Shadow pricing of labour and capital in an economy with unemployed labour

This paper derives the shadow prices of labour and capital to be used in the public sector in a situation of unemployment. The setting considered is that of a three-good, two-period general equilibrium model. Then shadow prices are compared to their corresponding market prices and shown to closely depend on own and cross-elasticities of supply and demand for labour and investment. In the first part, a rigid wage rate is the sole source of distortion; then, a tax on capital income is introduced so that our formula for the social rate of discount can be contrasted with that of Harberger, Sandmo and Drèze.     

Drèze equilibria and welfare maxima

We present an example of a production economy with incomplete markets, von Neumann–Morgenstern utility functions, and a unique Drèze equilibrium in order to illustrate and explain the following phenomenon. There exists a transfer scheme such that every shareholder’s utility after transfers and share adjustments increases the more the firm deviates from the Drèze equilibrium. However, shareholders’ welfare decreases the further the firm departs from the Drèze equilibrium. Shareholders’ welfare is defined as the sum of their utilities where every utility function is normalized such that the marginal utility of today’s consumption equals 1 at the Drèze equilibrium.     

Discount rates and shadow prices for public investment

This paper extends the Harberger–Sandmo–Drèze model for public discount rates to a many-good economy. It derives a formula for discount rates which are specific to each public enterprise or agency and used by them to discount future outputs and inputs evaluated at market prices. Such an approach is shown to be more efficient than that of simply using a single rate for all public projects. It is also more practical than asking each public firm to use second-best shadow prices in their analyses of investment projects.The general results are first provided; then, simple cases are considered and numerical examples presented to help interpret our formula and analyse its main determinants.     

The probability approach to general equilibrium with production

We develop an alternative approach to the general equilibrium analysis of a stochastic production economy when firms’ choices of investment influence the probability distributions of their output. Using a normative approach we derive the criterion that a firm should maximize to obtain a Pareto optimal equilibrium: the criterion expresses the firm’s contribution to the expected social utility of output, and is not the linear criterion of market value. If firms do not know agents utility functions, and are restricted to using the information conveyed by prices then they can construct an approximate criterion which leads to a second-best choice of investment which, in examples, is found to be close to the first best. We are grateful to participants in the 2006 Public Economic Theory Conference, Hanoi, the 2007 CARESS/COWLES workshop on General Equilibrium at Yale University, the 2007 SAET Conference at Kos, Greece, the NSF/NBER 2007 Conference on General Equilibrium at Northwestern University, and seminars at Rice University, the University of Southern California, Indiana University, and U.C. Davis for helpful comments. We particularly thank Jacques Drèze and David Cass for stimulating discussions, and a referee for helpful suggestions for improving the paper.     

The computation of quantity-constrained equilibria by virtual taxes

A method to compute Drèze equilibria is derived by defining virtual-tax equilibria, giving a constructional proof of the existence of such equilibria and showing the equivalence with Drèze equilibria. Some numerical examples conclude the paper.     

A bargaining theory of the firm

Suppose that a firm has several owners and that the future is uncertain in the sense that one out of many different states of nature will realize tomorrow. An owner’s time preference and risk attitude will determine the importance he places on payoffs in the different states. It is a well-known problem in the literature that under incomplete asset markets, a conflict about the firm’s objective function tends to arise among its owners. In this paper, we take a new approach to this problem, which is based on non-cooperative bargaining. The owners of the firm play a bargaining game in order to choose the firm’s production plan and a scheme of transfers which are payable before the uncertainty about the future state of nature is resolved. We analyze the resulting firm decision in the limit of subgame-perfect equilibria in stationary strategies. Given the distribution of bargaining power, we obtain a unique prediction for a production plan and a transfer scheme. When markets are complete, the production plan chosen corresponds to the profit-maximizing production plan as in the Arrow–Debreu model. Contrary to that model, owners typically do use transfers to redistribute profits. When markets are incomplete, the production plan chosen is almost always different from the one in a transfer-free Drèze (pseudo-)equilibrium and again owners use transfers to redistribute profits. Nevertheless, our results do support the Drèze criterion as the appropriate objective function of the firm.     

