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.     

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 Graphical Approach to the Standard Principal-Agent Model

An obstacle to the teaching of principal-agent theory is the technical complexity and intractability of the general model. Even in academic studies strong assumptions are often imposed so as to derive an analytical solution. The author describes a graphical approach to the standard principal-agent model. Characterizing equilibrium in the contract space defined by the incentive parameter and insurance component of pay under a linear contract, this approach provides a simple and intuitive method for analyzing the principal-agent problem, which can be easily understood by students of economics with basic knowledge of algebra and differentiation. The approach has shown to be convenient and rich for comparative statics analyses.     

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.     

On modeling the agricultural sector in developing economies: An integrated approach of micro and macroeconomics

The paper introduces a theoretically consistent and empirically implementable method for the construction of general equilibrium models of the agricultural sector in a developing economy. The point of departure is the agricultural household, for which the microeconomic behavioral relations are formulated based on the assumption of utility and profit maximization. These relations are estimated from microeconomic data. In the second step the estimated microeconomic behavioral relations are aggregated across households into the macroeconomic behavioral relations, i.e., the supply and demand functions for the agricultural sector. Third, the linkage equations between the agricultural sector and the rest of the economy are specified on the basis of alternative assumptions on environmental and institutional characteristics and they are estimated from macroeconomic data. Finally, the macroeconomic behavioral relations and linkage equations are combined to provide a general equilibrium solution of the agricultural sector. The solution of the alternative equilibrium models can be used for comparative statics analysis of government policies and of changes in other exogenous variables. The illustrative application of the model is based on Indian data.     

基于改进D-S模型的产业间贸易、垂直投资一体化模型研究

本文通过在标准的Dixit-Stiglitz模型中引入基于Yang-Heijdra公式的全新解法,构建了全新的产业间贸易、垂直投资一体化模型.这一模型的理论贡献有二:一是在一般均衡理论框架内将垂直型国际直接投资成功地融合在"新贸易理论"框架内;二是采用基于Yang-Heijdra公式的全新解法对模型的两种均衡结构进行了一般均衡分析、边际和超边际比较静态分析,并得出了许多与传统解法不同的相关结论.     

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.     

Fixed-price equilibria in a two-country model of trade: Existence and comparative statics

The Barro-Grossman-Malinvaud model of fixed-price equilibrium is extended to a two-country model of trade with a fixed exchange rate. There are various possible types of fixed-price equilibria for the international economy, depending on the structure of rationing. The existence and uniqueness of one type of fixed-price equilibrium are proved. Indeed the extension of ‘the simple macroeconomic model’ to a two-country economy allows a new treatment of the problem of uniqueness of the type of fixed-price equilibrium. At last, some comparative statics results are derived. Among others the model allows to meet on new grounds (i.e., with some microfoundations) some well known results of the conventional Keynesian approach. But much more general results can be derived, applying to a class of market states not already dealt with in international-trade theory.     

Continuity of the first price auction Nash equilibrium correspondence

Summary. Despite the complexity of the first price auction in the general asymmetric case, analytical results have started to emerge in the literature. Authors have also searched to gain insights by computing numerical estimates of the equilibria for some probability distributions of the valuations. This paper proves that the Nash equilibrium of the first price auction depends continuously, for the weak topology, on the valuation distributions and thus brings robustness to the numerical results as well as some theoretical results. As an example of application, we disprove a conjecture of comparative statics. Received: February 1, 1999; revised version: July 27, 2001     

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.     

Flip-flopping from primaries to general elections

I consider a model in which candidates must win a primary election to compete in the general election. Candidates may choose different policies in the primary and the general election, but doing so results in accusations of flip-flopping. I show that candidates adopt extreme policies in the primaries but then try to move closer to the center for the general election even though primary voters are forward-looking and anticipate this policy moderation. The extent to which candidates move closer to the center is constrained by flip-flopping costs, and candidates choose divergent policies in the general election. I obtain comparative statics results on candidate policy choices in terms of voter preferences.     

