The theory of mixed demand functions

The properties of Samuelson's mixed demand functions, which express demand as a function of a mixed set of prices and quantities, are derived. By analyzing compensated (or substitution) effects and uncompensated effects, the relationships between mixed demand functions and conditional (or rationed) demands are examined. This provides insights on the behavioral implications of consumer theory for alternative demand specifications.     

Existence, uniqueness and efficiency of equilibrium in hedonic markets with multidimensional types

We study equilibrium in hedonic markets, when consumers and suppliers have reservation utilities, and the utility functions are separable with respect to price. There is one indivisible good, which comes in different qualities; each consumer buys 0 or 1 unit, and each supplier sells 0 or 1 unit. Consumer types, supplier types and qualities can be either discrete of continuous, in which case they are allowed to be multidimensional. Prices play a double role: they keep some agents out of the market, and they match the remaining ones pairwise. We define equilibrium prices and equilibrium distributions, and we prove that equilibria exist, we investigate to what extend equilibrium prices and distributions are unique, and we prove that equilibria are efficient. In the particular case when there is a continuum of types, and a generalized Spence–Mirrlees condition is satisfied, we prove the existence of a pure equilibrium, where demand distributions are in fact demand functions, and we show to what extent it is unique. The proofs rely on convex analysis, and care has been given to illustrate the theory with examples.     

A general theory of demand for information about product quality

The purpose of this paper is to construct a general theory—analogous to the neoclassical theory of consumer demand—of demand for information about product quality. The model proposed here introduces uncertain product quality by assuming that commodities possess attributes which consumers desire and that an uncertain commodity possesses are unknown quantity of some attribute. It is assumed that information about the quality of uncertain products is available. The consumer's utility function of information is derived and his information demand function is obtained.Partial analogues of the neoclassical theorems are proved for information demand. Roughly, we find that the Slutsky matrix is symmetric and that a submatrix is negative definite. The negative definite submatrix contains those terms which measure the effect of (income compensated) changes in information prices on information demand.The analysis employed to obtain these results parallels—with some important modifications—the neoclassical analysis of commodity demand. The method used to obtain expressions for the Slutsky substitution terms is an extension of the approach introduced by McKenzie [10] and later used by Hurwicz and Uzawa [6]. This approach uses an “income compensation” function to arrive at an “income compensated” demand function.     

Notes on optimal transportation

We study equilibrium in hedonic markets, when consumers and suppliers have reservation utilities, and the utility functions are separable with respect to price. There is one indivisible good, which comes in different qualities; each consumer buys 0 or 1 unit, and each supplier sells 0 or 1 unit. Consumer types, supplier types and qualities can be either discrete of continuous, in which case they are allowed to be multidimensional. Prices play a double role: they keep some agents out of the market, and they match the remaining ones pairwise. We define equilibrium prices and equilibrium distributions, and we prove that equilibria exist, we investigate to what extend equilibrium prices and distributions are unique, and we prove that equilibria are efficient. In the particular case when there is a continuum of types, and a generalized Spence–Mirrlees condition is satisfied, we prove the existence of a pure equilibrium, where demand distributions are in fact demand functions, and we show to what extent it is unique. The proofs rely on convex analysis, and care has been given to illustrate the theory with examples.     

Incentive effects of paying demand response in wholesale electricity markets

Recently issued U.S. Federal Energy Regulatory Commission regulations require comparable treatment of demand reduction and generation in the wholesale electric market so that they are compensated at the same market clearing price. The new regulations measure demand reduction as a reduction from a “customer baseline,” a historically based estimate of the expected consumption. In this paper, we study the incentive effects on the efficiency of the demand response regulation using a static equilibrium model and a dynamic extension of the model. Our analysis provides three main results. Firstly, our analysis shows that the demand reduction payment will induce consumers to (1) inflate the customer baseline by increasing consumption above the already excessive level during normal peak periods and (2) exaggerate demand reduction by decreasing consumption beyond the efficient level during a demand response event. This result persists when applied to alternative baseline designs in a dynamic model. Secondly, we study alternative policy remedies to restore the efficiency of demand response regulation and introduce a new approach to define the customer baseline as a fixed proportion of an aggregate baseline. In particular, the aggregate baseline approach can significantly weaken or eliminate the incentive to inflate the baseline. Finally, we illustrate that if the baseline inflation problem is solved and demand and supply functions are linear, the current policy can produce a net social welfare gain. However, the welfare improvement requires that demand reduction be paid only when the wholesale price is at least twice the fixed retail rate. This argues that the policy should include a sufficiently high threshold price below which demand response is not dispatched.     

