Nash-equilibria in a heterogeneous oligopoly with fuzzy information

We consider a model of an oligopolistic market with heterogeneous firms and products where neither the cost nor the demand functions are common knowledge. Instead, each firm only has some vague ideas about the price strategies adopted by its competitors which is modelled by a fuzzy set. In analogy to the notion of an "equilibrium of actions and beliefs" we define and characterize a generalized Nash-equilibrium and show its existence under general conditions. Furthermore, the impact of the fuzzy information on the equilibrium outcome is analyzed by means of a comparative static analysis within a particular model framework.Received: 28 May 2002, Accepted: 25 December 2002, JEL Classification: D43, D80, L13We wish to thank Bernhard F. Arnold, the editor Murat Sertel , and two anonymous referees for helpful comments. Of course, we are responsible for all remaining errors.     

De produktiestructuur van Nederland in de periode 1950-1966

Summary In 1961 Arrow, Chenery, Minhas and Solow presented their C.E.S. production function, which was based on the relation between the real wage rate and the average labour productivity. They argued that, if the aggregate production function is continuous, lineair and homogeneous, then, with perfect competition and profit maximalization prevailing, the relation between the real wage rate and the average labour productivity is reflection of the production structure. This relation can, therefore, be used for specifying the production structure.In the present paper, the same line of thought is applied to the Dutch economy. Several hypotheses on the relation between wage rate and average labour productivity are tested. Statistically, it turns out that in the Dutch economy the elasticity of substitution between capital and labour is not a constant: it declines with increasing capital-labour ratio. Two statistically acceptable production equations that have this feature are presented.The efficiency parameter appearing as an integration constant in both production equations shows a decline: with labour productivity constant, the capital-labour ratio is falling over time. This means that the relation between labour productivity and capital-labour ratio shifts over time. Another outcome of this study is that technical progress is capitalaugmenting and that it brings about 50 percent of the growth in the labour productivity.De schrijvers zijn dank verschuldigd aan Prof. Dr. F. J. de Jong voor zijn stimulerende kritiek en aan de heren J. G. Althuis, F. J. van Bolhuis, J. D. Flikweert, H. Jager en B. S. Wilpstra, assistenten bij de afdeling Algemene Economie van de Economische Faculteit der Rijksuniversiteit te Groningen, voor hun bereidwillige medewerking aan dit onderzoek.     

Pricing, learning, and strategic behavior in a single-sale model

Summary. We analyze an infinite horizon model where a seller who owns an indivisible unit of a good for sale has incomplete information about the state of the world that determines not only the demand she faces but also her own valuation for the good. Over time, she randomly meets potential buyers who may have incentives to manipulate her learning process strategically. We show that i) the seller's incentives to post a high price and to experiment are not necessarily monotonic in the information conveyed by a buyer's rejection; and ii) as the discount factors tend to one, there are equilibria where the seller always ends up selling the good at an ex-post individually rational price. Received: January 6, 1999; revised version: July 15, 2000     

The effect of fertility on labour force participation: The Spanish evidence

Abstract. The aim of this paper is to estimate the effect of fertility on the decision of labour force participation of married females in Spain, allowing for the existence of unobserved characteristics that affect both fertility and participation. We use a pooling of five waves of the European Household Panel for Spain (1994–1998). Results indicate that not taking into account the unobserved characteristics that affect both variables imposes on average a strong downward bias on the true effect of fertility on participation. This bias is especially strong for highly educated females. We are grateful to Raquel Carrasco and an anonymous referee for helpful comments. Financial support from Gobierno Vasco (PI-1999-160)), Ministry of Education and Science (BE2000-1394), Instituto de la Mujer and Universidad del País Vasco (UPV 00035.321-13511/2001) is gratefully acknowledged.     

Long memory in volatilities of German stock returns

We show that there is strong evidence of long-range dependence in the volatilities of several German stock returns. This will be done by applying a method using the difference of the classical log-periodogram regression estimator for the memory parameter and of the tapered periodogram based estimator. Both estimators give similar values for the memory parameter for each series and this indicates long memory. To support our findings we apply also a methodology using the sample variance and a wavelet based estimator to the data. Also these two methods show clear evidence of long-range dependence in the volatilities of German stock returns.First version received: December 2001/Final version received: March 2003The computational assistance of Eleni Mitropoulou and Björn Stollenwerck as well as the helpful comments of two unknown referees are gratefully acknowledged. Research supported by Deutsche Forschungsgemeinschaft under SFB 475. Stock returns were obtained from Deutsche Finanzdatenbank (DFDB), Karlsruhe.     

Fit performance of several programs used for non-linear least squares problems

Seven computerprograms for non-linear regression or curve fitting problems are compared. The comparison of the programs, running in different computing centra, is restricted to the fit performance. Six model functions are fitted according to the least squares criterion to data series, arising from practical work. The special least squares minimization programs turned out to be better suited for these problems than general optimizing programs.     

Income Distribution, Taxation, and the Private Provision of Public Goods

This article investigates the role of taxation when public goods are privately provided. Externalities between consumers via the public good are shown to cause kinks in social indifference curves. As a result, a government restricted to income taxation should engineer enough inequality to ensure there are some non-contributors to the public good. Whether commodity taxation changes this conclusion depends on the extent to which consumers "see through" the government budget constraint. If they can, inequality should still be sought. When they cannot, in contrast to the case of an economy with only private goods, commodity taxation can be used in conjunction with income transfers to achieve the first-best.     

Technology-forcing through environmental regulation

This paper analyzes the demand characteristics of innovation in pollution abatement and the interaction between a regulator and a polluter under a technology-forcing policy. Important demand-driven determinants of innovation in pollution control are examined, such as uncertainties surrounding unexplored technologies, the length of the compliance period and the maximum abatement costs the regulator is willing to accept. We derive the formal condition that the regulator balances the marginal utility of emissions reduction against the marginal disutilities of a longer compliance time and the increased uncertainty about the feasibility of a more stringent standard.     

Regulation of Mobile Telephony across the European Union: An Empirical Analysis

In this paper I analyze the impact of regulatory policy on prices and demand for mobile telecommunications services across the European Union. I estimate a reduced form model of the mobile industry using panel data for the EU countries from 1998 to 2002. Among others, I find the following effects: liberalization of fixed telephone lines has a negative impact on prices and a positive impact on the demand for mobile services, and the introduction of mobile number portability has a negative impact on prices.*I am grateful to Toker Doganoglu, Gerd Hansen, Eric Kodjo Ralph, Guido Friebel, participants at the 30th EARIE Conference 2003, the 2nd International Industrial Organization Conference 2004 and the 19th Annual Congress of the EEA 2004, and anonymous referees for valuable comments. I would like to acknowledge the generous financial support from the Volkswagen Stiftung and the Munich Graduate School of Economics which made this research possible. All errors are mine.1 Source: European Commission (1994).