Optimal pollution taxation in a Cournot duopoly

It is well known that the optimal pollution tax in a competitive industry is equal to the marginal damage inflicted by the pollution. It has also been shown that the optimal pollution tax on a monopoly is less than the marginal damage. In this paper, I derive the optimal pollution tax for a Cournot duopoly. If firms have different production costs, the optimal tax rate may exceed the marginal damage. This is so because the tax may be an effective instrument for allocating production from the less to the more efficient firm. It is also shown that, if one firm has a positive most preferred pollution tax, the sum of consumer and producer surpluses will be declining in the tax at this level.     

International duopoly with overseas production and strategic trade policies

This paper examines the strategic export policies in a reciprocal market model of an international Cournot duopoly where two firms in domestic and foreign countries reciprocally supply their products to other countries through overseas production as well as export. It also considers the fact that the firms must incur export costs in addition to production costs. Thus, this paper shows, among others, that the effects of export policies on firms' output and export choices do not depend on the slopes of firms' reaction curves. It is also shown that firms' total outputs are independent of the export policies, and the optimal domestic and foreign export subsidies are zero (laissez-faire).     

R&D games in a Cournot duopoly with isoelastic demand functions: A comment

In a recent paper, Tramontana (Economic Modelling, 27; 350-357, 2010) investigates the stability properties of a Cournot Duopoly game when the demand function is isoelastic. In this note, we show that for some well known applications of two-stage Cournot games (D. Aspremont and Jacquemin, American Economic Review, 78, 1122-1137, 1988) an isoelastic demand function can guarantee both the existence and the uniqueness of a Nash Equilibrium even in cases where existence is not obtained with linear demands.     

Mixed ownership in a mixed duopoly with differentiated products

We determine optimal privatization in a symmetric differentiated duopoly when the public firms do not bear the full cost of production and hence their objective functions differ from the government’s objective function. In the social optimum firms will generally have mixed ownership, and it will depend on the type of uncovered cost, the degree of substitutability of the two products and the output decision rule of the partially public firms. Different types of mixed duopoly emerge, ranging from both firms being partially privatized, to one being fully privatized. We also derive an optimal tax-subsidy scheme as a substitute for privatization.      

一个具有双寡头垄断性质的三边贸易模型——以石油市场为例的国家福利实验模拟分析

中国作为大宗商品的国际大买家,争取国际定价权已经成为再也无法回避的问题.有鉴于此出,文章以石油为例,着重探讨石油定价战略选择的经济学机理,在一个具有双寡头垄断性质的三边贸易体系中,对OPEC和非OPEC石油输出国之间的博弈进行了一般均衡分析.根据模型设定参数及实验模拟发现,在Cournot双寡头垄断下,国家M的福利水平增加32.4%,而国家F的福利水平却下降0.8%.由此作出的解释是:与M相反,F是石油净进口国家,高油价和商品y较低的相对价格所产生的负面效应要大于闲暇带来的正面效应.此时,整个社会福利下降0.7%.石油在消费者效用函数中的权重较小时,石油生产的一个负向冲击对福利损失的影响非常有限.在F和M的纯策略集合{双寡头垄断,完全竞争,不生产石油}中,存在唯一的纳什均衡{完全竞争,完全竞争},这使得国家H和F从中获益.模型给人的启示是,除了尽快完善国家石油战略储备体系外,中国应积极参与到石油定价权的争夺中,改变目前完全被动承受油价变动影响的不利地位.     

Sunspot Fluctuations in Two-sector Economies with Heterogeneous Agents

We study a two-sector model with heterogeneous agents and borrowing constraint on labor income. We show that the relative capital intensity difference across sectors is crucial for the conditions required to get indeterminacy and endogenous fluctuations. The main result shows that when the consumption good is sufficiently capital intensive, local indeterminacy arises while the elasticities of capital–labor substitution in both sectors are slightly greater than unity and the elasticity of the offer curve is low enough. Locally indeterminate equilibria are thus compatible with a low elasticity of intertemporal substitution in consumption and a low elasticity of the labor supply. As recently shown in empirical analysis, these conditions appear to be in accordance with macroeconomic evidences. We would like to thank R. Becker, J.P. Drugeon and an anonymous referee for useful comments and suggestions. The current version also benefited from a presentation at the conference “Public Economic Theory 04”, Beijing, August 2004.     

Endogenous fluctuations in unionized economies with productive externalities

Summary. We discuss the effects of unions on steady-state multiplicity and welfare, and on the existence of endogenous fluctuations. We consider an OG economy with productive capital externalities and we focus on underemployment equilibria. We find that for wide regions in the parameter space, including an arbitrarily small degree of externalities and a Cobb-Douglas technology, unions increase steady state employment and welfare, and local indeterminacy (sunspots) emerges. Moreover with a CES technology multiplicity of steady states is only possible in the presence of unions. Our results also show that the role of unions in shaping local dynamics and bifurcations depends on technology (externalities and factors substitutability).Received: 16 January 2002, Revised: 18 March 2004, JEL Classification Numbers: E32, J51, D60, D62. Correspondence to: Leonor ModestoThis paper is a much revised version of our former working paper Unions, Increasing Returns and Endogenous Fluctuations. Financial support from Fundação para a Ciência e Tecnologia under the POCTI, is gratefuly acknowledged.     

Using the cost function to generate Marshallian demand systems

Limited data means that prior structure is needed when working with large demand systems. The cost function is a convenient vehicle for generating demand systems incorporating such structure. While the cost function directly yields Hicksian demand functions they will not usually have an explicit representation as Marshallian demand equations i.e. in terms of the observable variables. With fast hardware and modern software, however, this need not hinder the estimation of the (implied) Marshallian demand equations. This paper develops the formal theory for using cost functions in this context, and reports on initial trials on the operational feasibility of the method. First version received: September 1997/final version accepted: July 1999     

A Metzlerian business cycle model with nonlinear heterogeneous expectations

Metzler's model is an important contribution to our understanding of the dynamics of business cycles. In his model, the production of consumption goods depends on expected future sales. However, Metzler assumes that producers are homogeneous and follow a simple expectation formation rule. Taking into account that in reality producers might not only follow several expectation formation rules, but might also even switch between them, we reformulate Metzler's original model. As it turns out endogenous business cycles may emerge within our model, i.e. changes in production and inventory are (quasi-)periodic for certain parameter combinations.     

On local indeterminacy and endogenous cycles in Ramsey models with heterogeneous households

It is well-known that endogenous cycles can occur in Ramsey models with heterogeneous households and borrowing constraints. In this note, we address the issue of robustness in the more general case of endogenous labor supply and we explain the occurrence of local indeterminacy under progressive taxation.