Welfare variations and the comparative statics of demand

By employing order-theoretic comparative statics, we provide necessary and sufficient conditions on the direct utility function (alternatively, on the indirect utility function) to guarantee that the compensating and equivalent variations are monotonically increasing in income. We also show that these conditions are sufficient to guarantee normal demand. Our results do not depend on the smoothness or strict quasiconcavity of the utility function, and can be extended to a setting with non-linear prices.     

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.     

A life cycle analysis of social security

Summary We develop an applied general equilibrium model to examine the optimal social security replacement rate and the welfare benefits associated with it. Our setup consists of overlapping generations of 65-period lived individuals facing mortality risk and individual income risk. Private credit markets, including markets for private annuities, are closed by assumption. Unlike previous analyses, we find that an unfunded social security system may well enhance economic welfare. In our benchmark economy, the optimal social security replacement rate is 30%, and an empirically more plausible replacement rate of 60% raises welfare compared with an economy with no social security system.We would like to thank Andy Atkeson, V. V. Chari, Steve Davis, Paul Evans, Lars Hansen, Tim Kehoe, Nobu Kiyotaki, Ed Prescott, José-Victor Ríos-Rull, Richard Rogerson, Tom Sargent, Nancy Stokey, Dick Sweeney, Robert Townsend, and the participants of the NBER Economic Fluctuations Small Group Workshop on Micro and Macro Perspectives on the Aggregate Labor Market in Palo Alto, the NBER General Equilibrium Theory Conference in Minneapolis, the Money and Banking Workshop at the University of Chicago, and the NBER Summer Institute. An earlier version of this paper was titled A Dynamic Stochastic General Equilibrium Analysis of Social Security. This material is based upon work supported by the National Science Foundation under Grant No. SES-9210291. We also thank the Minnesota and San Diego Supercomputer Centers for their support.     

Market equilibrium in the presence of green consumers and responsible firms: A comparative statics analysis

This paper analyzes how the interaction between green consumers and responsible firms affects the market equilibrium. The main result is that a higher degree of responsibility of consumers and/or firms may both increase and decrease the total abatement and the social welfare. In general an increment in the degree of CSR of a firm entails an increase of its total clean-up and a reduction of the aggregate abatement of its rival. When the rival firm has a high degree of CSR this second effect is stronger than the first and total abatement falls down. At the same time, when the degree of consciousness of consumers and/or firms is very high, responsible firms overprovide environmental quality: in such case a further increment in the level of social responsibility of a market actor may trigger an increase of firms’ total clean-up but a reduction in social welfare.     

A life-cycle analysis of social security with housing

This paper incorporates two features of housing in a life-cycle analysis of social security: housing as a durable good and housing market frictions. We find that both housing quantities and homeownership rates respond strongly to eliminating social security. Accordingly, the aggregate impacts of this policy reform are significantly larger in an economy with explicit housing choices than in a standard life-cycle economy. Our analysis shows that the key mechanism behind these results is the substitution effects of a change in interest rates and, thus, the price of housing services on the choice of nondurable consumption versus housing services.     

A note on comparative statics and dynamics of stationary states

Certain results are communicated regarding effects of parameter changes, when the stationary state is stable, on the stationary state and an optimal paths in its neighbourhood in discrete time multi-sectoral optimal growth models where period utilities are discounted.     

Weak and strong monotone comparative statics

Summary This paper develops necessary and sufficient conditions for the set of solutions to an optimization problem to be nondecreasing in a weak sense still strong enough to guarantee the existence of an increasing selection, and thus strong enough to guarantee monotonicity when the solution is unique, as well as necessary and sufficient conditions for the set of optimizers to be nondecreasing in a strong sense which is strong enough to rule out the possibility of a decreasing selection. These necessary and sufficient conditions are variations of quasisupermodularity and the single crossing property introduced in Milgrom-Shannon [13]. Moreover, to determine when an objective function satisfies these conditions, this paper develops several characterizations of quasisupermodularity and the single crossing property and their variants, both in terms of differential conditions and in terms of restrictions on the structure of the level sets of these functions. Several examples are given to choice theory under loss aversion and to an auction problem.I am grateful to Don Brown and Paul Milgrom for numerous helpful conversations concerning earlier versions of this paper. This paper is a revised and expanded version of the paper An Ordinal Theory of Games with Strategic Complementarities (Shannon [15]). I am pleased to acknowledge the financial support of the National Science Foundation, and an Alfred P. Sloan Foundation Doctoral Dissertation Fellowship.     

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.     

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.     

