Violation of the Law of Demand

Following the classic work of Mitjuschin, Polterovich and Milleron, necessary and sufficient as well as sufficient conditions have been developed for when the multicommodity Law of Demand holds. We show when the widely cited Mitjuschin and Polterovich sufficient condition also becomes necessary. Using this result, violation regions for the very popular Modified Bergson (or hyperbolic absolute risk aversion) class of utility functions are fully characterized in terms of preference parameters. For a natural extension of the constant elasticity of substitution member of the Modified Bergson family that is neither homothetic nor quasihomothetic, we create the first simple, explicit example of which we are aware that (i) fully characterizes violation regions in both the preference parameter and commodity spaces and (ii) analyzes the range of relative income and price changes within which violations occur.     

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.     

Micro-foundation for a constant elasticity of substitution production function through mechanization

We consider an increase in the range of capital use as a form of mechanization. A constant elasticity of substitution (CES) production function is dynamically derived from Leontief production functions through the endogenous complementary relationship between capital accumulation and mechanization. This implies that a CES production function can be resolved into technological change that does not involve changes in total factor productivity. Furthermore, using the normalizing procedure of the CES production function developed by de La Grandville [de La Grandville, O., 1989. In quest of the Slutsky diamond. American Economic Review 79, 468–481], we investigate how mechanization is related to the elasticity of substitution in our endogenous growth model.     

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.     

Sustainable recursive social welfare functions

What ethical criterion for intergenerational justice should be adopted, e.g., when faced with the task of managing the global environment? Koopmans’ axiomatization of discounted utilitarianism is based on seemingly compelling conditions, yet this criterion leads to hard-to-justify outcomes. The present analysis considers a class of sustainable recursive social welfare functions within Koopmans’ general framework. This class is axiomatized by means of a weak equity condition (“Hammond Equity for the Future”) and general existence is established. Any member of the class satisfies the key axioms of Chichilnisky’s “sustainable preferences”. The analysis singles out one of Koopmans’ original separability conditions (his Postulate 3′a), here called “Independent Present”, as particularly questionable from an ethical perspective.     

General equilibrium models of monopolistic competition: A new approach

We analyze a class of ‘large group’ Chamberlinian monopolistic competition models by applying different concepts of functional separability to the same set of first-order conditions for utility maximization. We show that multiplicatively quasi-separable (MQS) functions yield ‘constant relative risk aversion’ (CRRA), and, therefore ‘constant elasticity of substitution’ (CES), functions, whereas additively quasi-separable (AQS) functions yield ‘constant absolute risk aversion’ (CARA) functions. We then show that the CARA specification sheds new light on: (i) pro-competitive effects, i.e., profit-maximizing prices are decreasing in the mass of competing firms; and (ii) a competitive limit, i.e., profit-maximizing prices converge to marginal costs when the mass of competing firms becomes arbitrarily large.     

Investment criteria for production processes of non-storable goods with periodic demand and constant production constraints

Following Pareto's principles a general economic optimum is worked out for the producer of a non-storable good who has to satisfy a periodic demand with a constant production capacity. It is found that the marginal cost pricing rule applies, with some accommodations when the production capability of the plant is inelastic.A general investment criterion is also obtained, and it is shown that this general criterion can take simplified forms when applied to some well-defined classes of actual production functions.These results should find a broad application in peak-load pricing and in investment policies for such industries as electricity production, railways, telephone, etc.,…, i.e., for producers of non-storable commodities subject to seasonal demand variations.     

The CES‐‐Translog Production Function, Returns to Scale and AES

The translog functional form imposes no a priori restrictions on the substitution possibilities between the factor inputs, by relaxing the assumption of strong separability, and the CES–translog cost function specification allows for testing homothetic technology with Hicks‐neutral technical change. In this paper an n ‐factor CES–translog production function is presented which develops the parameters to directly assess scale effects from those due to technology in the production structure. In addition, by applying Shephard's lemma it was possible to derive the input demand functions, as well as the partial elasticities of substitution and the cross‐partial price elasticities of demand for a generalized CES–translog production structure.     

