Coalition-proof supply function equilibria in oligopoly

In an industry where firms compete via supply functions, the set of equilibrium outcomes is large. If decreasing supply functions are ruled out, this set is reduced significantly, but remains large. Specifically, the set of prices that can be sustained by supply function equilibria is the interval between the competitive price and the Cournot price. In sharp contrast, when the number of firms is above a threshold we identify (e.g., three if demand is linear), only the Cournot outcome can be sustained by a coalition-proof supply function equilibrium.     

Duopoly competitions with capacity constrained input

This paper focuses on the duopoly substitutability product with an upstream input subjected to capacity constraints. The effects of capacity constraints are captured. Combining competition effect with constraint effect, some interesting conclusions are reached. First, the relationship between capacity constraints and firm size is addressed. We argue that the capacity constraints reduce market size difference and price difference under Cournot. Second, under the Stackelberg case, the existence of solution is proved, and Stackelberg competitions enlarge firm-size difference and price difference if the more efficient firm plays the leading position. When the weaker firm plays the leading position, the conclusions depend on the total capacity. Finally, under the Stackelberg case, when the stronger firm plays the leading position, the firm-size difference and price difference decrease with total input under capacity constraints, which is contrary to the conclusions under Cournot competitions.     

Oligopoly equilibria in electricity contract markets

This paper examines the implications of forward contracting on oligopoly environments by extending the model of Allaz and Vila to an environment with multiple firms and increasing marginal cost. Estimates of key parameters of this model are taken from existing electricity markets to predict the market impact of one round of public contracting, such as those seen in auctions for retail provision and resource procurement. The results imply that, when forward contracts are present, the importance of supplier concentration is greatly magnified relative to other determinants unilateral market power such as demand elasticity.      

Stability of supply function equilibria implications for daily versus hourly bids in a poolco market

We consider a supply function model of a poolco electricity market where demand varies significantly over a time horizon such as a day and also has a small responsiveness to price. Although there are equilibria yielding prices at peak that are close to Cournot prices, it is known that the wider the range of demand uncertainty the narrower the range of such supply function equilibria. Here we show that such equilibria are also typically unstable and consequently would be difficult to sustain in practice. This strengthens the results of Green and Newbery by ruling out many equilibria that have high prices. We demonstrate this result both theoretically under somewhat restrictive assumptions and also numerically using both a three-firm example system and a five-firm example system having generation capacity constraints. Hence, this reinforces the conclusion that the market outcome is significantly influenced by a requirement that offers into the poolco be consistent over the time horizon. This result contrasts with markets where bids can be changed on an hourly basis, where Cournot prices are possible outcomes. The stability analysis has important policy implications for the design of day-ahead electricity markets. The stability perspective also provides a narrowing of the equilibrium selection that strengthens empirical analysis.      

Supply function equilibria of pay-as-bid auctions

This paper characterizes the Nash equilibrium in a pay-as-bid (discriminatory), divisible-good, procurement auction. Demand by the auctioneer is uncertain as in the supply function equilibrium model. A closed form expression is derived for a one shot game. Existence of an equilibrium is ensured if the hazard rate of the demand distribution is monotonically decreasing with respect to the shock outcome and sellers have non-decreasing marginal costs. Multiple equilibria can be ruled out for markets, for which the auctioneer’s demand exceeds suppliers’ capacity with a positive probability. The derived equilibrium can be used to model strategic bidding behavior in pay-as-bid electricity auctions, such as the balancing mechanism of United Kingdom. Offer curves and mark-ups of the derived equilibrium are compared to results for the SFE of a uniform-price auction.      

