The demand for information: More heat than light

This paper produces a theory of value for Gaussian information with two states and two actions, tracing the solution of the option pricing formula, but for the process of beliefs. We derive explicit formulas for the value of information. The marginal value is convex and rising, concave and peaking, and finally convex and falling. As the price falls, demand is initially zero, and eventually logarithmic. Its elasticity exceeds one, and falls to zero with the price. Demand is hill-shaped in beliefs, zero at extremes. Our results approximate models where information means the sample size for weak discrete informative signals.     

INTEGER PRICING AND BERTRAND-EDGEWORTH OLIGOPOLY WITH STRICTLY CONVEX COSTS: IS IT WORTH MORE THAN A PENNY?

In this paper we analyse the implications of integer pricing for Bertrand Edgeworth oligopoly with strictly convex costs. When price is a continuous variable, there is a generic non-existence of pure-strategy equilibrium. In the case of integer pricing, this is not so. We characterize a set of possible single price equilibria around the competitive price, which if non-empty will constitute the set of single price equilibria if the industry is large enough. Furthermore, we provide an example in which the highest equilibrium price can be arbitrarily far from the competitive price.     

Inflation,oil price volatility and monetary policy

In a fully micro-founded New Keynesian framework, we characterize an analytical relationship between average inflation and oil price volatility by solving the rational expectations equilibrium of the model up to second order of accuracy. The model shows that higher oil price volatility induces higher levels of average inflation. We also show that when oil has low substitutability in the production function, the higher the weight the central bank assigns to inflation in the policy rule, the lower the level of average inflation is. The analytical solution further indicates that, for a given level of oil price volatility, average inflation is higher when marginal costs are convex in oil prices, the Phillips Curve is convex, and the degree of relative price dispersion is higher. The evolution of inflation during the 70s and 80s is consistent with the prediction of the model.     

On Stackelberg games in a homogeneous product market

In a homogeneous product duopoly with concave demand and strictly convex costs we bring together all the standard results of quantity Stackelberg games, provide some new results with price Stackelberg games and compare the equilibrium configuration of the quantity games with the price games. In the price Stackelberg game we show there is a unique SPNE where the leader chooses a lower price than the follower, but both get equal payoffs. We prove that generally quantity Stackelberg games are less competitive than price Stackelberg games. However, we also demonstrate the possibility of a reversal of this result.     

Nonlinearity and asymmetry in the exchange rate pass‐through: What role for nominal price stickiness?

This paper examines the importance of nominal rigidity for nonlinearity and asymmetry of exchange rate pass‐through. For this purpose, we rely on company‐level data of French importing firms. We find that the well established fact that “prices rise faster than they fall,” which is characterized by the convex import price reaction function, lies primarily with the presence of nominal rigidity. Once price stickiness is controlled for, there is empirical evidence that the import price reaction function is rather concave if the linearity assumption can be rejected, indicating that firms aim primarily to protect their market share.     

Linear economies are “gross substitute” systems

The uniqueness of the equilibrium price in linear exchange economies is proved by exploiting their “gross substitute” properties. A necessary and sufficient condition for the uniqueness is that no equilibrium price decomposes the economy. By a familiar mathematical tool — restriction and projection, the demand correspondence becomes a smooth function. We can then apply properties of the Jacobian matrix, which always has a dominant or quasi-dominant diagonal. The combination of convex and differential analysis can be used in piecewise linear economies. The uniqueness of the equilibrium price is a special case of the equilibrium index formula for regular piecewise linear economies.     

Collusive outcomes in price competition

In this paper we provide a sufficient condition for collusive outcomes in a single-shot game of simultaneous price choice in a homogeneous product market with symmetric firms and strictly convex costs. We also prove the counterintuitive result: if the second derivative of the cost function is nonincreasing in output, it is easier to sustain collusion when the number of firms increases.     

A generalized framework for endogenous timing in duopoly games and an application to price-quantity competition

This paper extends the analysis of duopoly market by distinguishing two types of competition: (i) the basic form of competition where each firm is unrestricted in its choice of price and quantity and (ii) the non-basic form of competition where firms’ strategic choices over price and quantity are limited a priori. Our analysis focuses on the former rather than the latter. Under a very general setting of concave industrial revenue and asymmetric convex costs, we show that each firm typically makes more profit in the subgame perfect Nash equilibrium (SPNE) of the leader-follower price-quantity competition, one of the basic competition forms, than in the SPNE of the leader-follower price competition and that each firm always makes more profit under simultaneous move price-quantity competition than under simultaneous move price competition. We establish a generalized framework for endogenous timing in duopoly games which is capable of embodying and overcoming the inconsistency across the existing three frameworks in the field. We highlight the advantages of a 3-period general framework.     

Contributions to Cournot oligopoly theory

This work contributes to a number of questions concerning oligopoly models. In particular, uniqueness of the Cournot equilibrium point is demonstrated under the assumption that either the unit price function is differentiable and the derivative is strictly negative or the cost functions are strictly convex. Also, under the assumption of either strictly decreasing unit price function or strictly convex cost functions, it is shown that (a) the total production level at equilibrium increases with entry of additional players, (b) that cooperation between some of the players necessarily entails profit for the others, and (c) cooperative grouping causes decrease in production levels.     

An export model for the Belgian industry

A two-equation model for the export volume and the export price of the Belgian industry is specified as a convex combination of demand and supply determinants and estimated using Bayesian inference methods. The results indicate that, in the medium run, industrial exports are mainly explained by the behaviour of price taking suppliers.     