A note on monopolistic quantity rationing

It is shown that under incomplete information it may be optimal for a monopolist to ration a single price taker in addition to setting prices, which is in contrast to the case of complete information. As a byproduct it is shown that the star-shaped hull of the offer curve of a price taker exactly consists of the points that can be supported as Drèze-optima.     

Backhouse and Boianovsky on “disequilibrium theory”. A review article of transforming modern macroeconomics. Exploring disequilibrium microfoundations, 1956–2003

Abstract

This article is an in-depth analysis of Backhouse and Boianovsky's book, Transforming Modern Macroeconomics: Exploring Disequilibrium Microfoundations, 1956–2003. I start with questioning Backhouse and Boianovsky's too broad understanding of the disequilibrium approach. Thereby they bring together theories that should be kept separate, those by Patinkin, Clower and Leijonhuvud on the one hand, and those by Barro and Grossman, Drèze and Benassy, on the other. I also substantiate my disagreement with their claim that an inner link exists between fixed price equilibrium theories and imperfect competition modelling. Finally, I put forward a few conjectures about the reason why fixed price modelling petered out.     

How modern economics learned French: Jacques Drèze and the foundation of CORE

The Center of Operations Research and Econometrics (CORE), founded in 1966, was one of the channels through which economic modelling practices were imported from the USA to Europe. Officially modelled after the Cowles Foundation for Economics Research, it reflected Jacques Drèze's broad experiences in the USA during the 1950s when modelling techniques were not yet anchored in disciplines. CORE gained an international reputation, however, through the rather exclusive community of Neo-Walrasian economists represented by Werner Hildenbrand, Jean Gabszewicz, and Gérard Debreu. After this community modified the disciplinary divisions at CORE, the influence of CORE on continental economics occurred mainly through disequilibrium economics, which still represents a “French accent” in modern macroeconomics. At the same time, operations research and econometrics prospered at CORE while receiving scant attention from economists. This essay tells the story of how CORE changed continental economics through the unique career path of its founder, Jacques Drèze.     

Prices,product differentiation and quality measurement: A comparison between hedonic and matched model methods

The paper provides an analysis of the problems of construction of quality-adjusted price indexes within the framework of the theory of product differentiation. In the general case of price-making behaviour on the part of firms, hedonic regressions are defined on the basis of reduced forms of the equation relating equilibrium prices to product characteristics. The paper considers the reduced form given by the marginal cost function and shows that the Laspeyres hedonic price index provides a lower bound to the quality-adjusted rate of price change while the Paasche hedonic price index provides an upper bound to the quality-adjusted rate of price change. The properties of hedonic price indexes are compared with those of matched model indexes. The theory is applied to the study of personal computer prices in Italy during the 1995–2000 period.     

Pricing power supplied on an interruptible basis

This paper deals with Pareto-optimal pricing of an electric utility whose demand is subject to random fluctuations. Its purpose is to extend previous results obtained by Boiteux and Drèze in two directions. First, the maximum power contracted by subscribers is charged instead of the variance of individual consumptions, which makes the model closer to most existing rate structures. Second, subscribers are allowed to choose among several types of supply differentiated by the probability with which their delivery is guaranteed. Most electricity companies are indeed known to supply power on an interruptible basis. In return for a reduction in their electricity bills, some customers give the company the right to cut off part of their supply when demand rises close to generating capacity.     

Average-cost pricing: Some evidence and implications

We present new survey evidence on pricing behavior for more than 14,000 European firms, and study its macroeconomic implications. Among firms that are price setters, roughly 75% respond that their prices are set as a markup on total costs, a business practice termed “full cost pricing”. Only 25% set prices as markups over variable or marginal costs. Moreover, using industry data for the U.S., we find that the correlation between changes in output prices and changes in variable input prices is significantly lower when fixed costs are likely to be more important.Since our results are similar to the findings in the classic and controversial paper of Hall and Hitch (1939) and subsequent survey evidence, we believe it worth studying the implications of full cost pricing for macroeconomics. We first propose a problem for the firm where full cost pricing can arise as optimizing behavior. We embed this problem, featuring an occasionally binding constraint, into a simple general equilibrium model. We show that when the model is hit by a shock that makes the constraint binding, the response of endogenous variables is amplified significantly more than it would be under the unconstrained regime.     

