Philippe Michel

First-order necessary conditions for infinite-horizon variational problems

AbstractWe establish rigorously several pointwise or asymptotic firstorder necessary conditions for infinite-horizon variational problems in general form, in the framework of continuous time. We obtain several new results, and we extend to general differentiable Lagrangiansn

Labor Mobility and Redistribution with Evolving Altruism: The Small Economy Case

L(t,x,dot x)

A theoretical measure of environmental efficiency

n some results known only in special cases. To realize this aim, we justify two different ways to associate a family of finite-horizon problems to an infinite-horizon problem.

Economic Consequences of Permits Allocation Rules

Abstract This chapter surveys intergenerational altruism in neoclassical growth models. It first examines Barros approach to intergenerational altruism, whereby successive generations are linked by recursive altruistic preferences. Individuals have an altruistic concern only for their children, who in turn also have altruistic feelings for their own children. Through such a recursive relation all generations of a single family (a dynasty) are linked together by a chain of private intergenerational transfers, countervailing any attempt by the government to redistribute resources across generations. This offsetting of public by private transfers operates only if bequests are positive. This is an important qualification to Barros debt neutrality result. The conditions under which the Ricardian equivalence (debt neutrality) theorem applies are specified. The effectiveness of fiscal policy is further analysed in the context of an economy populated by heterogeneous families differing with respect to their degree of intergenerational altruism. We also examine other forms of dynastic altruism consistent with Barros recursive definition of altruism, ascending altruism and two-sided altruism. These forms could be expected to deliver debt neutrality unconditionally, as families leaving zero bequests could be families characterised by child-to-parent gift under ascending altruism. We find that this is not the case and no form of dynastic altruism therefore ensures debt neutrality without condition. Even under two-sided altruism there are cases, in which both bequests and gifts are constrained and fiscal policy remains effective. We then review ad hoc forms of altruism and their implications for the debt neutrality results. Only one specific form of ad hoc altruism always guarantees debt neutrality; this form departs from the recursive approach underpinning dynastic altruism, with its objective function being formally equivalent to that of the social planner. Extensions to the fields of education and environmental are presented in a final section.