ω‐Homothetic Preferences: Theory and Applications

This paper develops a new class of homothetic preferences which generate Marshallian demand curves for individual goods which can be concave, convex or linear in own price under the assumption that agents treat aggregate price indices as given (as in Dixit‐Stiglitz, 1977). The preferences are represented by a cost function which has two parameters: one determining the curvature of the Marshallian demand; the other determining the elasticity of demand when all prices are equal. The elasticity of demand varies with relative prices. Illustrative examples are given of Cournot duopoly and exchange rate pass‐through.     

Non‐Homothetic Multisector Growth Models

Multisector growth (MSG) models are dynamic versions of computable general equilibrium (CGE) models. Non‐homothetic preference (utility) functions are required for the evolution of factor allocations and industrial structures in accordance with consumption expenditure patterns implied by the non‐unitary income elasticities observed in all budget data since Engel in the 1850s. But comparative static general equilibrium solutions and particularly solving the dynamics of MSG models require explicit specifications of all demand and cost (price) functions. On the demand side, the constant differences of elasticity of substitution (CDES) non‐homothetic indirect utility functions and Roy's identity provide the explicit Marshallian demand functions and budget shares. Sectorial constant elasticity of substitution (CES) cost functions and Shephard's lemma provide the explicit relative commodity price functions and the sectorial cost shares and capital–labor ratios. Walrasian equilibria are given by one equation and the multisector dynamics by three differential equations. Benchmark solutions are given for three cost regimes of a 10‐sector MSG model. History patterns of industrial/allocational evolutions are recognized.     

On the characterization of excess demand functions

Summary. In this paper, we give the necessary and sufficient conditions that characterize the individual excess demand function when it depends smoothly on prices and endowments. A given function is an excess demand function if and only if it satisfies, in addition to Walras law and zero homogeneity in prices, a set of first order partial differential equations, its substitution matrix is symmetric and negative semidefinite. Moreover, we show that these conditions are equivalent to the symmetry and negative semidefiniteness of Slutsky matrix, Walras law and zero homogeneity of Marshallian demand functions.Received: 25 November 2002, Revised: 11 March 2004, JEL Classification Numbers: D11.Marwan Aloqeili: I would like to thank an anonymous referee for helpful comments.     

交易成本对易货经济的影响——瓦尔拉斯均衡“不成立”的一种情形

本文首先用一种新的解析几何方法在易货经济 (即两种商品的纯交换经济 )条件下的一般均衡框架下揭示了价格与消费者的马歇尔需求之间的函数关系。在此基础上 ,由个人承担的交易成本被直接置入。然后 ,本文证明 :如果交易成本的固定项不为零 ,供、求函数将不连续 ;如果同时有非无穷小比例的人口进行同步化决策 ,那么瓦尔拉斯均衡将会被破坏     

Decomposition analysis of consumers' demand changes: an application to Greek consumption data

A decomposition analysis for consumer demand functions is developed. Changes in Marshallian demand or expenditure shares functions over time are decomposed into a total substitution effect, an income effect, and a habit effect. This framework is applied to post-war Greek consumption patterns through a habit persistence version of the Quadratic Almost Ideal Demand System (QUAIDS). It is found that for all commodity categories (i.e., food, beverages and tobacco, footwear and clothing, settling and housing, and others) the income effect was the main driving force in explaining changes in both quantity demanded and expenditure shares, followed by habit and total substitution effects.     

Measuring Welfare Changes and the Excess Burden of Taxation*

This paper examines methods used to evaluate the welfare effects of tax changes, with emphasis on the measurement problems involved. Welfare changes and excess burdens are defined, along with approximations. Aggregate measures, using a social welfare function, are examined. The special case of income taxation is then examined, leading to discussion of the marginal welfare cost of taxation and the marginal cost of funds. The measurement methods examined include the use and estimation of direct and indirect utility functions, along with the algebraic and numerical integration from estimated Marshallian demand functions to the compensated demands. The use of equivalent incomes to examine tax changes, using unit record data from household budget surveys, is then discussed.     