Location and the comparative statics of the theory of production

This paper applies modern methods of doing comparative static analysis to the theory of the firm when location as well as input levels are the firm's choice variables. Many results are obtained including all previously known results. Moreover, it is shown that traditional results in the theory of the firm such as downward sloping derived demand curves, generalize to the location problem. New results, such as an increase in a transportation rate decreasing transportation in terms of ton-miles of an input, are also obtained. Many new symmetry conditions are also found.     

A positive theory of social security

In this paper I make two points. First, I argue that social security programs around the world link public pensions to retirement: people do not lose their pensions if they make a million dollars a year in the stock market, but they do confront marginal tax rates of up to 100 percent if they choose to work. Second, after arguing that most existing theories cannot explain this fact, I construct a positive theory that is consistent with it. The main idea is that pensions are a means to induce retirement—that is, to buy the elderly out of the labor force because aggregate output is higher if the elderly do not work. This is modeled through positive externalities in the average stock of human capital: because skills depreciate with age, the elderly have lower-than-average skill and, as a result, have a negative effect on the productivity of the young. When the difference between the skill level of the young and that of the old is large enough, aggregate output in an economy where the elderly do not work is higher. Retirement is desirable in this case, and social security transfers are the means by which such retirement is induced. The theory developed in this paper is also shown to be consistent with a number of other regularities documented in Section 1.     

Core structure and comparative statics in a hybrid matching market

Flexible firms compete by means of wages in the Assignment market while rigid firms have no flexibility over terms of appointment in the Marriage market. Workers trade with both kinds of firms in the hybrid market.Examples show that standard results that characterize the core of the Marriage market (respectively, Assignment market) are not robust to the entrance of flexible (respectively, rigid) firms to this market. A new algebraic structure provides a different characterization for the core of the hybrid model and reflects a sort of robustness to the exit of rigid (respectively, flexible) firms from this market. Meaningful comparative static results are derived.     

浅析新农村的社会保障问题

社会保障是构建社会主义和谐社会的一项基础性制度建设,对调节收入分配、促进社会公平具有重要作用。本文从理论和实践的结合上,剖析了当前我国新农村建设中社会保障方面存在的根本性问题,同时对建设和完善符合我国国情的农村社会保障体系的发展思路进行了探讨。     

Uniqueness and comparative statics of Nash equilibrium in a tariff retaliation model

This paper considers uniqueness and comparative statics of Nash equilibrium of a tariff retaliation model. The approach to the problem is geometrical and reminiscent of the analysis for the free trade competitive equilibrium. If the countries have constant elasticity of substitution utility functions, some simple conditions can be used to prove uniqueness of the Nash equilibrium of the tariff retaliation game. The welfare effects of endowment changes are analyzed in terms of the standard terms of trade and volume of trade effects. If the elasticity of substitution of one of the countries is sufficiently high, immiserizing growth will not occur.      

社会保障的新理念与中国农民扶持性社会保障体制

中国的市场化改革使广大的中国农民直接暴露在现代市场经济风险下,而家庭联产承包制的实施又使改革开放前与计划经济体制相适应的保障体制无法运转,这样,中国广大农民成为了现代市场经济中最没有保障的弱势群体。因此,建立农民社会保障体系的意义重大。中国农民社会保障体制迟迟没有建立的原因有二:其一,传统社会保障理念仅考虑到其工具价值,忽视了其目的价值;其二,农民的组织化程度低,导致他们在社会利益分割过程中没有谈判地位。从建立农民社会保障体制的双重价值出发,建立保障农民生存权和基本发展权的农民扶持性社会保障体制具有重要意义。     

Monotone comparative statics: changes in preferences versus changes in the feasible set

Let a preference ordering on a lattice be perturbed. As is well known, single crossing conditions are necessary and sufficient for a monotone reaction of the set of optimal choices from every chain. Actually, there are several interpretations of monotonicity and several corresponding single crossing conditions. We describe restrictions on the preferences that ensure a monotone reaction of the set of optimal choices from every sublattice whenever a perturbation of preferences satisfies the corresponding single crossing condition. Quasisupermodularity is necessary if we want monotonicity in every conceivable sense; otherwise, weaker conditions will do.     

Disaggregation of excess demand and comparative statics with incomplete markets and nominal assets

Summary. We prove that locally, Walras' law and homogeneity characterize the structure of market excess demand functions when financial markets are incomplete and assets' returns are nominal. The method of proof is substantially different from all existing arguments as the properties of individual demand are also different. We show that this result has important implications and is part of a more general result that excess demand is an essentially arbitrary function not just of prices, but also of the exogenous parameters of the economy as asset returns, preferences, and endowments. Thus locally the equilibrium manifold, relating equilibrium prices to these parameters has also no structure. Received: September 17, 1996; revised version: November 7, 1997