Robust Quantitative Comparative Statics for a Multimarket Paradox

We introduce a quantitative approach to comparative statics that allows to bound the maximum effect of an exogenous parameter change on a system's equilibrium. The motivation for this approach is a well known paradox in multimarket Cournot competition, where a positive price shock on a monopoly market may actually reduce the monopolist's profit. We use our approach to quantify for the first time the worst case profit reduction for multimarket oligopolies exposed to arbitrary positive price shocks. For markets with affine price functions and firms with convex cost technologies, we show that the relative profit loss of any firm is at most 25% no matter how many firms compete in the oligopoly. We further investigate the impact of positive price shocks on total profit of all firms as well as on social welfare. We find tight bounds also for these measures showing that total profit and social welfare decreases by at most 25% and 16.6%, respectively. Finally, we show that in our model, mixed, correlated and coarse correlated equilibria are essentially unique, thus, all our bounds apply to these game solutions as well.Comment: 23 pages, 1 figur

NEW ESTIMATES OF WELFARE AND CONSUMER LOSSES IN U.S. FOOD MANUFACTURING

In the past 15 years, industrial-organization economists have significantly expanded the range of algorithms for calculating welfare losses due to imperfect competition. We compare eleven empirical estimates of economic losses due to market power in 47 U.S. food manufacturing industries, almost all of them previously unpublished. Each of the studies incorporate different theoretical assumptions about demand conditions, supply conditions, or industry pricing behavior; or they utilize various data sources, time periods, and assumptions about the proper competitive benchmark. The estimates of average allocative losses due imperfect competition range from 0.2 percent to an impossibly high 289 percent of industry output; consumer losses range from 6.0 percent to 816 percent. However, there is a high degree of congruence in the rankings of economic losses due to market power. Hence, from the perspective of antitrust enforcement, the choice of industry targets has not been greatly altered by advances in estimation techniques.Agribusiness,

Unit Vs. Ad Valorem Taxes in Multi-Product Cournot Oligopoly

The welfare dominance of ad valorem taxes over unit taxes in a single-market Cournot oligopoly is well-known. This article extends the analysis to multi-market oligopoly. Provided all ad valorem taxes are positive, unit costs are constant, firms are active in all considered markets, and a representative consumer has convex preferences, it is shown that ad valorem taxes dominate in multi-product equilibrium. We discuss the role of unit cost covariances across multi-product firms in determining the extent of cost efficiencies arising under ad valorem taxation. The issue of merger under oligopoly is also considered. Conditions are identified under which a merger increases the sum of consumer and producer surpluses while also increasing the revenue yield from a set of unit taxes. If not all firms are active in all considered markets, then it is also shown that additional conditions are required to ensure the dominance of ad valorem taxes. In multi-input Cournot oligopsony, however, unit taxation welfare dominates. This is because ad valorem taxes on inputs reduce demand elasticities, amplifying market power distortions.ad valorem tax; imperfect competition; oligopoly merger; quantity-setting game; specific tax; tax efficiency; tax revenue

Network Cournot Competition

Cournot competition is a fundamental economic model that represents firms competing in a single market of a homogeneous good. Each firm tries to maximize its utility---a function of the production cost as well as market price of the product---by deciding on the amount of production. In today's dynamic and diverse economy, many firms often compete in more than one market simultaneously, i.e., each market might be shared among a subset of these firms. In this situation, a bipartite graph models the access restriction where firms are on one side, markets are on the other side, and edges demonstrate whether a firm has access to a market or not. We call this game \emph{Network Cournot Competition} (NCC). In this paper, we propose algorithms for finding pure Nash equilibria of NCC games in different situations. First, we carefully design a potential function for NCC, when the price functions for markets are linear functions of the production in that market. However, for nonlinear price functions, this approach is not feasible. We model the problem as a nonlinear complementarity problem in this case, and design a polynomial-time algorithm that finds an equilibrium of the game for strongly convex cost functions and strongly monotone revenue functions. We also explore the class of price functions that ensures strong monotonicity of the revenue function, and show it consists of a broad class of functions. Moreover, we discuss the uniqueness of equilibria in both of these cases which means our algorithms find the unique equilibria of the games. Last but not least, when the cost of production in one market is independent from the cost of production in other markets for all firms, the problem can be separated into several independent classical \emph{Cournot Oligopoly} problems. We give the first combinatorial algorithm for this widely studied problem

Weitzman revisited: Emission standards vs. taxes with uncertain control costs and market power of polluting firms

It is well known that uncertainty concerning firms’ costs as well as market power of the latter have to be taken into account in order to design and choose environmental policy instruments in an optimal way. As a matter of fact, in most actual regulation settings the policy maker has to face both of these complications simultaneously. However, hitherto environmental economic theory has restricted to either of them when submitting conventional policy instruments to a comparative analysis. The article at hand takes a first step in closing this gap. It investigates the welfare effects of emission standards and taxes against the background of uncertain emission control costs and various degrees of the polluting firms’ market power.Cournot oligopoly, external diseconomies of pollution, cost uncertainty, emission standard, emission tax

Weitzman revisited: Emission standards vs. taxes with uncertain control costs and market power of polluting firms

It is well known that uncertainty concerning firms’ costs as well as market power of the latter have to be taken into account in order to design and choose environmental policy instruments in an optimal way. As a matter of fact, in most actual regulation settings the policy maker has to face both of these complications simultaneously. However, hitherto environmental economic theory has restricted to either of them when submitting conventional policy instruments to a comparative analysis. The article at hand takes a first step in closing this gap. It investigates the welfare effects of emission standards and taxes against the background of uncertain emission control costs and various degrees of the polluting firms’ market power.Cournot oligopoly, external diseconomies of pollution, cost uncertainty, emission standard, emission tax

Efficiency gains and mergers

In the theoretical literature, strong arguments have been provided in support of the efficiency defense in antitrust merger policy. One of the most often cited results is due to Williamson (1968) that shows how relatively small reduction in cost could offset the deadweight loss of a large price increase. Furthermore, Salant et al. (1983) demonstrate that (not for monopoly) mergers are unprofitable absent efficiency gains. The general result, drawn in a Cournot framework by Farrell and Shapiro (1990), is that (not too large) mergers that are profitable are always welfare improving. In the present work we challenge the conclusions of this literature in two aspects. First, we show that Williamson's results underestimate the welfare loss due to a price increase and overestimate the effect of efficiency gains. Then, we prove that the conditions for welfare improving mergers defined by Farrell and Shapiro (1990) hold true only when consumers are adversely affected. This seems an argument to disregard their policy prescriptions when antitrust authorities are more "consumers-oriented". In this respect, we provide a necessary and sufficient condition for a consumer surplus improving merger: in a two firm merger, efficiency gains must be larger than the pre-merger average markup