Savings and retail price reform in a queue-rationed economy

The paper addresses the effect on consumer saving behavior of queue rationing and of price reform in a Soviet-type economy in a lifecycle framework with overlapping generations. It is shown that consumers save less for retirement in a queue-rationed exchange economy with black markets than they would in a free-market system with the same endowments. The expectation of price reform is thus likely to cause an increase in consumer savings. In addition, an analysis is given of the effect of the increase in controlled prices on the black market prices and on the prices of unrationed goods.     

Smooth preferences and the regularity of equilibria

To study equilibria we describe an economy by its distribution of consumers' preferences and endowments. All preferences are smooth and weakly convex. Demand of an economy need not be single valued, but there is an open dense set of economies for which demand is a C¹-function in a neighborhood of the equilibrium prices. We call an economy regular if its excess demand is transversal to zero. A regular economy has locally unique equilibria. It is shown that regular economies form an open dense set on which the equilibrium price correspondence varies continuously and the number of equilibria is locally constant.     

Note on the optimality of unemployment equilibria

An equilibrium concept for an economy with rigid prices has been given by Drèze (1975). He formulated a model where for some commodity, either the supplies or the demands are rationed. In this note we discuss ‘unemployment equilibria’, i.e., fixed price equilibria for which the quantity rationing affects the supplies only. It can be proved that there exists a set of unemployment equilibria. Therefore we consider the question whether it is possible to characterize the set of undominated unemployment equilibria.     

Supply-constrained fixed price equilibria in monetary economies

In this paper we consider an economy with restrictions on the relative prices of non-money commodities. The non-money commodities are partitioned into two groups, index makers and price following commodities. Then two cases are considered, namely that the relative prices of the index makers are fixed, respectively free. In both cases the money prices are flexible, whereas the relative prices of the price following commodities are tied to the prices of the index makers. The existence of a supply-constrained equilibrium is proved with (i) no rationing on the money commodities (stores of value), and (ii) at least one non-money commodity is not rationed. If prices of the index makers are fixed the result strengthens a theorem of Dehez and Drèze, if the prices are free a theorem of Kurz is strengthened. This paper is not only concerned with these existence results, but also with the question whether supply-constrained equilibria should appear more frequently than demand-constrained equilibria.     

Equilibrium in incomplete markets: I : A basic model of generic existence

This paper demonstrates the generic existence of general equilibria in incomplete markets. Our economy is a model of two periods, with uncertainty over the state of nature to be revealed in the second period. Securities are claims to commodity bundles in the second period that are contingent on the state of nature, and are insufficient in number to span all state contingent claims to value, regardless of the announced spot commodity prices. Under smooth preference assumptions, equilibria exist except for an exceptional set of endowments and securities, a closed set of measure zero. The paper includes partial results for fixed securities, showing the existence of equilibria except for an exceptional set of endowments.     

Equilibria with coordination failures

This paper extends the literature on equilibria with coordination failures to arbitrary convex sets of admissible prices. This makes it possible to address coordination failures for cases with price indexation or more general price linkages between commodities. We introduce a new equilibrium concept, called quantity constrained equilibrium (QCE), giving a unified treatment to all cases considered in the literature so far. At a QCE the expected trade opportunities on supply and demand are completely determined by a rationing vector satisfying that the prevailing price system maximizes the value of the rationing vector within the set of admissible prices. When the set of admissible prices is compact, we show the existence of a connected set of QCEs. This set connects two trivial no-trade equilibria, one with completely pessimistic expectations concerning supply opportunities and one with completely pessimistic expectations concerning demand opportunities. Moreover, the set contains for every commodity a generalized Drèze equilibrium, being a QCE at which for that commodity no binding trade opportunities on both supply and demand are expected, and also a generalized supply-constrained equilibrium at which no binding constraints on demand opportunities are expected and for at least one commodity also not on supply. We apply this main result to several special cases, and also discuss the case of an unbounded set of admissible prices.     

