Transfer price and equilibrium in multidivisional firms: an examination of divisional autonomy and central control

The problem faced by a firm that oversees two divisions, one of which produces and one of which uses an intermediate good, is considered. Since divisions have information that is not available to the centre, it is useful to allow the divisions some autonomy in their sales and procurement decisions. The analysis allows the centre to specify the transfer price that must be used in trades between divisions as well as placing restraints on their ability to trade with outside firms. In most of the models presented in this paper, the centre cannot observe the market price of the intermediate product, and in some models it cannot observe divisional costs. It is shown how the centre can obtain the full information solution in the simplest case by using a penalty factor that encourages internal trade. However, when divisional costs are not observable, the full information outcome is not obtainable. In this case, the optimal value of the penalty factor implies a tradeoff between the benefits of allowing divisions to act to take advantage of price opportunities in outside markets and savings in transactions costs of trades between divisions.     

Location equilibrium with asymmetric firms: the role of licensing

It is known that if exogenous cost heterogeneities between the firms in a spatial duopoly model are large, then the model does not have a pure-strategy equilibrium in location choices. It is also known that when these heterogeneities are stochastically determined after firms choose their locations, spatial agglomeration can appear. To tackle these issues, the current paper modifies the spatial framework by allowing firms to exchange the cost-efficient production technology via royalties. It is shown that technology transfer guarantees the existence of a location equilibrium in pure strategies and that maximum differentiation appears in the market.     

Measuring market power when firms price discriminate

We propose conduct parameter-based market power measures within a model of price discrimination, extending work by Hazledine (Econ Lett 93:413–420, 2006) and Kutlu (Econ Lett 117:540–543, 2012) to certain forms of second-degree price discrimination. We use our model to estimate the market power of US airlines in a price discrimination environment. We find that a slightly modified version of our original theoretical measure is positively related to market concentration. Moreover, on average, market power for high-end segment is greater than that of low-end segment.     

Optimal inventories and equilibrium price behavior

This paper departs from the established tradition of equilibrium inventory theory by examining the relationship between inventories and market prices when production is instantaneous but distribution is costly. Inventory holdings are not buffer stocks and do not facilitate production smoothing; rather, production variability exceeds the variability of final sales. Voluntary holdings of marketable finished goods are not restricted to occasional “speculation” during periods of unexpectedly low demand, but may persist even when capital losses are anticipated. In these respects, the paper reconciles important features of the inventory decision problem with the results of modern investment theory.     

Endogenous fixprices and sticky price adjustment of risk-averse firms

A risk-averse price-setting firm which knows the quantity demanded at the status quo price but has imperfect information otherwise may choose not to change it although an otherwise identical risk-neutral firm would do so, provided the variance of the firm's subjective probability distribution over quantities demanded as a function of price displays a kink at the status quo. This is equivalent to risk aversion of order one. When no such endogenous fixprice exists, the size of price adjustment still tends to zero as risk aversion tends to infinity, and to any arbitrarily small menu cost there exists a degree of risk aversion so that the firm will not adjust.     

Asymmetric capacity constraints and equilibrium price dispersion

Price dispersion arises despite perfect information about prices. In equilibrium the higher capacity firm adopts a high-price, high-availability strategy, the lower capacity firm adopts a low-price, low-availability strategy, and consumers are more likely to shop at the high-price firm.     

Endogenous uncertainty in a general equilibrium model with price contingent contracts

Summary This paper views uncertainty and economic fluctuations as being primarily endogenous and internally propagated phenomena. The most important Endogenous Uncertainty examined in this paper is price uncertainty which arises when agents do not have structural knowledge and are complelled to make decisions on the basis of their beliefs. We assume that agents adopt Rational Beliefs as in Kurz [1994a]. The trading of endogenous uncertainty is accomplished by using Price Contingent Contracts (PCC) rather than the Arrow-Debreu state contingent contracts. The paper provides a full construction of the price state space which requires the expansion of the exogenous state space to include the state of beliefs. This construction is central to the analysis of equilibrium with endogenous uncertainty and the paper provides an existence theorem for a Rational Belief Equilibrium with PCC. It shows how the PCC completes the markets for trading endogenous uncertainty and lead to an allocation which is Pareto optimal. This paper also demonstrates that endogenous uncertainty is generically present in this new equilibrium.This research was supported in part by the Fondazione Eni Enrico Mattei of Milan, Italy, and by the National Science Council of Taiwan. The authors thank Carsten K. Nielsen for valuable suggestions.     

