THE AD-AS MODEL AND ITS SOLUTIONS: SOME NEW RESULTS IN A DISEQUILIBRIUM PERSPECTIVE*

This paper discusses the logical foundation and the solutions of a microfounded aggregate demand … aggregate supply model under the disequilibrium hypothesis. We first show that a) the latter hypothesis is the only one ensuring model consistent expectations and that b) price predetermination, more than price flexibility, should be embodied in an AD-AS framework. Then we develop a full AD-AS scheme, both under excess supply and excess demand for labour. We prove that in the latter case no well defined equilibrium exists. Finally, we discuss stability and perform some comparative statics exercises.     

Towards a More Complete Efficiency Wage Theory

The efficiency wage is an important topic in the theory of employment. In a traditional efficiency wage model, only the representative firm is optimizing against an assumed S‐shaped effort supply function. This S‐shaped supply curve is critical for the model and the absence of a derivation of the curve in the literature means that it is an incomplete theory. In the present paper, we extend the model by specifying a worker's representative utility function so that the corresponding argmax function will be the S‐shaped effort supply curve. This will make the worker's decision process endogenous and will produce a more complete model. The importance of this extension is clear. The characterization of the utility function will make explicit the necessary conditions and crucial assumptions of the traditional model. More importantly, the extension will allow researchers to introduce employment compensation factors into the worker's utility function for analysis. This has important bearings on future development in employment theory. For example, a worker's satisfaction from shirking (net of dismissal risks), or his or her willingness to search for jobs (net of search cost), can now be included in his or her utility function to form an optimal work or search strategy. Incorporating the worker's optimization behaviour into the model will also enable researchers to study policy directed not just towards firms but also towards the worker's decision process. Furthermore, this approach provides a framework for researchers to generate comparative statics. These comparative statics can lead to interesting topics for econometric models or to further research within this field.     

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.     

Supply and demand explanations and their ceteris paribusclauses

This paper argues that supply and demand explantions are causal explanations and that it is helpful to recognize this fact explicity, for then one can appreciate that the variables impounded in the ceteris paribusclauses attached to supply and demand curves are other causes. One can then specify clearly the conditions of membership in a ceteris pairbusclause: 1) include all those factors that within the given time period significantly affect the amount supplied or demanded but; 2) do not include any factors that themselves within the given time period significantly depend on the price of the particular commodity or service. Note the vague word ‘significantly’. If one insists on the general interdependencies established in general equilibrium analyses, one must reject partial equilibrium analyses altogether, but to do so would rule out work that may be enlightening and useful. Such theoretical purism is also indefensible, since general equilibrium analyse rely on similar causal approximations. This analyses of ceteris paribusclauses is helpful in understanding where supply and demand analysis or comparative statics goes wrong, as in traditional functional distribution theory.     

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.     

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.     

Capital Inflow in the Presence of Endogenous Labour Supply and Monopolistic Competition

This paper examines the impact of capital mobility within the context of a simple general equilibrium model where the supply of labour is endogenous and the producer services sector is subject to monopolistic competition. It is shown that the presence of monopolistic competition influences the size of all comparative static results. The paper also shows that the size of the elasticity of substitution between leisure and consumption of the final good plays a crucial role in determining the impact of changes in the supply of capital on utility-maximising labour supply and welfare. Specifically, it is shown that capital mobility has no impact on optimal labour supply if the elasticity of substitution is equal to unity. The impact of a small capital inflow on welfare can be negative if the elasticity of substitution is sufficiently larger than unity.     

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.     

Strong comparative statics of equilibria

Some results in the monotone comparative statics literature tell us that if a parameter increases, some old equilibria are smaller than some new equilibria. We give a sufficient condition such that at a new parameter value every old equilibrium is smaller than every new equilibrium. We also adapt a standard algorithm to compute a minimal such newer parameter value and apply this algorithm to a game of network externalities. Our results are independent of a theory of equilibrium selection and are valid for games of strategic complementarities.     

The impact of taxes on female labour supply

There is little agreement in economics on the factors influencing labour supply and hence on the impact of taxes. Within the marginal model, real wages and incomes are directing people's labour market behaviour independent of time and space, whereas the human resources approach takes account of the social environment and past behaviour. Even if strong assumptions are made, the neoclassical theory cannot predict the outcome of a wage increase. The labour supply response depends on the relative strengths of the substitution and the income effect. Since nonparticipation in the labour market is explained by a reservation wage being higher than the market wage, this is the only situation in which neoclassical theory would predict a rise in labour force participation with a wage increase. This case occured in a ‘natural experiment’ in Sweden. The Swedish tax system changed in 1971 from joint to separate taxation of spouses resulting in a substantial increase in the net wage of married women. This article investigates the impact of the change in the Swedish tax system on female labour force participation, concluding that it cannot explain the substantial rise in the participation rates of Swedish women. This is a significant result, questioning standard neoclassical theory and supporting the more institutional views of human labour market behaviour. That is that time and space as well as the social environment are important when analyzing labour supply. This will have consequences for international comparisons. Only factors which explain developments within one country might be relevant for explaining international differences, e.g. in labour force participation.     