Regular economies and sets of measure zero in Banach spaces

Using concepts of measure zero in Banach spaces, Debreu result guaranteeing full measure for the economies with stable and finite number of equilibria is generalized. Here, we include utility functions as well as initial endowments in the definition of an economy.     

On pure-strategy Nash equilibria in price–quantity games

This paper examines the existence and characteristics of pure-strategy Nash equilibria in oligopoly models in which firms simultaneously set prices and quantities. Existence of a pure-strategy equilibrium is proved for a class of price–quantity games. If the demand function is continuous, then the equilibrium outcome is similar to that of a price-only model. With discontinuous demand and limited spillover, there are rationing equilibria in which combined production falls short of market demand. Moreover, there might again be an equilibrium reflecting the outcome of a price game. Competition in price and quantity thus yields Bertrand outcomes under a variety of market conditions.     

Voting, bargaining, and factor income distribution

The effect of possible price control on factor income distribution under a democratic system is examined in the context of a collective bargaining model. A solution concept of the cooperative game theory called the Harsanyi-Shapley value is chosen to predict a likely outcome. The explicit solution for a non-atomic production economy, with two production factors and a fixed coefficient technology, is obtained. We find that this solution can be realized through prices. It is observed that in this solution, factor income shares respond to the ratio of the total endowments of two factors.     

Gains and losses at core allocations

The search for a coalition which can possibly improve upon a given allocation and the redistribution of endowments within such a coalition are conducted through the use of prices. Prices permit the expression of how much every agent gains or loses in the allocation. With any feasible allocation one can associate a price system such that either the total loss of all losers does not exceed a certain bound independent of the number of agents or the losers can improve. The definition of gains and losses that we use implies that the total gain is also bounded in core allocations. Our theorem is closely related to that of Vind (1965).     

Existence of a competitive equilibrium when all goods are indivisible

This paper investigates an economy where all consumption goods are indivisible at the individual level, but perfectly divisible at the overall level of the economy. In order to facilitate trading of goods, we introduce a perfectly divisible parameter that does not enter into consumer preferences — fiat money. When consumption goods are indivisible, a Walras equilibrium does not necessarily exist. We introduce the rationing equilibrium concept and prove its existence. Unlike the standard Arrow–Debreu model, fiat money can always have a strictly positive price at the rationing equilibrium. In our set up, if the initial endowment of fiat money is dispersed, then a rationing equilibrium is a Walras equilibrium. This result implies the existence of a dividend equilibrium or a Walras equilibrium with slack.     

An equivalence theorem for a differential information economy

In a pure exchange economy with differential information and a finite set of traders, physical commodities and states of nature, we characterize the Walrasian expectations or Radner equilibria by using the veto power of the grand coalition. We prove that an allocation x is a Radner equilibrium allocation if and only if it is “privately non-dominated” by the grand coalition in every economy obtained by perturbing the original initial endowments in the direction of x. The first and second welfare theorems become particular cases of our main result. Since the deterministic Arrow–Debreu–McKenzie model is a special case of the differential information economy model we also provide a new characterization of the Walrasian equilibria.     

International pharmaceutical supply prices: Definitions — problems — policy implications

In cases where the buyer and the seller of goods and services are companies belonging to the same group the prices charged for goods and services are called ‘international delivery prices’ or ‘international transfer prices’. The peculiarities of research-based companies are such that attempts to ascertain in practice what constitutes an ‘appropriate’ international delivery price are beset by a number of problems. Any scheme that is devised to solve the problems of international transfer prices should feature general ‘rules’ on how the various countries ought to share in central costs. As international transfer prices are a prerequisite for an efficient world economy based on the division of labour an agreement should be reached on the design and content of suitable delivery price systems for a research-intensive industry.     

