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.     

Aggregated and disaggregated import demand in China: An empirical study

This paper re-estimates both the aggregated and disaggregated import demand functions for China. We consider six groups of goods for the disaggregated imports based on the Standard International Trade Classification (SITC). The empirical findings from the dynamic ordinary least squares and autoregressive distributed lag regressions indicate that there are positive effects of the domestic income on imports. Second, contrary to theory but in line with previous studies, we obtain negative coefficients for the real effective exchange rate—a real appreciation in the Renminbi (RMB) would reduce import demand. Third, the period of the great global recession is negatively associated with the import demand in China. Fourth, the perception of tail risk negatively affects demand for the aggregated imports and five of six groups for the disaggregated imports. Fifth, the exchange rate reform had a positive impact on the aggregated imports, but our estimations report mixed results for the disaggregated imports. Finally, our results indicate that there is no aggregation bias for import demand in China.     

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.     

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.     

Discrete choice model analysis of mobile telephone service demand in Japan

This paper analyzes the demand for mobile telephones including second generation (2G) and third generation (3G) by using a discrete choice model called a mixed logit model. First, we examine the substitution patterns of the demand for mobile telephones and show that demand substitutability among alternatives is stronger within the provider nest category than within the standard nest category in mobile telephone services. The closest substitute for NTT’s 3G service is NTT’s 2G service, rather than KDDI’s 3G service, for example. Second, we investigate the elasticities of demand for various functions including e-mail, Web browsing, and moving picture delivery. Consequently, we cannot observe marked differences between 2G and 3G services based on these calculated elasticities, indicating that it takes time for 3G subscribers to gain proficiency with such new services.      

Impacts of meat product recalls on consumer demand in the USA

The impact of meat product recall events on consumer demand (beef, pork, poultry, and other consumption goods) in the USA is tested empirically. Beef, pork, and poultry recall indices are constructed from both the Food Safety Inspection Service's meat recall events and from newspaper reports over the period 1982–1998. Following previous product recall studies, recall indices are incorporated as shift variables in consumers’ demand functions. Estimating an absolute price version of the Rotterdam demand model, findings indicate that Food Safety Inspection Service's meat recall events significantly impact demand, and newspaper reports do not. Moreover, although elasticities related to recall events are significant they are small in magnitude relative to price and income effects. Any favourable effects on the demands of meat substitutes for a recall are offset by a more general negative effect on meat demand. The general negative effect indicates a shift out of meat to non-meat consumption goods.     

Competitive equilibrium when preferences change over time

Summary. We show the existence of a competitive equilibrium in an economy with many consumers whose preferences may change over time. The demand correspondence of an individual consumer is determined by the set of subgame-perfect equilibrium outcomes in his intrapersonal game. For additively separable preferences with concave period utility functions that are unbounded above, this demand correspondence will satisfy the usual boundary conditions. Whenever consumers can recall their own mixed actions, this correspondence is convex-valued. This ensures the existence of a symmetric competitive equilibrium.Received: 29 July 2004, Revised: 17 November 2004, JEL Classification Numbers: D51, D91, C73. Correspondence to: Thomas MariottiWe thank Michele Piccione for useful comments and suggestions. The views expressed herein are those of the authors and not necessarily those of the Federal Reserve Bank of Minneapolis or the Federal Reserve System.     

CHANGES IN DEMAND FUNCTION IN COURNOT OLIGOPOLY

Abstract.  The effects of change in the market (inverse) demand function are systematically analysed for Cournot oligopoly without product differentiation. The general comparative-static results are stated using the original data on firms' cost functions and inverse demand function. Three special models are examined in light of our results. The stability condition is shown to be insufficient for determinate comparative statics.     

投资主体决策异质性与货币政策效果差异

本文在对中国近期投资需求现实考察的基础上,构建了各类主体的投资需求新古典模型,根据不同投资主体目标函数和约束条件的差异得出结论:(1)以调整利率(准备金)为主的货币政策对于私营企业固定资产投资、住宅投资具有较大效应,而对于国有企业投资作用相对较小,对于地方政府投资的效应为0,甚至作用相反。(2)以控制信贷规模为主的货币政策对于私营企业投资、家庭具有较明显的作用,对于国有企业投资作用较小,对于政府投资作用非常微小。(3)政府对国有企业上缴利润比例的调整对于国有企业的投资变化具有较强影响,而房地产调控政策如果发挥作用,则对于地方政府投资和住宅投资具有较大效应。     

An analysis of entry-then-privatization model: welfare and policy implications

This study formulates a new model of mixed oligopolies in free entry markets. A state-owned public enterprise is established before the game, private enterprises enter the market, and then the government chooses the degree of privatization of the public enterprise (termed the entry-then-privatization model herein). We find that under general demand and cost functions, the timing of privatization does not affect consumer surplus or the output of each private firm, while it does affect the equilibrium degree of privatization, number of entering firms, and output of the public firm. The equilibrium degree of privatization is too high (low) for both domestic and world welfare if private firms are domestic (foreign).     

