An equilibrium model of a second economy market in a centrally planned economy

We study a CPE in which an identical good is sold on the official market (OM) and a “second economy” market (SEM ). Planners set parameters. Managers divide inputs between markets to maximize expected utility of wealth. Consumers are expected utility maximizers who purchase the good on the OM or SEM. On the OM, excess demand exists at the non-Walrasian price; delivery date is stochastic. The SEM offers immediate availability. Our solution concept involves the rational expectations of managers, the consistency of consumers' decisions, and a market-clearing SEM. We solve for SEM price and supply and investigate various comparative statics.     

Status-Seeking, Catching-Up, and Comparative Statics in a Dynamic Heckscher–Ohlin Model

This paper examines a two‐country dynamic general equilibrium model with status‐seeking agents. We show that the introduction of status‐seeking behavior brings about new properties in equilibrium dynamics. While there exists a continuum of steady states in the standard dynamic models, the present framework demonstrates that, under some conditions, there uniquely exists an incompletely specialized steady state, which is locally saddle‐point stable. Therefore, catching‐up and overtaking phenomena seen in economic development can be explained, and comparative statics analysis also is made possible. Our comparative statics analysis illustrates, for example, that trade pattern is determined in the Heckscher–Ohlin manner; the patient country acts just like a capital abundant one to export the capital‐intensive good. Furthermore, as distinct from the existing literature, the present study shows that the existence of an incompletely specialized steady state can be ensured even if the two countries conduct different policies.     

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.     

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.     

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.     

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.     

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).     

Disequilibrium growth theory with insider–outsider effects

Ito has applied the non-Walrasian regime switching methodology to the Solovian neoclassical growth model and discussed the occurrence of regimes of full employment, overemployment and underemployment and the different dynamical systems (to be patched up) these regimes give rise to. We shall show in this paper that nothing of this sort really characterizes Solovian growth with non market-clearing real wages if over- or under-time work of the workforce within the firms (the insiders) is taken into account. This simple extension of the two-dimensional dynamical systems of Ito by one dimension implies that there is only one regime possible (the Goodwinian classical regime) with a 3D dynamics that are easily made globally stable and which moreover are often globally asymptotically stable, and this even more when substitution and endogenous growth are added to the model.     

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 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     

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 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.     

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.     

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.     

On the price discriminating labour cooperative

This paper considers labor cooperatives selling in a competitive international product market and a monopolistic domestic market simultaneously. It is shown that output of the cooperative is smaller than that of a profit maximizing firm. Both firms have the same domestic sales. Output will decrease if domestic demand rises but it may rise or fall when foreign demand increases. These contrast with the single market comparative statics of Ward.     

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.     

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.     

Wages and productivity growth in a competitive industry

We describe the evolution of productivity growth in a competitive industry with free entry and exit. The exogenous wage rate determines the firms’ engagement in labor productivity enhancing process innovation. There is a unique steady state of the industry dynamics, which is globally asymptotically stable. In the steady state, the number of active firms, their unit labor cost and supply depend on the growth rate but not on the level of the wage rate. In addition to providing comparative statics of the steady state, the paper characterizes the industry's adjustment path.     

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.     

A Renewable Resource-based Ramsey Model with Costly Resource Extraction

This paper derives the analytical solution of arenewable resource-based Ramsey economy withcostly resource extraction. The goal is toascertain whether costly resource extractioncan induce nonlinear dynamical properties in the system. We find that the solution for a model with constant technology can exhibit multiple steady states,and the comparative statics effects for consumption,utility, and the stock of nature capital areambiguous in a number of different cases. Moreover, thesolution for a model with exogenous technological progress exhibits unusual comparative dynamics andthe possibility of multiple balanced growthpaths. An increase in the rate of technologicalprogress induces a long-run growth rate in per capitaconsumption that depends on parameters of the productionfunction. Overall, technological progress inthe model can be less beneficial than in the standardeconomic growth model in which resourceextraction is costless.