Expected utility maximization and demand behavior

This paper extends the non-parametric approach to consumer demand analysis to the case of expected utility maximization. We provide necessary and sufficient conditions for a set of price-quantity pairs to be consistent with expected utility maximization, and investigate their relationship to revealed preference conditions. Extensions to incomplete markets and intertemporal resolution of uncertainty are also considered.     

Nonstandard foundations of equilibrium search models

We develop an equilibrium sequential search model which includes most of the literature as special cases. In particular, the model can accommodate heterogeneity in buyers’ search costs and demand functions and firms’ cost functions, with general demand and cost functions. We identify conditions which ensure existence of equilibrium in pure strategies, utilizing recent progress in the theory of large games by Khan and Sun. These conditions elucidate the essential structure of equilibrium search models. Although we focus on sequential search, our methodology can be used for other classes of equilibrium search models as well.     

A systemic approach to modelling and estimating demand for money(ies)

This article uses a consumer theory-based systemic approach to model the demand for monetary liquid asset holdings in Chile. We implement the suggestions and caveats of aggregation theory for the estimation of a demand system for liquid assets (monies) in static, dynamic and time-varying parameters setups. Our results are robust and theoretically consistent with consumer theory restrictions, as a system derived from a utility maximizing framework and a quasi concave utility function. In our estimations, we find stability of interest rate elasticities, in contrast to previous related literature. We also document evidence that long (short) maturity rates are associated to less (more) liquid assets.     

Estimating and testing the compensated double-log demand model

In spite of the proliferation of flexible functional forms for consumer demand systems, the double-log demand model continues to be popular, especially in applied work calling for single-equation models. It is usually estimated in uncompensated form. It can also be estimated in compensated form, by deflating the income variable alone using Stone's price index. The compensated form has the same right-hand side as a single-equation version of the popular linear approximation to the Almost Ideal demand model, facilitating the construction of a test for choosing between the two alternatives. This paper demonstrates these results, develops the specification test, and illustrates its application using US meat consumption data. Simulations suggest that the test is well-behaved with good power in typical applications.     

Consumer demand for meat and the evaluation of agricultural policy

This study utilizes an econometric model of equilibrium in the U.S. livestock and feedgrain markets to investigate a number of questions of economic methodology and policy. Both nonlinear consumer demand equations that obey the constraints of neoclassical demand theory and a model of supply are used. This approach allows for the measurement of the effects on consumer welfare of actual government policies. In particular, the model is employed to analyze the welfare effects of an actual policy situation — the sale of U.S. grain to the Soviet Union in the third quarter of 1972.     

Adaptive behavior,demand and preferences

This paper extends the work on endogenous change of tastes of Von Weizsäcker to the n-commodity framework and for a general adaptive behavior process. The paper examines the relation between the effect of taste changes to income and price changes. It provides sufficient conditions for stability of the underlying dynamic process, establishes uniqueness of the equilibrium demand vector and some useful relations between the long-run demand functions and the equilibrium short-run demand functions. It is also shown that the long-run demand functions can be rationalized by a utility function if and only if the short-run utility function is such that any good that experiences learning or taste change is separable from all other goods.     

Inframarginal values and demand: Contra Dwight Lee

Happiness studies show that there has been no discernable rise in happiness in the United States between 1959 and 2004, yet the same period saw per capita income nearly triple. Dwight Lee modifies the theory of consumer demand to resolve this apparent conflict. Using the concepts of consumer surplus and rising incomes causing demand shifts, Lee posits that the law of downward sloping demand only fleetingly applies. He hypothesizes that the values of all units consumed become the same as the value of the last unit soon after the change in income. This makes the demand curve horizontal for all units consumed, and that makes the existence of consumer surplus ephemeral. There are difficulties with this; some are: (1) His formulation gives rise to predictions that are at odds with commonly observed market phenomena; (2) The attempted resolution is quixotic because the theory of demand and consumer surplus holds time, place, and circumstances constant, while happiness surveys do not and, indeed, cannot hold things constant over decades; and (3) because standard economic theory is timeless it is inapplicable to many phenomena that occur over extended periods.     