Consumption externality, efficiency and optimal taxation in one-sector growth model

In an economy with consumption externalities, existing studies find that a competitive equilibrium is efficient in the long run and remains efficient in transitions if preferences are homothetic. This paper revisits the efficiency issue in an otherwise standard one-sector growth model where consumption externalities affect a utility via their effects on the time preference. We find that even if preferences are homothetic, the externality changes the marginal rate of substitution between now and future and leads to a disparity in the intertemporal elasticity of substitution between the centrally planned economy and a decentralized economy. As a result, a competitive equilibrium is inefficient in transition dynamics. We characterize an optimal tax/subsidy structure that enables the allocation in a decentralized economy to replicate the social optimum.     

Uniqueness of asset prices in an exchange economy with unbounded utility

Summary. This paper studies conditions under which the price of an asset is uniquely determined by its fundamental value – i.e., no bubbles can arise – in Lucas-type asset pricing models with unbounded utility. After discussing Gilles and LeRoy's (1992) example, we construct an example of a two-period, representative agent economy to demonstrate that bubbles can arise in a standard model if utility is unbounded below, in which case the stochastic Euler equation may be violated. In an infinite horizon framework, we show that bubbles cannot arise if the optimal sequence of asset holdings can be lowered uniformly without incurring an infinite utility loss. Using this result, we develop conditions for the nonexistence of bubbles. The conditions depend exclusively on the asymptotic behavior of marginal utility at zero and infinity. They are satisfied by many unbounded utility functions, including the entire CRRA (constant relative risk aversion) class. The Appendix provides a complete market version of our two-period example. Received: January 22, 1996; revised version: February 18, 1997     

The Nonparametric Approach to Applied Welfare Analysis

Changes in total surplus are traditional measures of economic welfare. We propose necessary and sufficient conditions for rationalizing individual and aggregate consumer demand data with individual quasilinear and homothetic utility functions. Under these conditions, consumer surplus is a valid measure of consumer welfare. For nonmarketed goods, we propose necessary and sufficient conditions on input market data for efficient production, i.e. production at minimum cost. Under these conditions we derive a cost function for the nonmarketed good, where producer surplus is the area above the marginal cost curve. We are greatful to helpful remarks and comments of the referees and the editor. The work is partially supported by the Spanish Ministry of Science and Technology, through Grant BEC2002-2130, the Generalitat de Catlaunya, through Grant 2005SGR-00454 and the Barcelona Economics Program (CREA).     

Pricing inputs to induce efficient Make-or-Buy decisions

We investigate input pricing regimes that induce efficient Make-or-Buy decisions by entrants when there is constant returns in the production of the input(s) and simultaneous noncooperative price competition in downstream retail markets. Necessary and sufficient conditions for efficient Make-or-Buy decisions are derived. The necessary condition shows that input prices are relevant for Make-or-Buy decisions except under restrictive and often unverifiable assumptions on the demand structure, and that the least informationally-demanding way to ensure efficient Make-or-Buy decisions is to price inputs at marginal cost provided changes in the entrant’s cost have a “normal” effect on the entrant’s profit. The conditions also show that pricing the incumbent’s input at the entrant’s marginal cost always ensures efficient Make- or-Buy decisions. The extent to which input prices can depart from marginal cost while still inducing efficient Make-or-Buy decisions increases with the efficiency differential between the incumbent and entrant and with the demand displacement ratio.      

A differential approach to input-output analysis

The differential production theory approach is applied to input-output analysis under the assumption that each industrial sector behaves as a homothetic cost-minimizing firm. This yields substitution terms which take a simple form under input independence.     

Existence and stability of rational expectation-equilibria in a simple overlapping generation model

We consider a simple overlapping generation model with outside money and one consumption good. For a big class of preference relations, it is shown that globally no self-fulfilling expectation exists (except the trivial one) if the information set contains only past and present prices. Even locally, positive results can be obtained for homothetic preferences only. To get asymptotic stability this class must be restricted again: The elasticity of substitution must be very small. The implications of this are very negative: A Learning process can never reach rationality.     

DIVERSE ORGANIZATIONS AND THE COMPETITION FOR TALENT

We propose a theory of firm production that requires diverse inputs. We show that in a competitive labor market, firms differ in their skill composition. Organizations with higher total factor productivity (TFP) are larger and hire from a broader range of skills. Technological progress leads to an increase of all wages and results in downsizing. Quantifying productivity using our model shows that a constant elasticity of substitution (CES) production function generates unbiased estimates of TFP but biased estimates of marginal product and elasticity of substitution across skills. Our model also generates estimates of the TFP distribution based on CEO compensation alone.     

