COMPARATIVE STATICS OF A MONOPOLISTIC FIRM FACING RATE‐OF‐RETURN AND COMMAND‐AND‐CONTROL POLLUTION CONSTRAINTS

The intrinsic comparative statics properties of a general rate‐of‐return regulated, profit‐maximizing model of a monopolist facing a command‐and‐control pollution constraint are derived. Recent advances in the theory of comparative statics are used to derive the basic comparative statics of the model, which are contained in an observable negative semi‐definite matrix and possess the form of Slutsky‐like expressions. We consider several command‐and‐control pollution constraints that are commonly implemented in practice, and conclude that the intrinsic comparative statics properties of the model are qualitatively invariant to the type of command‐and‐control pollution constraint imposed. We compare our results with those extant, and find that several basic results from the standard A–J model no longer hold in our model.     

Existence of a Universal Comparative Statics Matrix for Differentiable Optimization Problems

A universal existence theorem is established that yields exhaustive and constraint-free comparative statics information for a general, differentiable optimization problem in the preferred form of a semidefinite matrix. It subsumes all comparative statics formulations of differentiable optimization problems. Its relationship to comparative statics methods extant is establishedWe are grateful to an anonymous referee for a particularly helpful comment on the contents of this paper.     

Mean-Variance Preferences and Investor Behaviour

We study the comparative statics implications of mean-variance preferences for optimal portfolios. Specifically, we show that all risk-averse mean-variance investors raise their investment in a risky asset in response to a change in that asset's return distribution if and only if the change lowers both the mean and standard deviation of the return by the same percentage. Besides being of interest in its own right, our results allow us to compare some comparative statics implications and the expected utility and mean-variance models systematically.     

An experimental study of bidding in contests of incomplete information

In many contest situations, such as R&D competition and rent seeking, participants’ costs are private information. We report the results of an experimental study of bidding in contests under different information and symmetry conditions about players’ costs of effort. The theory predicts qualitatively different comparative statics between bids under complete and incomplete information in contests of two and more than two players. We use a 2×3 experimental design, (n=2, n=4)×(symmetric complete information, asymmetric complete information, incomplete information), to test the theoretical predictions. We find the comparative statics of bids across the information and symmetry conditions, and the qualitative differences in comparative statics across group sizes, in partial agreement with the theory.     

Comparative Statics of Money-goods Specifications of the Utility Function

The introduction of real-cash balances into the neoclassical model of the consumer wrecks havoc, in general, on the empirically observable refutable comparative statics properties of the model. We provide the most general solution of this problem to date by deriving a symmetric and negative semidefinite generalized Slutsky matrix that is empirically observable and which contains all other such comparative statics results as a special case. In addition, we clarify and correct two aspects of Samuelson and Sato's (1984) treatment of this problem. Received March 9, 2001; revised version received September 3, 2001     

Mixed-Strategy Nash Equilibrium Based upon Expected Utility and Quadratic Utility

The notion of a mixed-strategy Nash equilibrium suffers from three inherent difficulties. First, given the equilibrium strategies of other players, there are many best replies. Second, the equilibrium is unstable. Third, comparative statics results are counterintuitive. We demonstrate that these difficulties all have their origin in von Neumann and Morgenstern′s expected utility. In contrast, players with "quadratic utility" have unique best replies and the Nash equilibrium appears to yield intuitive comparative statics results. Journal of Economic Literature Classification Number: C72.     

Comparative statics in the large based on a fixed point algorithm

The purpose of this paper is to present a theorem on comparative statics in the large by making use of theorems on a fixed point algorithm, and also to show its economic applications focused on Hicksian laws. We provide a unified approach to comparative statics in the large, and obtain laws of demand globally valid for generalized gross-substitute systems.     

Nash equilibrium vs. maximin : A comparative game statics analysis

This paper derives comparative game statics results for both maximin and Nash strategies, thereby allowing a more systematic comparison between these two approaches.     

Comparative Statics Predictions for Changes in Uncertainty in the Portfolio and Savings Problems

The paper investigates comparative statics effects of changes in uncertainty for a general family of problems that encompasses both the portfolio and saving decisions. Conditions are derived on preferences that are necessary and sufficient for unambiguous comparative statics predictions. The paper consolidates and completes the statement of restrictions on attitudes toward risk–bearing needed for determinate predictions in the portfolio and saving problems.     

Higher-order generalizations of Arrow-Pratt and Ross risk aversion: A comparative statics approach

We analyze comparative risk aversion in a new way, through a comparative statics problem in which, for a cost, agents can shift from an initial probability distribution toward a preferred distribution. The Ross characterization arises when the original distribution is riskier than the preferred distribution and the cost is monetary, and the Arrow-Pratt characterization arises when the original distribution differs from the preferred distribution by a simple mean-preserving spread and the cost is a utility cost. Higher-order increases in risk lead to higher-order generalizations, and the comparative statics method yields a unified approach to the problem of comparative risk attitudes.     