The integrability of consumer demand functions

The purpose of this paper is to characterize the class of systems of consumer demand functions that are representable as ratios of first-order polynomial functions and are integrable. Starting from a general system of consumer demand functions representable as ratios, we impose successively the restrictions corresponding to homogeneity, summability, symmetry, non-negativity, and monotonicity. We find that the only such systems which are capable of modeling arbitrary own- and cross-substitution effects are the systems generated by transcendental logarithmic utility functions.     

On the theory of effective demand under stochastic rationing

The concept of effective demand under stochastic manipulable quantity rationing is shown to be compatible with the existence of nontrivial equilibrium. It is argued that stochastic rationing is unavoidable for any satisfactory definition of effective demand. Moreover, manipulability of the rationing mechanism is necessary for reasons of logical consistency, at least if the distribution over realisations for each agent depends on his own action and on the aggregate values of demand and supply only. In that case, anonymous stochastic rationing schemes reduce to those random functions, the mean value function of which is the uniform proportional rationing mechanism.     

Information sharing about a demand shock

This paper examines two questions in asymmetric Cournot and Bertrand oligopoly with a demand shock. Under which conditions is information sharing a subgame-perfect equilibrium? What is the welfare effect when firms are better off? Given these questions, the normal assumptions in the earlier literature can be relaxed in three ways: demand functions can be asymmetric; a demand shock can affect firms differently; distributions of the demand shock and information signals can be arbitrary. Under these general assumptions, the answer to the first question is: every firm's response to the demand shock is stronger when all firms have perfect information than when one firm does so alone; the answer to the second question is: social welfare increases in Cournot competition, and consumer surplus decreases in Bertrand competition.     

Limited knowledge of demand and oligopoly equilibria

In a standard model of oligopoly with differentiated products, the existence of an equilibrium at which the first-order conditions for profit maximisation are simultaneously satisfied for all firms is proved and this is done without imposing any restrictions on the demand functions. This is an equilibrium in the following sense: although some firms may not necessarily be maximising their profits, nevertheless if each firm's knowledge of demand is limited to the linear approximation of its own demand curve, then it will believe that it is indeed maximising its profits.     

Cournot games with biconcave demand

Biconcavity is a simple condition on inverse demand that corresponds to the ordinary concept of concavity after simultaneous parameterized transformations of price and quantity. The notion is employed here in the framework of the homogeneous-good Cournot model with potentially heterogeneous firms. The analysis leads to unified conditions, respectively, for the existence of a pure-strategy equilibrium via nonincreasing best-response selections, for existence via quasiconcavity, and for the uniqueness of the equilibrium. The usefulness of the generalizations is illustrated in cases where inverse demand is either “nearly linear” or isoelastic. It is also shown that commonly made assumptions regarding large outputs are often redundant.     

Cournot equilibrium without apology: Existence and the Cournot inverse demand function

In a multi-commodity framework with absence of wealth effects, we prove the existence of equilibrium for Cournot oligopoly, and that the concept is completely non-ambiguous. We also obtain a uniquely defined endogenous inverse demand function, depending only on the competitive sector.     

Existence of equilibrium in an overlapping-generations model with government debt

The Diamond overlapping generations (OLG) model with government debt has been widely utilized in economics, but the existence of the steady-state equilibrium is either assumed or illustrated numerically. This paper provides easily checkable conditions for the existence and uniqueness of steady-state equilibrium in this model. By checking the first derivatives of the production and utility functions and their interactions, we can determine whether the model has a nontrivial equilibrium or not. We show that the level of government debt, production technology, individual preference, and the growth rate are important for the existence of equilibrium. If government debt exceeds a certain level, equilibrium will not exist. Given technology, preference, and the growth rate, the upper-bounds of the government debt-output ratio in equilibrium can be determined based on our results.