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.     

Liquidating large security positions strategically: a pragmatic and empirical approach

This article investigates static liquidation strategies for large security positions in illiquid markets. Under the assumption that the liquidation horizon is given exogenously, a discretionary liquidity trader solves for the optimal sales trajectory so as to maximize an objective function that considers the expected liquidation revenues and their standard deviation. Although existing literature tends to focus on theoretical aspects with the intention of deriving closed-form solutions for special types of market impact functions, this article considers a framework that is able to capture important empirical phenomena in the stock market, such as the intraday U-shaped pattern of price impact and the resiliency of the order book. The new model is very flexible since it allows for liquidation intervals of varying length and foregoes the assumption of constant speed of trading. Examples with real-world order book data demonstrate how the setup can be implemented numerically and provide deeper insight into relevant properties of the model.     

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.     

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.     

上市公司资本结构的现状及其优化对策——来自纺织服装行业的实践

资本结构是企业融资决策的核心内容,资本结构是否合理关系到企业经营绩效的高低、财务目标的实现和能否可持续发展。本文基于现代资本结构理论,运用比较分析法剖析了纺织服装上市公司资本结构的现状、问题和形成的内部因素,并提出了优化纺织服装上市公司资本结构的对策。     

几何布朗运动市场中的最优变现策略研究

利用相对价格冲击函数的Box-Cox变换和存在比例交易费用的线性函数,研究了非瓦尔拉斯均衡金融市场上风险资产的价格变现策略,当资产价格变化服从几何布朗运动时,资产变现时间内生情形下投资者最优变现策略问题可以转化为具有随机跳出时间的随机最优控制,通过对带有广义狄利克雷边界条件的贝尔曼方程的粘性求解,可以实现最优变现策略。