A dynamic,policy oriented model of the regulated housing market: The Swedish prototype

The design and preliminary implementation of a dynamic, policy oriented model of the regulated housing market is presented. The model is developed in the context of the Swedish housing market institutions which combine nearly all features encountered in other nations. Free buying and selling by homeowners, black markets, swapping of dwellings and rationing of price controlled dwellings both by landlords and a public authority are included as explicit transaction options (with distinct costs) available to existing and newly formed households in the market. The model simulates a sequence of temporary annual equilibria which are obtained by balancing effective demands with effective supplies. Household mobility choices, landlords' selling decisions and the rationing of dwellings at fixed prices are derived from stochastic maximization resulting in multinomial or nested logit models of choice behavior. An aggregated preliminary 16-equation version is calibrated with partly real, partly guesstimated data for the Greater Stockholm region in the mid-seventies. Qualitative comparative statatics and income compensated policy simulations with this version illustrate some unintended effects of Swedish housing policy resulting from the manipulation of the income tax, an income tax dependent property tax and housing allowances. The model provides a tool whereby deregulating institutional changes which are potentially Pareto improving can be identified. If, however, current institutions such as the rationing of dwellings result in sufficiently lower transactions costs for households relative to the free market, then deregulation is not Pareto preferred.     

General consumption constraints and regular economies

In the spirit of Smale’s work, we consider pure exchange economies with general consumption sets. In this paper, the consumption set of each household is described in terms of a function called possibility function. The main innovation comes from the dependency of each possibility function with respect to the individual endowments. We prove that, generically in the space of endowments and possibility functions, economies are regular. A regular economy has a finite number of equilibria, which locally depend on endowments and possibility functions in a continuous manner.     

The value of scarce water: Measuring the inefficiency of municipal regulations

Rather than allowing urban water prices to reflect scarcity rents during periods of drought-induced excess demand, policy makers have mandated command-and-control approaches, primarily rationing the use of water outdoors. While such policies are ubiquitous and likely inefficient, economists have not had access to sufficient data to estimate their economic impact. Using unique panel data on residential end-uses of water in 11 North American cities, we examine the welfare implications of urban water rationing in response to drought. Using estimates of expected marginal prices that vary both across and within markets, we estimate price elasticities specific to indoor and outdoor water use. Our results suggest that current policies do target water uses that households, themselves, are most willing to forgo. Nevertheless, we find that rationing outdoor water in cities has costly welfare implications, primarily due to household heterogeneity in willingness-to-pay for scarce water. We find that replacing rationing policies with a market-clearing “drought price” would result in welfare gains of more than 29% of what households in the sample spend each year on water.     

Existence and uniqueness of price equilibria: Theory and application to discrete choice models

Continuous excess demand systems which do not obey homogeneity of degree zero or Walras's Law are proved to have equilibria if they satisfy certain mild regularity conditions when prices tend to the extremes of a price domain which need not be closed or bounded. A straightforward generalization of Brouwer's theorem is used. Systems also obeying a weak balance condition (of which Walras's Law is a special case) and homogeneity are treated as corollaries to the main theorem. Sufficient conditions for differentiable excess demand systems to have unique equilibria are developed in three separate theorems. The usefulness of these general existence and uniqueness theorems is demonstrated by applying them to three specific models constructed from discrete choice theory: (1) a competitive rental housing market, (2) a regulated rental housing market with fixed rents and rationing and (3) an interregional labor market in which laborers can choose among regions for employment (or voluntary unemployment) as well as the work hours they will supply.     

Equilibrium price dynamics in an overlapping-generations exchange economy

An extension to the Yaari (1965)–Blanchard (1985) continuous time overlapping generations model for an endowment Arrow–Debreu economy with an age-structured population is presented. It is proved that Arrow–Debreu equilibrium prices are represented by a double linear integral equation, and depend on the age-distributions of population and endowments. For an economy with a balanced growth, and logarithmic utility, we prove that bubbles may exist if endowments are distributed earlier than some critical age.     

Price Equilibria in Pure Strategies for Homogeneous Oligopoly

For a homogeneous product oligopoly market, possibilities for pure strategy Nash equilibria in prices are studied. Consumers, who each nonstrategically purchase one unit up to a common reservation price, are hypothesized to be more concerned with large price differences (and therefore buy from the cheapest firm) than slightly different prices. For the duopoly case, existence, uniqueness, and characterization results are provided. Linear examples are given with 2 and n firms.