase in the discount rate or the stock decay rate favor the use of taxes. Taxes certainly dominate quotas if the length of a period during which decisions are constant is sufficiently small. An empirical illustration suggests that taxes dominate quotas for the control of greenhouse gasses.

Dynamic Games and International Trade: An Application to the World Corn Market

Dynamic games are a conceptually useful way of analyzing imperfect markets where both buyers and sellers have potential market power. Previous analysis of imperfect markets was static and limited to either exporters or importers. A dynamic game allows the inclusion of both importers and exporters in a multiperiod framework allowing the derivation of reaction functions. A Nash noncooperative difference game is applied to the international corn market to explore the plausibility of numerical results. The results are reasonable and show that the game approach based on a more comprehensive econometric model has a promising future in policy analysis.

A maximum entropy approach to estimation and inference in dynamic models or Counting fish in the sea using maximum entropy

In this paper we consider estimation problems based on dynamic discrete time models. The first problem involves noisy state observations, where the state equation and the observation equation are nonlinear. The objective is to estimate the unknown parameters of the state and observation equations and the unknown values of the state variable. Next we consider the problem of estimating the parameters of the objective function and of the state equation in a linear-quadratic control problem. In each case, given time series observations, we suggest a nonlinear inversion procedure that permits the unknown underlying parameters to be estimated. Examples are presented to suggest the operational nature of the results.

Depreciation erodes the coase conjecture

If a durable good monopolist produces at constant marginal costs and the good depreciates, there exists a family of Strong Markov Perfect Equilibrium (SMPE) with an infinitesimal period of commitment. One member of this family entails instantaneous production of the level of stock produced in a competitive equilibrium; this is consistent with the Coase Conjecture. Other SMPE in the family entail steady state production at a stock level lower than in the competitive equilibrium. In these equilibria, there may be a jump to the steady state, or the steady state may be approached asymptotically. Monopoly profits are postive in these equilibria, and the Coase Conjecture fails. We contrast this result to other papers which use non-Markov strategies to construct multiple equilibria.