Portfolio delegation under short-selling constraints

Summary. In this paper we study delegated portfolio management when the manager’s ability to short-sell is restricted. Contrary to previous results, we show that under moral hazard, linear performance-adjusted contracts do provide portfolio managers with incentives to gather information. We find that the risk-averse manager’s effort is an increasing function of her share in the portfolio’s return. This result affects the risk-averse investor’s choice of contracts. Unlike previous results, the purely risk-sharing contract is now shown to be suboptimal. Using numerical methods we show that under the optimal linear contract, the manager’s share in the portfolio return is higher than what it is under a purely risk sharing contract. Additionally, this deviation is shown to be: (i) increasing in the manager’s risk aversion and (ii) larger for tighter short-selling restrictions. As the constraint is relaxed the deviation converges to zero.Received: 25 July 2002, Revised: 12 December 2004, JEL Classification Numbers: D81, D82, J33.Juan-Pedro Gómez: Correspondence toAn earlier version of the paper was circulated under the title “Providing Managerial Incentives: Do Benchmarks Matter?” We are grateful to an anonymous referee whose comments helped to improve the paper. We also thank comments by Viral Acharya, Alexei Goriaev, Ernst Maug, Kristian Rydqvist, Neil Stoughton, Rangarajan Sundaram, Fernando Zapatero and seminar participants at the 1999 SED meetings in Sardinia, the 1999 Workshop in Mutual Fund Performance at EIASM, Brussels, the 2000 EFA meetings in London, the Bank of Norway, the Stockholm Schools of Economics, the Norwegian School of Management and the 2001 WFA meetings in Tucson. Sharma gratefully acknowledges financial support from the Asociacion Mexicana de Cultura.     

Evaluating international financial integration under leverage constraints

The global financial crisis has undermined many economists' views about the benefits of open financial markets. Anecdotal evidence seems to indicate that financial linkages may propagate shocks during crises. This paper develops a simple two-country model in which financial liberalisation across countries takes place in the presence of credit market distortions within countries. Countries may be subject to macro risk coming from productivity shocks and direct shocks to the credit system (‘financial shocks’). Three different degrees of financial linkages between countries are examined. It is shown that the type of financial integration is critical for both macroeconomic outcomes and welfare. In particular, financial integration in bond markets alone may increase aggregate consumption volatility and reduce welfare. Financial integration in both bond and equity markets generates high positive co-movement across countries, but is welfare-improving.     

On the continuous equilibria of affiliated-value,all-pay auctions with private budget constraints

We consider all-pay auctions in the presence of interdependent, affiliated valuations and private budget constraints. For the sealed-bid, all-pay auction we characterize a symmetric equilibrium in continuous strategies for the case of N bidders. Budget constraints encourage more aggressive bidding among participants with large endowments and intermediate valuations. We extend our results to the war of attrition where we show that budget constraints lead to a uniform amplification of equilibrium bids among bidders with sufficient endowments. An example shows that with both interdependent valuations and private budget constraints, a revenue ranking between the two auction formats is generally not possible. Equilibria with discontinuous bidding strategies are discussed.     

A study on Spanish female labour supply with job offer restrictions

This paper analyses female working time taking into account restrictions on hours. Moreover, we compare two different specifications of employment opportunities. The first one assumes that the probabilities of receiving different job offers are constant whereas in the second one we incorporate the hypothesis that these probabilities depend on individual characteristics. The model is estimated using a sample of Spanish women from the Encuesta Piloto sobre Ganancias y Subempleo (1990). The results suggest that incorporating job restrictions is a valuable extension and that individual variables affect the availability of job offers.JEL Classification: J22This paper is based on the second chapter of my Ph. D. thesis defended at the University of Oviedo in December 2000. I am very grateful to Víctor M. Fernández and Jaume García for their valuable help and to Emla Fitzsimons for her linguistic revision of the text. I am also grateful to two anonymous referees for their suggestions that have significantly improved this paper. Any remaining errors are my responsibility. Financial support from the Banco Herrero is gratefully acknowledged.     

A note on budget balance under interim participation constraints: the case of independent types

We provide a simple proof of the equivalence between ex ante and ex post budget balance constraints in Bayesian mechanism design with independent types when participation decisions are made at the interim stage. The result is given an interpretation in terms of efficient allocation of risk.