Inverting systems of demand functions

This note gives a set of sufficient conditions under which a system of demand functions for “gross substitutes” can be inverted to obtain an equivalent system of inverse demand functions, and vice versa. These conditions also ensure that either system can be inverted to obtain a system of “mixed” demand functions, i.e., a mixture of demand and inverse demand functions. In addition, the resultant functions possess intuitive properties expected of gross substitutes.     

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.     

A reformulation of the theory of demand by compensated demand functions

We present a formal approach to consumer demand by compensated demand functions. In accordance with the integrability theory or with the theory of revealed preference, we do not require the existence of a utility function, but we do assume certain hypotheses concerning functions describing rational behavior. In view of their properties, these functions can be interpreted as compensated demand functions. According to traditional neoclassical consumer theory, Shephard's lemma and the symmetry and negative semidefiniteness of the Slutsky-Hicks matrix can be shown. We shall also see that a convex, continuous, and monotonic preference ordering, which is representable by income compensation functions, can be introduced. It can also be shown that the existence of a compensated equilibrium can be derived within this approach by compensated demand functions. In order to obtain the existence of a compensated equilibrium under less stringent conditions we finally generalize the axioms assuming that a compensated demand correspondence is given.     

Adaptive behavior and the existence of Weizsäcker's long-run indifference curves

Suppose that past consumptions of the first r commodities (r < n) influence present consumption. Then, the long-run demand function to which demand converges maximizes the equilibrium short-run utility function only under very restrictive conditions. The long-run demand functions can be rationalized by a utility function, different from the equilibrium short-run utility function, if and only if the short-run utility function is such that past consumptions of any good that experience, learning, or taste changes is separable from all other goods. The class of such utility functions has been found.     

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.     

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.     

Product R&D Investment Policies in an International Duopoly

This study analyzes the optimal product R&D investment policies of a developed and a developing country in an international Cournot duopoly where firms from these two countries compete through endogenous quality–quantity decisions. We explore a new international trade model by using demand functions derived from utility functions. We find that the optimal product R&D investment policies for both countries are subsidies. This study counters a finding that used Hotelling‐type demand functions and it partially modifies another result that adopted the same demand functions but with an international Bertrand duopoly.     

Modelling money demand for a panel of eight transitional economies

In this article, we estimate money demand functions for a panel of eight transitional economies, using quarterly data for the period 1995:01 1995 to 2005:03. We find that real M1 and real M2 and their determinants, namely real income and short-term domestic interest rate, are cointegrated, both for individual countries as well as for the panel. Long-run elasticities suggest that consistent with theory, real income positively and nominal interest rate negatively impact real money demand. Our test for panel Granger causality suggests short-run bidirectional causality between M1 and M2 and their determinants. Finally, our tests for stability of the money demand functions reveal more cases of unstable money demand functions when M2 is used as a proxy for money demand.     

Equilibrium prices in the Bertrand and Cournot oligopolies

The equilibrium prices for the Bertrand and Cournot oligopolies with product differentiation are compared. If all firms have linear demand and cost functions, and if, in addition, the Jacobian matrix of the demand functions has a dominant negative diagonal, the Cournot equilibrium prices are not lower than the Bertrand ones. The general condition for the comparison of the Bertrand and Cournot equilibrium prices can be derived even if the nonlinearity is involved in the cost and/or demand functions.     

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.     

Simultaneous technologies and demand and supply conditions in international trade

If a country is not small enough to behave as a price taker in its export market, foreign demand conditions must be taken into account when estimating export supply functions. Also, when estimating demand or supply functions, it is desirable to use all prior theoretical knowledge and to estimate these functions jointly with the other demand and supply functions derived from the same technology. This calls for the simultaneous estimation of the technologies of all trading partners. For Canadian exports to the United States, we find that the simultaneous and joint estimation procedures bear heavily on the estimated price elasticities.     

Beyond implicit prices: recovering theoretically consistent and transferable values for noise avoidance from a hedonic property price model

Using a two-stage hedonic pricing methodology we estimate a system of structural demand equations for different sources of transport-related noise. In the first stage, we identify market segments using model-based clustering techniques and estimate separate hedonic price functions (HPFs) for each segment. In so doing, we show how a semiparametric spatial smoothing estimator outperforms other standard specifications of the HPF. In the second stage, we control for non-linearity of the budget constraint and identify demand relationships using techniques that account for problems of endogeneity and censoring of the dependent variable. Our estimated demand functions provide welfare estimates for peace and quiet that we believe to be the first derived from property market data in a theoretically consistent manner.      

Country asymmetry,trade agreements,and transfers

Using a standard 2 × 2 trade agreement model, I show that the welfare effects of a free trade agreement (FTA) depend on the asymmetry on supply and demand functions. When countries are sufficiently asymmetric with respect to the size or the demand functions, the small country tends to be better off, while the large country is worse off. Thus, the small country must compensate the large country for the FTA to be incentive‐compatible. However, in the presence of sufficient asymmetry in the supply functions, the small country is worse off, while the bigger is better off. In this case, the transfer must flow from the large to the small country. This last finding helps explain why some FTAs between rich and poor countries provide for adjustment transfers to the latter.     

Some evidence of Keynes' finance motive

This paper provides evidence from India that firms' demand functions for cash for financial purposes may be quite strong.     

Habit formation and long-run utility functions

This paper extends the work on habit formation of Pollak [Habit formation and dynamic demand functions. J. Polit. Econ. (1970)] and provides a critical counterexample to a conjecture of von Weizsäcker [Notes on endogenous changes of tastes, J. Econ. Theory (1971)] concerning the existence of a “long-run utility function.“ A linear specification of habit formation is applied to a general system of demand functions with linear Engel curves. It is shown that there exists a utility function which rationalizes the long-run demand functions if and only if they are the steady-state solution to a system of short-run demand functions generated by an additive utility function.     

The (in)stability of money demand in the euro area: lessons from a cross-country analysis

The instability of standard money demand functions has undermined the role of monetary aggregates for monetary policy analysis in the euro area. This paper uses country-specific monetary aggregates to shed more light on the economics behind the instability of euro area money demand. Our results obtained from panel estimation indicate that the observed instability of standard money demand functions could be explained by omitted variables like e.g. technological progress that are important for money demand but constant across member countries.     

Balance of Payments Constrained Growth and Developing Countries: An examination of Thirlwall's hypothesis

Thirlwall's hypothesis of balance of payments constrained growth has been widely tested for developed countries, but much less for developing countries. Further, previous tests have used dated estimates derived using non-robust econometric techniques. After discussing the conditions under which Thirlwall's hypothesis would be valid and the econometric issues involved, this study reports error correction estimates of import and export demand functions for a large sample of developing countries. Deriving the long run income elasticities of demand from these functions, the study reports tests for different specifications of Thirlwall's hypothesis on this sample and finds some support for it.     

Excess demand functions with incomplete markets—a global result

The purpose of this paper is to give a global characterization of excess demand functions in a two-period exchange economy with incomplete real asset markets. We show that continuity, homogeneity and Walras’ law characterize the aggregate excess demand functions on any compact price set which maintains the dimension of the budget set.     

Errors of aggregation and errors of specification in a consumer demand model: a theoretical note

Abstract .  Consumer demand models based on the concept of a representative or average consumer suffer from aggregation error. Misspecification of the underlying micro utility-maximizing model, which is virtually inevitable, also results in error. This note provides a theoretical investigation of the relationship between the two types of error. Misspecified expenditure support functions for demand systems at the micro level induce the same misspecified structure in the corresponding expenditure functions at the macro level, and the errors at the two levels are shown to be of similar order.