A systematic analysis of the links amongst the Marshallian,Hicksian, and Frischian demand functions: A note

Three types of demand functions are central to contemporary consumer theory: the Marshallian, the Hicksian, and the Frischian demand functions. This paper presents a systematic definition of the analytical relationships amongst these demand functions under the maintained hypothesis that the decision maker is a profit maximizer.     

Global restrictions on the parameters of the CDES indirect utility function

This paper extends the analytical and empirical application of the basic indirect utility function of Houthakker–Hanoch—called the CDES specification (constant differences of elasticities of substitution). The non-homothetic CDES preferences are the natural parametric extension on the global domain of the homothetic CES preferences with many commodities, and CDES can conveniently be used in specifying CGE multisector models with a demand side satisfying observable Engel curve patterns. Moreover, all Marshallian own-price elasticities are no longer restricted to exceed one, and positive and negative cross-price effects are allowed for in empirical demand analyses. Explicit calculations of the Allen elasticities of substitution are instrumental in demonstrating the economic implications of the parameters of indirect utility functions with global regularity properties and flexibility of the derived demand systems.     

Welfare and Distribution Effects of Water Pricing Policies

In this paper, distribution and welfare effects of changes in block price systems are evaluated. A method is discussed to determine, for a Marshallian demand function, equivalent variation in case of a block price system. The method is applied to compare, for the Metropolitan Region of São Paulo, alternative pricing policies on the basis of their demand, welfare and distribution effects of changing water prices. Results show that there is a trade off between average welfare and income distribution. A pro-poor price system may result in lower average welfare than a flat price system, but in higher individual welfare for the poor. Moreover, there is a trade off between revenues for the water company and income distribution. Even though pro-poor price systems may not be as good for average welfare as flat price systems, their direct effects on poverty are important. Introducing pro-poor price systems, however, may have financial consequences for the water companies.     

What Is Supply-and-Demand? The Marshallian Cross Versus Classical Economics

This study argues that the supply-and-demand apparatus of the ‘Marshallian cross’ is an unsatisfactory representation of actual supply and demand forces, which are better characterized in the manner of the classical economists. Most particularly the rising supply function but also the conventional demand function, are shown to have no compelling general theoretical justification. There is no plausible basis for a presumption in favour of the former—other than the marginal productivity theory of factor pricing, which is itself unsatisfactory. Multiple reasons are suggested for the rise of the apparatus of supply-and-demand functions, notwithstanding its intrinsic implausibility. The classical conception of supply-and-demand is restated and reaffirmed.     

A New Approach to Modelling Gnp Functions: an Application of Two-Stage Technologies and Modifying Function Framework

This paper first demonstrates that two-stage technologies together with Lewbel's modifying function framework can provide a general procedure for combining profit functions and nominal value-added functions to obtain new specifications of GNP functions suitable for empirical trade analysis. Next, it illustrates the usefulness of this procedure by proposing a new parametric form of a GNP function in which the derived import demand and output supply systems can be easily constrained to be regular, and the functional structure is parsimonious in the number of additional parameters. We also compare our estimates with those obtained using the familiar Translog flexible form. Results indicate that the proposed procedure is feasible and promising as a tool for generating regular and realistic import demand and output supply equations.     

Disaggregation of excess demand and comparative statics with incomplete markets and nominal assets

Summary. We prove that locally, Walras' law and homogeneity characterize the structure of market excess demand functions when financial markets are incomplete and assets' returns are nominal. The method of proof is substantially different from all existing arguments as the properties of individual demand are also different. We show that this result has important implications and is part of a more general result that excess demand is an essentially arbitrary function not just of prices, but also of the exogenous parameters of the economy as asset returns, preferences, and endowments. Thus locally the equilibrium manifold, relating equilibrium prices to these parameters has also no structure. Received: September 17, 1996; revised version: November 7, 1997     