CES Production Functions and Economic Growth

We examine inconsistencies and controversies related to the use of CES production functions in growth models. First, we show that not all variants of CES functions commonly used are consistently specified. Second, using a simple growth model, we find that a higher elasticity of substitution leads to a higher steady state and makes the emergence of permanent growth more probable. It is also pointed out that the effect of a higher elasticity of substitution on the speed of convergence depends on the relative scarcity of the factors of production. Finally, we discuss possible explanations of variations in the elasticity of substitution.
JEL classification: O 41; O 11     

New measures of factor productivity in Australia: a Sato approach

This article derives new results of the Elasticity of Substitution (ES) between capital and labour and factor productivity for Australia, an economy which experienced major economic reform that substantially increased the flexibility of its labour, product and capital markets throughout the 1980s and 1990s. It employs a Sato production function specification which has unique properties that enable the estimation of capital–labour substitution elasticity and changing marginal productivities through time. These estimates reveal that the substitution elasticity and labour productivity in Australia rose significantly from the mid-1960s and remained elevated during the economic reform period. A novel contribution of this article is the depiction of Australia's production isoquants to convey how combining labour and capital to produce real Gross Domestic Product (GDP) has changed over recent decades.     

PETROLEUM REFINING INDUSTRY: AN ASSESSMENT OF ITS PRODUCTION STRUCTURE*

Cost structure of petroleum refining industry in Kuwait has been examined, with specific focus on factor substitution, and economies of scale and utilisation. This has been done by estimating translog cost functions, both long‐run and short‐run, using annual time‐series data covering the period from 1976 to 1998. The results indicate that the implied production structure is non‐homothetic, and the pattern of scale effect is labour and capital saving but material using. The evidence also supports presence of induced exogenous technical change, which is non‐neutral (labour and capital using, and material saving). The elasticity of substitution between capital and labour is negative, implying that the two inputs are complements. The results also indicate absence of economies and diseconomies of scale in the petroleum refining industry.     

Government spending, capital accumulation and the optimal policy rule: The role of public service capital

In this paper, we modify the Djajić [Djajić, S., 1987. “Government Spending and the Optimal Rates of Consumption and Capital Accumulation,” Canadian Journal of Economics 20, 544–554.] model in such a way that government consumption expenditure provides utility to households via the total stock of government services rather than the government consumption flow alone. By using such a framework, we show that the optimality condition for the public service capital stock is the marginal rate of substitution between public service capital and consumption that equals the intertemporal marginal rate of transformation between the two goods. In addition, we show that the relationship between private consumption and public service capital in a household's utility plays an important role in determining the transitional behavior of relevant variables. We also examine the second-best government consumption expenditure policy. By contrast, in the standard flow specification, e.g., Turnovsky and Brock [Turnovsky, S.J. and Brock, W.A., 1980. “Time Consistency and Optimal Government Policies in Perfect Foresight Equilibrium,” Journal of Public Economics 13, 183–212.], Ihori [Ihori, T., 1990. “Government Spending and Private Consumption,” Canadian Journal of Economics 23, 60–69.], and Turnovsky and Fisher [Turnovsky, S.J. and Fisher, W.H., 1995. “The Composition of Government Expenditure and its Consequences for Macroeconomic Performance,” Journal of Economic Dynamics and Control 19, 747–786.], the second-best government consumption expenditure is decided on the basis that the marginal utility of consumption is equal to the discounted sum of the marginal utility of the government's flow spending.     

The irreversibility effect in environmental decisionmaking

We provide a new, more general, definition for the irreversibility effect and demonstrate its relevance to problems involving environmental and other decisions under uncertainty. We establish several analytical and numerical results that suggest both that the effect holds more widely than generally recognized, and that an existing result (Epstein’s Theorem), giving a sufficient condition for determining whether the effect holds, can be applied more widely than previously indicated, in particular to problems involving intertemporally nonseparable benefit functions. We further show that a low elasticity of intertemporal substitution will however result in failure of the effect.