An Inframarginal Analysis of the Ricardian Model

This paper shows that a 2 × 2 Ricardian model has a unique general equilibrium, and the comparative statics of the equilibrium involve discontinuous jumps. If partial division of labor occurs in equilibrium, the country producing both goods would impose a tariff, whereas the country producing a single good would prefer unilateral free trade. If complete division of labor occurs in equilibrium, both countries would negotiate to achieve free trade. In a model with three countries, the country which does not have a comparative advantage relative to the other two countries, and/or which has low transaction efficiency, may be excluded from trade.     

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.     

Conjectural variations, symmetric equilibria and economic policy

In this paper, we consider conjectural variations in a simple static general equilibrium model under oligopolistic competition. The modeling of conjectures captures the role played by beliefs in a micro-founded model. So, the economy may have three kinds of symmetric general equilibria. Furthermore, these equilibria can be Pareto-ranked by the conjectural variation parameter. Finally, we consider the implementation of a tax on the strategic behaviors in case of balanced-budget rule. The comparative statics illustrates the idea according to which the effectiveness of the multiplier mechanism to mitigate the market distortions depends on the symmetric equilibrium considered. Therefore, the effect of the tax on the prices and economic activity depends on the degree of market power which is conjectured by the agents.     

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.     

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.     

Endogenous ranking and equilibrium Lorenz curve across (ex-ante) identical countries: A generalization

This paper proposes a symmetry-breaking model of trade with a finite number of identical countries and a continuum of tradeable consumption goods, which differ in their dependence on nontradeable intermediate inputs, “producer services”. Productivity of each country is endogenous due to country-specific external economies of scale in its service sector. It is shown that, in any stable equilibrium, the countries sort themselves into specializing in different sets of tradeable goods and that a strict ranking of countries in per capita income, TFP, the service sector share, and the capital–labor ratio emerge endogenously. Furthermore, the distribution of country shares, the Lorenz curve, is unique and analytically solvable in the limit, as the number of countries grows unbounded. Using this limit as an approximation allows us to study what determines the shape of distribution, perform various comparative statics and to evaluate the welfare effects of trade. In doing so, this paper extends the analysis of Matsuyama (Econometrica, 81:5 (September 2013), 2009–2031) for more general and flexible forms of scale economies. It turns out that the technique introduced in Matsuyama (Econometrica, 81:5 (September 2013), 2009–2031) is useful for the equilibrium characterization in this general case as well. Although some results of comparative statics and on welfare inevitably need to be modified, they change in ways that illuminate the underlying mechanism of symmetry-breaking.     

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.     

Structure of distortion equilibria and welfare in a multiregional economy

Summary We consider a convex economy with multiregions, each region facing different specific tax-subsidies. The model reduces to a model of a closed economy with an aggregate production set when there is a single region. It can also represent a model of an international economy through a reinterpretation of variables. We show that there is a unique path of allocations from a distortion equilibrium to the optimum that can be followed by proportionate changes of price distortions. Welfare monotonically increases as one follows the path towards optimum. The information on the structure of equilibria reduces multidimensional comparative statics into a one dimensional problem. The global Newton method of Smale can be used to follow the path in the direction of increasing welfare, allowing us to do comparative statics computationally. Global considerations directly show that, under a sign condition of the Jacobian of a tax function, piecemeal proportional reductions of price distortions improve welfare. A variation of the condition unifies other such conditions in the literature.I would like to thank William Brock, Takashi Fukushima, Tatsuo Hatta, Michael Jerison, Taesung Kim and referees of this Journal who provided me with many constructive comments and references. Previous versions of this paper were presented at the Far Eastern Meeting of the Econometric Society, the Midwestern Mathematical Economics Conference, and the International Conference of Korean Economists. I wish to thank the participants of these conferences for many nice comments. I also wish to thank Bruce Dieffenbach, Thad Mirer and editors of this journal who helped to streamline exposition.