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.     

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.     

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.     

Comparative statics for integrable Nash equilibria

This paper derives comparative statics results for stable Nash equilibria in integrable, concave orthogonal games. Application of these results to cost curve shifts in the asymmetric Cournot oligopoly immediately uncovers some apparently new comparative statics results.     

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.     

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     

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.     

On Pareto-improving redistributions of aggregate economic gains

This paper considers the existence and characterization of directions of tariff, commodity tax, and transfer payment reforms to ensure a Pareto improvement following a change in the economy's endowments, technology, preferences, or trading possibilities. Motzkin's theorem on the existence of solutions to dual sets of linear inequalities is extended to the case of non-homogeneous systems, and is applied to the comparative statics of the general equilibrium of a large trading economy. By allowing free disposal of commodities to the government, the problem of temporary inefficiency is eliminated.     

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.     

Monotone Matching in Perfect and Imperfect Worlds

We study frictionless matching in large economies with and without market imperfections, providing sufficient conditions for monotone matching that are weaker than those previously known. Necessary conditions, which depend on a key analytical object we call the surplus function , are also offered. Changes in the surplus yield valuable information about the comparative statics of matching patterns across environments. We apply our framework to some examples adapted from the literature, accounting for and extending several comparative–static and welfare results. We also explore the dependence of the matching pattern on the type distribution.     

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.     

Topics in nonparametric comparative statics and stability

This paper presents the analysis of the Jacobian matrix of a small, macroeconomic model to determine the robustness of the model's comparative statics. The values of the model's coefficients are assessed with respect to seven alternative estimation strategies such as ordinary least squares or two-stage least squares. For each alternative version, the invertibility and stability of the Jacobian matrix is studied. The model is robust to the degree that these characteristics are shared by any matrix with the same sign pattern or other similar nonparametric conditions on its entries. One way to address the relative success of the different estimation strategies is through the robustness of the comparative statics of the resulting model.     

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.     

Coca Substitution and Free Trade in Bolivia: The Pending Crisis

This paper uses the factors proportion model of production and trade with ten inputs to analyze the potential impact of the Free Trade Agreement of the Americas (FTAA) on the coca substitution program in Bolivia. With six crops including coca, the model produces comparative statics elasticities of changing prices on factor prices and output. Results show that the coca substitution program with free trade will result in large income redistribution in the coca‐producing region as a result of increased competition from larger and more efficient economies. Increased subsidies and institutional changes will be needed to sustain the coca substitution program in the long run.     

Stochastic dominance and thick-tailed wealth distributions

Right-skewed and thick-tailed wealth distributions have been documented as an empirical regularity across space and time. A key mechanism for explaining these distributional features is proportional random growth. We investigate the comparative statics of a well-defined class of random growth models when allowing for stochastically ordered shifts in the wealth return process. An order-contingent monotone comparative statics property is identified, according to which pure increases in risk (e.g. higher volatility of capital returns) foster top wealth concentration whereas first-order stochastically dominated shifts in the return process (induced by e.g. proportional capital income taxation) rather lower inequality at the upper end of the distribution. Our analysis points to the potentially ambiguous effects on top wealth inequality of introducing or modifying capital income tax treatments in the presence of stochastic returns.     

Efficiency,incentives, and individual labor supply in the labor-managed firm

Parallels are drawn between the approach to the theory of individual labor supply used by Sen (“Labor Allocation in a Co-operative Enterprise.” Rev. Econ. Stud.33: 361–371, Oct. 1966) and approaches of more recent contributions. The paper considers questions of comparative statics in a general model and attempts to distinguish between behavior in labor-managed firms and profit-maximizing firms. Diagrammatic analysis is used for a simple case where income effects are absent. Questions of efficiency and comparative statics are studied in the short run (membership fixed) and in the medium term (membership variable). Finally an incentive scheme to promote efficiency is described.     

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.