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.     

Fire department demand and supply in large cities

The purpose of this study is to estimate demand and production functions for fire fighters provided in major cities. Several factors, including the level of fire losses in the communityper capitaincome, relative wages of fire fighters, population density, city size, and poverty are used in the analysis.

This study differs from earlier ones in two ways. First, multiple measures of community fire losses, instead of the usual one, are used in the analysis. Second, in contrast with earlier studies of fire protection which have typically relied on ordinary least squares regression analysis (OLS) to study either demand or production, this study employs two stage least squares regression analysis (2SLS) to simultaneously estimate demand and production relations.

Evidence is found that demand for fire fighting is affected by both fire losses and relative size of per capitaincome to fire fighter wages. Losses, in turn, are affected by fire fighting hours, by poverty and by density. There is some evidence for economies of scale. The results were consistently found for the variety of loss measures used. The 2SLS results indicated that, as expected, there are simultaneous effects occurring in demand and supply.     

ECONOMIC UNCERTAINTY,MONETARY UNCERTAINTY AND THE DEMAND FOR MONEY IN AUSTRALIA

The demand for money and its stability in Australia has received a great deal of attention in the past and has resulted in its own literature. Depending upon estimation method and period of analysis, previous research has provided mixed findings. By including a measure of economic uncertainty and a measure of monetary uncertainty (both GARCH‐based) in the long‐run money demand for M3, and by using the bounds testing approach under which variables could be stationary or non‐stationary, we provide strong evidence that the M3 money demand in Australia is stable. Both uncertainty measures do have short‐run as well as long‐run effects on the demand for M3 in Australia, factors that previous research did not consider.     

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.     

ESTIMATING IMPORT AND EXPORT DEMAND ELASTICITIES FOR MAURITIUS AND SOUTH AFRICA

In this paper, we re‐estimate the import and the export demand functions for Mauritius and South Africa using time series data. We use the bounds tests for cointegration and find evidence of a long‐run relationship between import demand, income and prices for both countries. Our long run elasticities reveal that domestic income and relative prices have significant effects on the import demand for both countries, with income being the most important determinant. Furthermore, we find that while South Africa's export demand is not responsive to relative prices or income; for Mauritius income is statistically significant.     

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.     

Strategic Product R&D Investment Policy under International Rivalry in the Presence of Demand Spillover Effects

Abstract

We develop a model of product (i.e., quality-improving) research and development (R&D) investment competition in a horizontally differentiated duopoly. In particular, based on a third-country market model, we consider the optimal product R&D investment policy under international rivalry in the presence of demand spillover effects associated with improving the quality level of a product. We show how the optimality of a non-cooperative and a cooperative R&D investment policy depends on the strength of demand spillover effects. Furthermore, we consider the same issues in the case of heterogeneous consumers and alternative utility functions.     

Effective global regularity and empirical modelling of direct, inverse, and mixed demand systems

Abstract .  This paper utilizes the notion of 'effective global regularity' and the intuition stemming from Cooper and McLaren (1996)'s General Exponential Form to develop a family of 'composite' (product and ratio) direct, inverse and mixed demand systems. Apart from having larger regularity regions, the resulting specifications are also of potentially arbitrary rank, which can better approximate non-linear Engel curves. We also make extensive use of duality theory and a numerical inversion estimation method to rectify the endogeneity problem encountered in the estimation of the mixed demand systems. We illustrate the techniques by estimating different types of demand systems for Japanese quarterly meat and fish consumption.     

Demand-Creating R&D in a Symmetric Oligopoly

Spillovers with demand-creating research and development (R&D) activities are investigated by revisiting a widely employed market share rivalry demand structure. Positive technological spillovers may inflict positive or negative side effects on rivals and this has important implications for the effects on innovative efforts of loose or tight R&D cooperation in symmetric oligopolies. A comparison with the effects that apply with linear demand structures and implications for empirical research are also touched upon.     

Consumer cohorts and purchases of nonalcoholic beverages

Age, period and cohort (APC) variables are included in a demand system that is used to estimate Norwegian purchases of nonalcoholic beverages. To take account of censoring, a two-step method is used. In the first step, the probabilities of purchasing milk, carbonated soft drinks and other soft drinks are estimated by probit models. The APC variables are highly significant. Older cohorts have higher probabilities of purchasing milk and lower probabilities of purchasing carbonated soft drinks than younger cohorts. In the second step, the probability density functions and the cumulative density function are used to correct for censoring. In the corrected demand system, there are positive cohort and negative age effects for milk. These effects suggest that the replacement of older by younger cohorts, in an increasingly older population, will result in reduced per capita purchases of milk. For carbonated soft drinks, there are no cohort or negative age effects, while there are positive age but no cohort effects for other soft drinks.