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.     

Computing minimal state space recursive equilibrium in OLG models with stochastic production

Using order-theoretic methods, we derive sufficient conditions for the existence, characterization, and computation of minimal state space recursive equilibrium (RE), as well as Stationary Markov equilibrium (SME) for various classes of stochastic overlapping generations models. In contrast to previous work, our methods focus on constructive methods. Our existence results are obtained for models that include public policy (e.g., social security policies, transfers, taxes, etc), production nonconvexities, elastic labor supply, non-monotone income processes, and long-lived agents. We distinguish conditions under which there exist various subclasses of minimal state space RE, including bounded, monotone, non-monotone, semicontinuous, Lipschitz continuous RE. Finally, we provide monotone equilibrium comparative statics results on the space of economies for some RE.     

Marx Inside the Circuit: Discipline device,wage bargaining and unemployment in a sequential monetary economy

The aim of this paper is to show that Marxian labour theory of value can be consistently interpreted in terms of the monetary circuit model, where firms need initial finance to start production and where the money supply is endogenous. In contrast to the recently revived Marxian monetary models, in particular the New Interpretation, it is argued here that although the money wage is bargained for on the labour market, the real wage is determined by firms' choices, since firms autonomously determine the structure of production and hence real consumption for the working class as a whole. This does not mean that firms are able to set the real wage without economic and social constraints. Starting from our circuitist reading of the labour theory of value and distribution, a model is developed in order to determine the level of employment and income distribution, on the assumptions that (i) the industrial reserve army affects wage bargaining and labour effort and that (ii) workers react to the failure of their expectations on the real wage by reducing their work intensity. In this context, it is shown that firms may increase their share of profits over time only be means of innovations.     

A note on nominal government expenditure targets

In IS-LM models, government expenditure is usually fixed in real terms. In this short note, we examine some of the implications of nominal government expenditure targets for both model stability and comparative statics. When a fixed money supply policy is in operation, nominal government expenditure targets may stabilize an otherwise unstable system. If this is the case, an increase in the nominal stock of money will reduce the price level in the long run.     

A general equilibrium approach to aggregate capital–energy complementarity

Capital–energy complementarity is examined through the comparative statics of a simple aggregate model. An exact formula is given for the direction of interaction in terms of derivatives of the production function and factor supply elasticities.     

Sampling variability: some observations from a labour supply equation

In economics, the number of observations available for empirical work is often predetermined. Researchers assume some large sample distribution and carry through with measurement and testing applied to data sets of varying sizes. The consequences of sampling variability are generally ignored. It is shown in a re-sampling experiment, using data sets of different sizes and estimating log-linear male labour supply equations, that a wide range of what appears to be statistically supported estimates of the wage elasticity of labour supply are generated. Testing based on bootstrapped estimates shows that 4000 observations are required to reduce sampling variability to statistically acceptable levels.     

Education, Work and Wages in the UK

Abstract. This paper is concerned with the relationship between education, wages and working behaviour. The work is partly motivated by the sharp distinction in the literature between the returns to education and the effect of wages on labour supply. Education is the investment that cumulates in the form of human capital while labour supply is the utilization rate of that stock. Yet, variation in education is usually the basis for identifying labour supply models – education is assumed to determine wages but not affect labour supply. Moreover, it is commonly assumed that the private rate of return to education can be found from the schooling coefficient in a log-wage equation. Yet, the costs of education are largely independent of its subsequent utilization but the benefits will be higher the greater the utilization rate. Thus the returns will depend on how intensively that capital is utilized and we would expect that those who intend to work least to also invest least in human capital. Indeed, the net (of tax liabilities and welfare entitlements) return to education will be a complex function of labour supply and budget constraint considerations.
Here we attempt to model the relationship between wages, work, education and the tax/welfare system allowing for the endogeneity of education as well for the correlations between the unobservable components of wages and working behaviour. We use the estimates to simulate the effect of a new UK policy designed to increase education for children from low-income households.     

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.     

Further results on comparative statics under uncertainty. A comment on Machnes

This paper re-examines the results in Machnes (1993). When a risk-averse firm faces both uncertain demand and uncertain fixed costs, the Arrow-Pratt theory of decreasing absolute risk aversion may be too weak to yield unambiguous comparative statics. Herein, it is shown that the stronger notions of risk behavior proposed by Ross (1981) and Kimball (1993) are useful in providing intuitive results in this context.     

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.