Reconsidering the welfare cost of inflation in the US: a nonparametric estimation of the nonlinear long-run money-demand equation using projection pursuit regressions

This paper, first, estimates the appropriate, log–log or semi-log, linear long-run money-demand relationship capturing the behavior US money demand over the period of 1980:Q1–2010:Q4, using the standard linear cointegration procedures found in the literature, and the corresponding nonparametric version of the same based on projection pursuit regression (PPR) methods. We then, compare the resulting welfare costs of inflation obtained from the linear and nonlinear money-demand cointegrating equations. We make the following observations: (i) the appropriate money-demand relationship for the period of 1980:Q1–2010:Q4 is captured by a semi-log function; (ii) based on the estimation of semi-log cointegrating equations, the welfare cost of inflation was found to at the most lie between 0.0131 % of GDP and 0.2186 % of GDP for inflation rates between 0 and 10 %, and; (iii) in comparison, the welfare cost of inflation obtained from the semi-log non-linear long-run money-demand function, derived using the PPR method, for 0–10 % of inflation ranges between 0.4930 and 1.9468 % of GDP. However, the standard errors associated with the welfare cost estimates obtained from PPR relative to the linear models tend to indicate that the nonlinear money demand provides more precise estimates of the welfare costs primarily for higher rates of inflation.     

An almost ideal demand system for alcoholic beverages in British Columbia

An almost ideal demand system for alcoholic beverages in British Columbia is estimated based on five beverage categories. Estimates of the model unrestricted and restricted to satisfy homogeneity and symmetry are presented. The restrictions are tested: as is common in applied demand analysis a number of rejections are encountered, although within-equation tests tend to support homogeneity. The rejections which are encountered are not mitigated by the inclusion of dynamic elements. The Slutsky matrix is used to examine the concavity of the expenditure function, which is found to be mildly violated. Marshallian and Hicksian own-, cross-price, and income elasticities are calculated and are found to be largely consistent with previous findings, although some noteworthy results are obtained.     

Exit, sunk costs and the selection of firms

Summary. This paper aims to identify the cost characteristics of exiting firms whenever firms are playing an infinite horizon supergame with time-invariant cost and demand functions. With more than two firms, the problem of which firms exit is quite similar to a coalition formation one. Solving this coalition formation problem, we obtain that the exiting firms are those with higher average cost functions whenever reentry is costless while, whenever reentry is unprofitable, the exiting firms are those with lower marginal (and possibly average) cost functions. Since reentry costs are typically sunk, our analysis points out that the presence of sunk costs affects not only the size (as it is well known) but also the composition of the industry. Received: April 5, 1995; revised version: January 28, 1998     

Sraffa and the Assumption of Constant Returns to Scale: A Critique of Samuelson and Etula

In a recent paper Samuelson and Etula claim to have providedthree examples of the presence of a constant returns to scaleassumption in Sraffa's Production of Commodities. The presentpaper is a refutation of their interpretation of Sraffa's propositions.It shows that they mistakenly take Sraffa's logical propositionsfor empirical propositions. This article also provides evidenceto refute Samuelson's hypothesis that Sraffa consistently confusedthe concept of Marshallian "constant cost" with the generalequilibrium concept of "constant returns to scale". The paperalso argues that Sraffa's prices are not necessarily "equilibrium"prices, and that it is not true that Sraffa maintained thatchanges in demand had no impact on prices; his position appearsrather to be that the impact of demand on prices is unpredictable.     

Strategic trade policy under asymmetric information with screening

The design of strategic rent-extracting trade policies requires information that may be private, such as the cost structure of an industry or parameters of the demand function. As a consequence, under asymmetric information, the design of these policies is problematic. We propose screening menus consisting of different instruments (tariff vs. quota) designed to solve this informational issue. We first use a simple model that examines a Cournot duopoly between a domestic firm and a foreign firm with linear demand and cost functions, with both firms supplying a homogeneous good on the domestic market. In this scenario, if the government does not have information regarding the demand parameter, which is known by both firms, a menu consisting of a rent-extracting tariff for a low demand parameter and a rent-extracting quota for a high demand parameter maximizes the government's objective function. This menu leads the domestic firm to reveal private information. We then generalize this framework to a scenario with imperfect information regarding the firms' marginal cost. Finally, we discuss the issue of quotas generating public revenues and study the case of a menu consisting of a tariff and a free quota.     