Existence of an equilibrium in first price auctions

Summary We study the first price auction game with an arbitrary number of bidders when the bidders' valuations are independent from each other. In technical words, we work within the independent private value model. We show that if the supports of the valuation probability distributions have the same minimum and if this minimum is not a mass point of any of these distributions, then a Nash equilibrium of the first price auction exists. We then modify the first price auction game by adding a closed interval of messages. Every bidder has to send a message with the bid he submits. These messages are used in the resolution of the ties. The winner of the auction is chosen randomly among the highest bidders with the highest value of the message among the highest bidders. In the general case, we prove the existence of a Nash equilibrium for this augmented first price auction.I wish to thank Mamoru Kaneko and a referee for their comments on an earlier draft.     

Asset price bubbles in Arrow-Debreu and sequential equilibrium

Summary. Price bubbles in an Arrow-Debreu equilibrium in an infinite-time economy are a manifestation of lack of countable additivity of valuation of assets. In contrast, the known examples of price bubbles in a sequential equilibrium in infinite time cannot be attributed to the lack of countable additivity of valuation. In this paper we develop a theory of valuation of assets in sequential markets (with no uncertainty) and study the nature of price bubbles in light of this theory. We define a payoff pricing operator that maps a sequence of payoffs to the minimum cost of an asset holding strategy that generates it. We show that the payoff pricing functional is linear and countably additive on the set of positive payoffs if and only if there is no Ponzi scheme, provided that there is no restriction on long positions in the assets. In the known examples of equilibrium price bubbles in sequential markets valuation is linear and countably additive. The presence of a price bubble means that the dividends of an asset can be purchased in sequential markets at a cost lower than the asset's price. We present further examples of equilibrium price bubbles in which valuation is nonlinear, or linear but not countably additive.     

A martingale characterization of equilibrium asset price processes

Summary. Bick (1987,1990) and He and Leland (1993) demonstrated that not every arbitrage-free Markovian diffusion price process is consistent with an equilibrium approach. We propose a unified framework for these results and we derive a new martingale characterization of equilibrium.     

A general existence theorem for equilibrium price dispersions

This paper presents sufficient conditions for the existence of non-degenerate equilibrium price dispersions in economies with sequentially searching consumers. This existence result is obtained by fully utilizing the fixed-point property of equilibrium price dispersions. Compared with the existing literature, the formal framework used in this paper is very general. Consequently, the results of the paper are valid for a large class of economic models.     

On price competition with complementary goods

We consider a duopoly industry with two separate firms each selling an indivisible product. The joint consumption of these goods has a specific value for the consumers which exceeds the mere addition of utilities when products are consumed in isolation: the higher this excess, the larger the complementarity between the goods. We analyse price equilibria in this market as related to the degree of complementarity existing between the two products.     

On games with identical equilibrium payoffs

Summary. This paper compares the sets of Nash, coalition- proof Nash and strong Nash equilibrium payoffs of normal form games which are closely related. We propose sufficient conditions for equivalent or closely related games to have identical sets of equilibrium payoffs. Received: April 23, 1999; revised version: November 23, 1999     

Continuity of the first price auction Nash equilibrium correspondence

Summary. Despite the complexity of the first price auction in the general asymmetric case, analytical results have started to emerge in the literature. Authors have also searched to gain insights by computing numerical estimates of the equilibria for some probability distributions of the valuations. This paper proves that the Nash equilibrium of the first price auction depends continuously, for the weak topology, on the valuation distributions and thus brings robustness to the numerical results as well as some theoretical results. As an example of application, we disprove a conjecture of comparative statics. Received: February 1, 1999; revised version: July 27, 2001     

Regulating a multi-product monopolist

The purpose of the present paper is to construct a regulatory scheme that serves to correct suboptimal behavior of a multi-product monopolist in a situation of doubly asymmetric information, where the regulator cannot observe the monopolist's cost structure and consumers' preference while the monopolist cannot identify consumer types. We construct a tax scheme that induces the monopolist to offer socially optimal qualities to all types of consumers and discuss some interesting features of the scheme.The authors gratefully acknowledge the helpful comments of two anonymous referees.     

Wage and price controls in the equilibrium sequential search model

In this paper, we study the effects of wage and price controls on employment, output, and welfare in a simplified version of the Bénabou (J. Econom. Theory 60 (1993) 140) equilibrium sequential search model with bilateral heterogeneity. We show that a price ceiling increases output but the change in welfare depends on three effects: the reduction in aggregate search costs, the increase in surplus due to increased output, and the transfer of production to the least efficient firm. The model is formally identical to a standard equilibrium search model of the labor market so analogous results hold for the minimum wage.     

Keynesian unemployment as a nash equilibrium with endogenous wage/price setting: An example

A simple 3 good, 1 consumer, 1 firm model of fixed price, quantity constrained equilibrium is developed. A game is then defined on the set of (globally unique) equilibria. The consumer sets the money wage, the firm sets the money price of output (money is numeraire). Nash solutions of the game exist and may involve Keynesian unemployment but never involve Classical unemployment or Repressed inflation.