This note derives the dynamic programming equation (DPE) to a differentiable Markov Perfect equilibrium in a problem with non-constant discounting and general functional forms. Beginning with a discrete stage model and taking the limit as the length of the stage goes to 0 leads to the DPE corresponding to the continuous time problem. The note discusses the multiplicity of equilibria under non-constant discounting, calculates the bounds of the set of candidate steady states, and Pareto ranks the equilibria.

This paper attempts to provide a balanced view of the neoclassical economists' perspective on trade liberalization, with an emphasis on the agricultural sector. I review the basic arguments in favor of competitive markets in general and free trade in particular. These arguments are based on restrictive assumptions which often fail to hold. Under more realistic assumptions, the arguments in favor of free trade are invalid. Economists remain skeptical of the benefits of trade restrictions, but this is a nuanced judgment, rather than a theoretical certainty. I describe a number of situations where market failures imply that trade restrictions can improve efficiency.

The use of a constant discount rate to study long-lived environmental problems such as global warming has two disadvantages: the prescribed policy is sensitive to the discount rate, and with moderate discount rates, large future damages have almost no effect on current decisions. Time-consistent quasi-hyperbolic discounting alleviates both of these modeling problems, and is a plausible description of how people think about the future. We analyze the time-consistent Markov Perfect equilibrium in a general model with a stock pollutant. The solution to the linear-quadratic specialization illustrates the role of hyperbolic discounting in a model of global warming.

Disagreement over the form of regulation of greenhouse gasses motivates a comparison of market based and command and control policies. More efficient policies can increase aggregate marginal abatement cost, resulting in higher emissions. Multiple investment equilibria and “regulatory uncertainty” arise when firms anticipate command and control policies. Market based policies eliminate this uncertainty. Command and control policies cause firms to imitate other firms’ investment decisions, leading to similar costs and small potential efficiency gains from trade. Market based policies induce firms to make different investment decisions, leading to different costs and large gains from trade. We imbed the regulatory problem in a “global game” and show that the unique equilibrium to that game is constrained socially optimal.

We study a model in which the level of environmental regulation depends on abatement cost, which depend on aggregate levels of investment in abatement capital. Firms are non-strategic. When emissions quotas are not tradable, there are multiple competitive equilibria to the investment problem. Allowing trade in permits leads to a unique socially optimal equilibrium. For a given distribution of investment, allowing trade in permits has an ambiguous effect on the optimal level of regulation. Previous results on coordination games with non-atomic agents are applied to the problem of environmental regulation with endogenous investment in abatement capital.

We compare dynamic taxes and quotas in a stationary environment where a regulator and a non-strategic firm have asymmetric information. The regulator is able to learn about the unknown cost parameter either by using a tax or a quota that is slack with positive probability. With a tax, the information asymmetry is resolved in one period. Optimal learning using a quota is less transparent, though we show that this search problem has a simple solution. In particular, it is never optimal for the regulator to learn gradually. In the first period, he either ignores the possibility of learning, or he tries to improve his information. Regardless of the outcome in the first period, he never experiments in subsequent periods. We use this result to assess the informational advantage of taxes compared to quotas under asymmetric information.

Recent papers show that imperfect property rights to a natural resource--a sector-specific factor--can be a source of comparative advantage. in these models, weaker property rights attract labor--the only mobile factor--to the resource sector, increasing the country's comparative advantage for that sector. If capital in addition to labor is mobile, and if the benefits of capital are non-excludable or if the degree of property rights is endogenous, a deterioration of property rights has ambiguous effects on comparative advantage and on the equilibrium wage-rental ratio.

Recent papers show that imperfect property rights to a natural resource - a sector-specific factor - can be a source of comparative advantage. In these models, weaker property rights attract labor - the only mobile factor - to the resource sector, increasing the country's comparative advantage for that sector. If capital in addition to labor is mobile, and if the benefits of capital are non-excludable or if the degree of property rights is endogenous, a deterioration of property rights has ambiguous effects on comparative advantage and on the equilibrium wage/rental ratio. (c) 2005 Elsevier B.V. All rights reserved.

This paper studies the optimal tariff in a dynamic framework. The effects of the supplier's rationality and of the type of strategy available to the importer are discussed. With rational sellers, the optimal tariff is dynamically inconsistent; the consistent tariff is extremely myopic and may be worse than free trade for the importer. The paper concentrates on the case in which the traded good is a reproducible commodity. This is compared to the situation in which the traded good is a nonrenewable resource. The plausibility of the consistent equilibrium, in the absence of binding commitments, is discussed.