Factor movements with three factors and two goods in the U.S. economy

Ruffin's (1981) theoretical finding that extreme factors must be enemies and the middle factor must be a friend of both extreme factors, with constant product prices, in a three-factor, two-good general equilibrium model, is confirmed empirically for the United States. Results are used to explain the positions factor owners take on issues of factor movement policies.     

Arbitrage and equilibrium with portfolio constraints

We consider a multiperiod financial exchange economy with nominal assets and restricted participation, where each agent’s portfolio choice is restricted to a closed, convex set containing zero, as in Siconolfi (Non-linear Dynamics in Economics and Social Sciences, 1989). Using an approach that dates back to Cass (CARESS Working Paper, 1984; J Math Econ 42:384–405, 2006) in the unconstrained case, we seek to isolate arbitrage-free asset prices that are also quasi-equilibrium or equilibrium asset prices. In the presence of such portfolio restrictions, we need to confine our attention to aggregate arbitrage-free asset prices, i.e., for which there is no arbitrage in the space of marketed portfolios. Our main result states that such asset prices are quasi-equilibrium prices under standard assumptions and then deduces that they are equilibrium prices under a suitable condition on the accessibility of payoffs by agents, i.e., every payoff that is attainable in the aggregate can be marketed through some agent’s portfolio set. This latter result extends previous work by Martins-da-Rocha and Triki (Working Paper, University of Paris 1, 2005).     

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.     

Repetitive risk aversion

We propose a reasonable condition, which we call repetitive risk aversion (RRA), to be imposed on any utility function to account for the observed data on the relationship between the degree of absolute risk aversion and wealth. We deduce this condition from the concept of the fear of ruin (Aumann and Kurz 1977) and show it to be equivalent to the behaviorally meaningful condition that the risk premium is increasing at a non-increasing rate with the size of the bet. We drive mixed risk aversion, which is known to be stronger than standard and thus proper risk aversion, from RRA. We present several economic applications of RRA to demonstrate that it delivers better comparative static results.I am thankful to Jacques Drèze and Louis Eeckhoudt for their comments. I greatly appreciate the comments of an anonymous reviewer of this journal which have resulted in substantial improvement to both the content and presentation of the paper. An earlier version of this paper was presented at seminars at Brown, CORE, Hopkins, HKUST, Yale, and IMS     

Non-connectedness of the set of equilibrium money prices: The static economy

A static economy in which nominal taxes and transfers are balanced, under certain conditions, has a set of equilibrium money prices containing a proper interval. Two examples are given in which the entire set must consist of a proper interval. Then, an example is presented in which the set of equilibrium money prices is not connected. While the set contains a proper interval for balanced fiscal policies, the entire set is not in general a single interval.     

On Choquet prices in a GEI-model with intermediation costs

This article analyses whether the representation of asset prices by Choquet integration can be justified from a general equilibrium point of view. We demonstrate that if transaction costs functionals are increasing in the volume of trade, positive homogeneous and satisfy an additivity condition, the equilibrium price functional typically does not satisfy all the Choquet properties. Whereas subadditivity and positive homogeneity can be shown to hold for the equilibrium price functional, this is generally not the case for monotonicity and additivity of prices for comonotone income streams.     

Price normalization under imperfect competition

In general equilibrium models of imperfect competition the equilibria depend on how prices are normalized. This note shows that a price normalization preserves convexity properties if and only if prices are measured in terms of a fixed commodity bundle. I am grateful to an anonymous referee for helpful comments, inspiring a simplification in the proof of the main result, and the argument in the Remark.