A Dynamic Heckscher–Ohlin Model: The Case of Costly Factor Reallocation

The role of the static Heckscher–Ohlin model in providing general equilibrium comparative statics is emphasized. It is shown that (i) market-clearing dynamics can be constructed if and only if the costly reallocation of factors is accommodated, and (ii) the introduction of market-clearing and resource-using dynamics fails to sharpen (and may even blunt) the comparative statics. Thus, a new (non-)Correspondence Principle is derived.     

A unified approach to comparative statics puzzles in experiments

The paper shows that several game-theoretic solution concepts provide similar comparative statics predictions over a wide class of games. I start from the observation that, in many experiments, behavior is affected by parameter shifts that leave the Nash equilibrium unchanged. I explain the direction of change with a heuristic structural approach, using properties such as strategic complementarities and increasing differences. I show that the approach is consistent with general comparative statics results for (i) the Nash equilibrium of a game with perturbed payoff functions, (ii) the quantal response equilibrium, (iii) level-k reasoning. I also relate the structural approach to equilibrium selection concepts.     

The Sonnenschein–Debreu–Mantel Proposition and the Theory of International Trade

Much of the comparative statics of trade theory rests on the unrealistic assumption that in each trading country all households are alike or behave collectively as though they are alike. In the present paper the authors show that two well–known comparative statical propositions are highly sensitive to the relaxation of the assumption, and suggest that many other results are equally fragile.     

Comparative statics at irregular extrema

This note shows that standard comparative statics techniques, properly reinterpreted, can be used to obtain correct qualitative results for irregular extrema, even though the conditions for application of the Implicit Function Theorem are not satisfied for them.     

On Price Caps Under Uncertainty

This paper shows how standard arguments supporting the imposition of price caps break down in the presence of demand uncertainty. In particular, though in the deterministic case the introduction or lowering of a price cap (above marginal cost) results in increased production, increased total welfare, decreased prices, and increased consumer welfare, we show that all of the above comparative statics predictions fail for generic uncertain demand functions. For example, for price caps sufficiently close to marginal cost, a decrease in the price cap always leads to a decrease in production and total welfare under certain mild conditions. Under stronger regularity assumptions, all of the monotone comparative statics predictions from the deterministic case also do not hold for a generic uncertain demand if we restrict attention to price caps in an arbitrary fixed interval (as long as the price caps are binding for some values in that interval).     

Welfare and comparative statics implications of fair social security : A steady-state analysis

This paper examines the steady-state welfare and comparative statics implications of fair social security in an overlapping generations model with uncertain lifetime. The model is designed to capture the effects of lifetime uncertainty extending over the individual's entire lifespan, the effects of intentional and unintentional bequests, and the effects of the earning profile. He shows that the welfare effects depend on the size of the benefits and the structure of the social security tax. In particular, even fair social security may have negative welfare implications if the underlying tax structure is ill-designed. Some comparative statics implications are analyzed.     

Counter-intuitive results in game theory

General comparative game statics results are derived in order to provide testable hypotheses in game-like situations. These results run counter to ordinary economic intuition. It becomes necessary to initially define whether a situation represents perfect competition or monopoly on the one hand or a game-like situation on the other hand because these different assumptions lead to greatly differing results. Several empirical applications of the theory are suggested.     

CHANGES IN DEMAND FUNCTION IN COURNOT OLIGOPOLY

Abstract.  The effects of change in the market (inverse) demand function are systematically analysed for Cournot oligopoly without product differentiation. The general comparative-static results are stated using the original data on firms' cost functions and inverse demand function. Three special models are examined in light of our results. The stability condition is shown to be insufficient for determinate comparative statics.     

Generalized monotonicity analysis

Complex economic models often lack the structure for the application of standard techniques in monotone comparative statics. Generalized monotonicity analysis (GMA) extends the available methods in several directions. First, it provides a way of finding parameter moves that yield monotonicity of model solutions. Second, it allows studying the monotonicity of functions or subsets of variables. Third, GMA naturally provides bounds on the sensitivity of variables to parameter changes. Fourth, GMA may be used to derive conditions under which monotonicity obtains with respect to functions of parameters, corresponding to imposed parameter moves. Fifth, GMA contributes insights into the theory of comparative statics, for example, with respect to dealing with constraints or exploiting additional information about the model structure. Several applications of GMA are presented, including constrained optimization, nonsupermodular games, aggregation, robust inference, and monotone comparative dynamics.