Effects of tax benefits on the price elasticity of charitable contributions in South Korea

Using South Korean panel data from 2008 to 2019 and censored quantile regression method, this study calculates the effects of different tax incentives on charitable contributions. We observe price elasticity under two different tax-benefit systems in South Korea and find that, first, taxpayers tend to be more sensitive to tax incentives under a tax deduction system than a tax credit system. The price elasticity gap between a tax deduction and tax credit is approximately −2.3 to −1.0. Second, we show the existence of heterogeneity in taxpayers’ behaviour: the price elasticity of charitable contributions exhibits a convex shape, where more significant donors have lesser reactions to tax incentives. We further show that socioeconomic contexts, such as income, gender, marital status, and education, affect people's attitudes. In sum, the results are as expected: tax deductions work more efficiently than tax credits.     

Price or quantity setting under uncertain demand and capacity constraints: An examination of the profits

This article considers price formation and quantity setting of a capacity-constrained risk-neutral firm facing uncertain demand. It is shown that the optimal price of a price-setting risk-neutral monopolist decreases with demand uncertainty. With a strictly convex demand function expected profits increase with uncertainty for a quantity-setting monopolist whereas expected profits decrease for a price-setting monopolist. Furthermore, similar results on the effect of uncertainty are derived for a differentiated goods industry.     

Economic natural selection in Bertrand and Cournot settings

We study economic natural selection in classical oligopoly settings. When underlying pure strategies consist of a finite number of prices, convex monotonic dynamics always converge under a weak condition to the smallest price in the support of the initial state that exceeds marginal cost. When underlying pure strategies consist of a finite number of quantities, monotonic dynamics always converge under a specific condition to a quantity equal or similar to classical Cournot equilibrium.     

A SPATIAL MODEL OF CARTEL STABILITY: THE INFLUENCE OF PRODUCTION COST CONVEXITY

We uniquely introduce convex production costs into a cartel model involving spatial price discrimination. We demonstrate that greater convexity improves cartel stability and that for sufficient convexity first best locations will be adopted. We show that allowing locations to vary over the game reduces cartel stability but that greater convexity continues to improve that stability. Moreover, when the degree of convexity does not support the first best collusive locations, other collusive locations exist that require less stability and these may either increase or decrease social welfare relative to competition. Critically, these locations that require less stability are more dispersed in sharp contrast to the known result assuming linear production costs.     

Trend-reverting fluctuations in the life-cycle model

Aggregate time series provide evidence of short-term dynamic adjustment that appears to be governed by complex or negative real eigenvalues. This finding is at odds with the predictions of reasonably parameterized, convex one-sector growth models with complete markets. We study life-cycle economies in which aggregate saving depends non-trivially on the distribution of wealth among cohorts. If consumption goods are weak gross substitutes near the steady-state price vector, we prove that the unique equilibrium of a life-cycle exchange economy converges to the unique non-monetary steady state via damped oscillations. We also discuss examples and extensions.     

Matching for teams

We are given a list of tasks Z and a population divided into several groups X _j of equal size. Performing one task z requires constituting a team with exactly one member x _j from every group. There is a cost (or reward) for participation: if type x _j chooses task z, he receives p _j (z); utilities are quasi-linear. One seeks an equilibrium price, that is, a price system that distributes all the agents into distinct teams. We prove existence of equilibria and fully characterize them as solutions to some convex optimization problems. The main mathematical tools are convex duality and mass transportation theory. Uniqueness and purity of equilibria are discussed. We will also give an alternative linear-programming formulation as in the recent work of Chiappori et al. (Econ Theory, to appear).     

Why the Lens Condition Cannot Imply Factor Price Equalization

This paper explains why the lens condition cannot imply the factor price equalization condition when the rank of the factor use matrix is larger than two, but smaller than the number of goods. This arises from production substitution and the degeneration of the convex polyhedrons consisting of the possible output vectors of a country where the factor market is cleared. Two kinds of necessary and sufficient conditions for the factor price equalization condition are given. As a byproduct, a simple proof is given on equivalence between the lens condition and the factor price equalization condition in the case where the rank of the factor use matrix is two.     

Decentralizing Edgeworth equilibria in economies with many commodities

Summary. This paper proves core-equivalence theorems for exchange economies without ordered preferences, defined on locally convex Riesz commodity spaces such that the price space is a lattice. Properness assumptions are borrowed from some recent equilibrium existence results. Received: January 15, 1998; revised version: August 19, 1998     

STORABLE GOOD MARKET WITH INTERTEMPORAL COST VARIATIONS

We investigate a firm's dynamic pricing policy in a storable good market where the cost of production varies over time. In anticipation of a cost increase, the firm selects its prices to affect consumer storage. Price dynamics hinge upon the curvature of demand and the magnitude of the consumer storage cost. When demand is not too convex, the consumers' reluctance to store leads the firm to reduce prices to stimulate consumer storage. This shapes the firm's cost pass-through and the price commitment effects. Our analysis provides a novel explanation for the well-documented puzzling patterns of incomplete and negative cost pass-through.     

Competitive prices for a stochastic input–output model with infinite time horizon

Consider a one-sector stochastic input–output model with infinite time horizon. The technology in each time period exhibits constant returns to scale on positive linear combinations of a finite number of basic input–output pairs. Furthermore, perfect information is available as a filtration generated by finite partitions of the state space. By definition, competitive prices require expected profit maximization in every time period. The Riesz representation of a sequence of competitive price functionals yields a state-price deflator with a supermartingale property. We show that there exists a competitive price system for some feasible program if and only if there is No Free Production (NFP). Furthermore, there exists a competitive price system for a particular program if and only if if NFP holds and the program is short-run efficient. This model includes a securities market model with or without convex cone trading constraints as a special case. Under these circumstances, NFP reduces to No Arbitrage and we recover a version of the fundamental theorem of asset pricing. The author expresses gratitude for the advice of two anonymous referees, one who pointed out the simple way to prove the key lemma and the other who helped integrate the conclusions into the existent literature.