Optimal investment with vintage capital: Equilibrium distributions

The paper concerns the study of equilibrium points, or steady states, of economic systems arising in modeling optimal investment with vintage capital, namely, systems where all key variables (capitals, investments, prices) are indexed not only by time but also by age. Capital accumulation is hence described as a partial differential equation (briefly, PDE), and equilibrium points are in fact equilibrium distributions in the variable of ages. A general method is developed to compute and study equilibrium points of a wide range of infinite dimensional, infinite horizon, optimal control problems. We apply the method to optimal investment with vintage capital, for a variety of data, deriving existence and uniqueness of equilibrium distribution, as well as analytic formulas for optimal controls and trajectories in the long run. The examples suggest that the same method can be applied to other economic problems displaying heterogeneity. This shows how effective the theoretical machinery of optimal control in infinite dimension is in computing explicitly equilibrium distributions. To this extent, the results of this work constitute a first crucial step towards a thorough understanding of the behavior of optimal paths in the long run.     

Environmental taxes with heterogeneous consumers: an application to energy consumption in France

This paper constructs a model with four groups of households who have preferences over labor supply, consumption of polluting (energy related) and non-polluting (non-energy) goods, and emissions. It quantifies the model for the French economy and computes its optimal tax equilibria under nine second-best tax regimes. We find that the redistributive role of environmental taxes requires the polluting goods to be taxed at a rate much below their marginal social damage. These goods may even require an outright subsidy if the society values equality ‘a lot’. Secondly, if environmental taxes that have an exclusively externality-correcting role, they benefit all types—although the gains are rather modest. The gains and losses become more substantial when environmental taxes have a redistributive role as well. Third, setting the environmental tax at its Pigouvian level, rather than its optimal externality-correcting-cum-redistributive level, benefits the high-income group at the expense of the low-income groups. Fourth, nonlinear taxation of polluting goods, and nonlinear commodity taxation in general, is a powerful redistributive mechanism. Fifth, introducing environmental taxes in the current French tax system, with its suboptimal income taxes, results in substantial welfare gains for the highest income group and a sizable loss for the least well-off persons.     

Is the Optimal Labor Income Tax Progressive in a Unionized Economy?*

This paper concerns optimal nonlinear labor income taxation in an economy with union wage setting and endogenous hours of work. The purpose is to study the determinants of tax progression. We show that the optimal degree of progression of the labor income tax depends on the extent to which the government can influence the wage rate via tax policy as well as on its ability to redistribute income across individuals. In addition, the argument for progressive labor income taxation depends on whether hours of work are chosen by the employed themselves or the union.     

Public finance and the optimal speed of transition*

We develop a general equilibrium model that jointly considers the influence of capital accumulation constraints and of labour market frictions on the process of transition. We endogenize the economic and budgetary costs of different government policies and show that, early in transition, governments ought to subsidize state firms. Provided that intertemporal commitment is feasible, this policy limits the initial output fall, which relaxes capital accumulation constraints, accelerates transition, and increases welfare. Moreover, by resorting to indirect – instead of direct – taxes, governments can bring the path of transition closer to the first best. Yet, political pressures may induce a policy of suboptimal subsidization.     

Short sales, price pressure, and the stock price response to convertible bond calls

The announcement of a convertible bond call is associated with an average contemporaneous abnormal stock price decline of 1.75% and an ensuing price recovery in the conversion period. A price fall and the subsequent recovery suggest price pressure as the explanation for the announcement effect. However, in general the option to convert is not exercised early and hence, the increase in the number of shares outstanding does not occur at the announcement date. Instead, this paper argues and provides evidence that hedging-induced short selling causes at least part of the short-run price pressure.     

On the smoothness of optimal paths II: some local turnpike results

We study the local turnpike property for two classes of infinite-horizon discrete-time deterministic maximization problems which have common applications, e.g., optimal growth theory. We follow a functional-analytic approach and rely on an implicit function theorem for the space of the sequences which converge to zero. We shall assume the existence of an optimal path which is not necessarily a steady-state. Relying on material developped in Blot and Crettez (Decis Econo Finance 27:1–34, 2004), “On the smoothness of optimal paths” Decis Econ Finance, 21:1–34, 2004), we provide conditions under which a variation in the initial conditions (i.e., capital stock and discount rate) yields an optimal solution which converges toward a reference solution when time becomes infinite. We also provide new results on bounded solutions of difference equations. We gratefully thank the editor, Silvano Holzer, and two anonymous referees for remarks and advices on a previous version of this paper.     

试论企业的终端营销攻略

本文分析了销售终端在企业经营战略中的重大意义，并主要以海尔为例对当今市场经济条件下企业销售终端的建立，提出了若干思路和建议。