This study explores the meaning, some basic implications, and the reasonableness, of adding a modium of topological structure to social choice functions. Only very elementary topological ideas are used, and no previous knowledge of them is required.
A social choice function is said to be implementable if and only if there exists a game form such that for all preference profiles an equilibrium strategy n-tuple exists and any equilibrium strategy n-tuples of the game yield outcomes in the social choice set. A social choice function is defined to be minimally democratic if and only if whenever there exists an alternative which is ranked first by n − 1 voters and is no lower than second for the last voter, then the social choice must be uniquely that alternative. No constraints are placed on the social choice function for other preference profiles. Using the classical definitions of equilibria for n-person games—namely Nash and strong equilibria, it is shown here that over unrestricted preference domains, as long as there are at least as many alternatives as individuals, no minimally democratic social choice function is implementable. A similar result holds in certain restricted domains of the type assumed by economists over public goods spaces. We then show that a different notion of equilibrium—namely that of sophisticated equilibrium—allows for implementation of democratic social choice functions also having further appealing properties.
In this paper, we first present a competitive macroeconomic model of an open economy which is suitable for estimation and contrast this with a non-competitive model. We then derive unemployment equations from the various models and estimate them over annual data from 1948–1979. We draw the following conclusions. (i) The competitive model of the labour market does not fit the facts. (ii) The non-competitive model generates an equation for the constant inflation rate of unemployment which reveals how, at certain times such as the mid 1970s, a combination of factors conspired to raise this level forcing the government into a deflationary stance to prevent inflation rising drastically. (iii) A number of factors have raised the level of unemployment in a secular fashion since the war, in particular the increase in the variation of relative prices, the increase in the benefit to income ratio, the introduction of employment protection legislation and the rise in the intersectoral shifts of the labour force.
The function of monetary policy to alter the informational content of money price signals is examined in a model where traders can observe an economy wide financial signal and a local commodity price. Under a passive policy, money demand disturbances, which are not directly observable, are shown to be confused with real productivity shocks and thereby preclude prices from fully reflecting all information. Even when the policy authority has no informational advantage, prospective money growth feedback rules can “improve” the structure of available information.
The planned level of output is an important variable in modelling Centrally Planned Economies and the present paper discusses several disequilibrium models in which the plan level is an endogenous variable. A key relationship in such a model is the plan-adjustment equation which is the counterpart of the usual price-adjustment equation employed in models of free economies. Seemingly minor differences in assumptions lead to markedly different econometric models. The coherency properties of these are studied and several likelihood functions are derived. The most complex of the models includes both endogenous plan levels and endogenous prices.
We develop a model in which a monopolist uses differences across consumers in their valuation of time to imperfectly price discriminate. Though it is customary to analyse price discrimination problems by the calculus of variations after postulating a continuum of types, we assume a finite number of types and exploit the geometry and duality of the contract set and the structure of the programming specification. We analyse in detail the qualitative properties of the model's solution and show by construction that our results exhaust the implications of the model for equilibrium contract pairs. We show that imperfect discrimination is not bounded in welfare terms between perfect discrimination and single-price monopoly and that the deadweight loss, consumer surplus and output comparisons between single-price monopoly and imperfect discrimination are ambiguous.
Past work on aggregation of production functions has focused on aggregation over firms where technology is embodied in fixed capital. This paper shows that much of the stringency of the necessary conditions for aggregation resides in the nature of aggregation over firms and not in the immobility of capital. Roughly, when capital is mobile, aggregation is permitted for any group of factors under the union of the conditions which otherwise applied to aggregation of fixed or aggregation of movable factors, respectively. No truly new conditions appear. The results are also interpreted in terms of output aggregation.
We prove the existence of approximate equilibria in exchange economies, giving bounds on the excess demand in terms of the number of traders and norms of the endowments, but independent of the preferences.
We develop a model in which each firm chooses a hiring standard as well as a wage schedule and an application fee, we then characterize the set of Nash equilibria, and establish necessary and sufficient conditions for the existence of equilibrium. If the distribution of productivities within each ability type is Gaussian, workers who pass the test will be paid more than the value of their marginal product, while workers who fail the test will receive a wage, net of the application fee, below the value of their marginal product.