Retail Demand for Meat in Australia: A Utility Theory Approach*

This paper examines Australian retail demand for meat for the post-war period 1949-50 to 1978-79. Several systems of demand equations are estimated, each system (comprising equations for beef, mutton, lamb, pork and chicken) being derived from an underlying static utility function. Model selection procedures are used to determine the preferred specifications). The validity of the utility theory approach is investigated by: testing for the presence of autocorrelation; examining the monotonicity and convexity properties of the utility functions; and comparing the estimated price and expenditure elasticities with those of other Australian studies. Serial correlation does arise as a problem, but other results provide support for the theory.     

The Marshallian Market and the Walrasian Economy. Two Incompatible Bedfellows

The aim of this paper is to question a view which is usually taken for granted, namely that the Marshallian partial equilibrium and Walrasian general equilibrium analysis stand in a relationship of continuity. It will be claimed that the contrary is true: the generalisation of the Marshallian market does not lead to a Walrasian economy or, conversely, the Walrasian economy is not composed of Marshallian markets. To bring this point home, the basic methodological choices underpinning the analysis of the Marshallian market and of the Walrasian economy will be compared. The issue of why no full-fledged Marshallian representation of the economy has arisen which might stand as an alternative to the Walrasian account will also be investigated and a series of reasons for this lack of generalisation of the Marshallian market will be considered. Finally, it will be claimed that if the Marshallian economy concept has no explicit existence, it has nonetheless an implicit one. It forms the background against which a series of reasoning about the working of the economy as a whole, which cannot fit the Walrasian economy framework, are developed. No less prestigious names than those of Keynes, Hicks, Patinkin, Friedman, Clower and Leijonhufvud will be adduced as witnesses.     

An application of dynamic specifications of factor demand equations to interfuel substitution in US industrial energy demand

In a recent paper, Jones (1995) [A dynamic analysis of the interfuel substitution in US industrial energy demand. J. Bus. Econ. Stat. 13 (4), 459–465] presents a dynamic analysis of interfuel substitution in US industry energy demand. The author concludes that a dynamic linear logit model is ‘superior' to a comparable dynamic translog model. The latter in fact violates concavity conditions whilst the logit formulation does not. This paper shows first of all that the dynamic formulation of the translog used in Jones (1995) is mis-specified. In fact, a parsimonious error-correction model (ECM) ‘dominates' alternative dynamic formulations, amongst which the partial adjustment mechanism used by the author. The ECM is able to generate optimal estimates of long-run and short-run elasticities, and it satisfies the concavity conditions of the cost function. Further, the theoretical framework used in this paper is the one recently proposed by Urga (1996) [On the identification problem in testing dynamic specification of factor demand equations. Econ. Lett. 52, 205–210] and Allen and Urga (1998) [Derivation and estimation of interrelated factor demands from dynamic cost function. Forthcoming in Economica]. It allows one to identify all coefficients (long-run and short-run) of the dynamic formulation via the joint estimation of the ‘effective' (short-run) cost function and the set of factor demand equations. This strategy solves, amongst other things, the parameter identification problem within the set of demand equations themselves, an issue which was originally noted by Anderson and Blundell (1982) [Estimation and hypothesis testing in dynamic singular equation systems. Econometrica, 1559–1571], re-addressed by Friesen (1992) [Testing dynamic specification of factor demand equations for US manufacturing. Rev. Econ. Stat. LXXIV (2), 240–250] and, more recently, by Urga (1996) and Allen and Urga (1998).