This paper is concerned with tax policies designed to obtain an improved competitive allocation in the presence of consumption externalities. It is known that the full optimum can, in general, be attained only through the imposition of excise taxes at different levels for different individuals. Since these may be ruled out (possibly because of implementation costs), one is confined to consider second-best taxes. The common interpretation of the Pigouvian principle has called for taxes on the externality-creating commodities. With no relationships between the consumption of different commodities the Pigouvian principle is obviously impeccable. But the existence of substitutes or complements for an externality-causing commodity raises the possibility of indirect policies: treating the externality through the markets for related goods. Obviously, if the direct policy is not feasible, the indirect treatment may provide some partial remedy. We show, however, that even when direct policies are available, the overall optimum may involve only indirect policies. An example with such a result is provided in the paper. We also list a number of cases in which the traditional prescription is confirmed, and the overall optimum involves only direct policies.

Taxation of capital gains at realization may distort individuals' decisions regarding holding or selling during an asset's lifetime. This creates the problem of designing a tax structure for capital gains so as to induce efficient patterns of holding an selling. Several tax structures are explored in this paper. Linear taxation, at rates which rise with the holding period, can achieve the first best, even under the conditions of limited information that we postulate. The form of the optimal tax is independent of the stochastic structure of rates of return. We also derive the optimal nonlinear tax under the constraint that it be independent of the holding period. Second-best tax rules are examined. Results in a two-period model are contrasted with those in a continuous time framework. Also treated is the case in which the returns to the asset under consideration depend on the aggregate quantity invested

Taxation of capital gains at realization may distort individuals' decisions regarding holding or selling during an asset's lifetime. This creates the problem of designing a tax structure for capital gains so as to induce efficient patterns of holding an selling. Several tax structures are explored in this paper. Linear taxation, at rates which rise with the holding period, can achieve the first best, even under the conditions of limited information that we postulate. The form of the optimal tax is independent of the stochastic structure of rates of return. We also derive the optimal nonlinear tax under the constraint that it be independent of the holding period. Second-best tax rules are examined. Results in a two-period model are contrasted with those in a continuous time framework. Also treated is the case in which the returns to the asset under consideration depend on the aggregate quantity invested

Tournaments, reward structures based on rank order, are compared with individual contracts in a model with one risk-neutral principal and many risk-averse agents. Each agent's output is a stochastic function of his effort level plus an additive shock term that is common to all the agents. The principal observes only the output levels of the agents. It is shown that, in the absence of a common shock, using optimal independent contracts dominates using the optimal tournament. Conversely, if the distribution of the common shock is sufficiently diffuse, using the optimal tournament dominates using optimal independent contracts. Finally, it is shown that for a sufficiently large number of agents, a principal who cannot observe the common shock but uses the optimal tournament does as well as one who can observe the shock and uses independent contracts.

Tournaments, reward structures based on rank order, are compared with individual contracts in a model with one risk-neutral principal and many risk-averse agents. Each agent's output is a stochastic function of his effort level plus an additive shock term that is common to all the agents. The principal observes only the output levels of the agents. It is shown that, in the absence of a common shock, using optimal independent contracts dominates using the optimal tournament. Conversely, if the distribution of the common shock is sufficiently diffuse, using the optimal tournament dominates using optimal independent contracts. Finally, it is shown that for a sufficiently large number of agents, a principal who cannot observe the common shock but uses the optimal tournament does as well as one who can observe the shock and uses independent contracts.

[Our tax system was designed for an economy with little or no inflation. The current paper shows that inflation causes capricious changes in the effective rate of tax on capital income and therefore in the real net rate of return that savers receive. This is not only a temporary disequilibrium effect but one which persists in steady-state equilibrium. Unlike earlier papers by Feldstein and by Green and Sheshinski, the current study recognizes that firms finance investment by both debt and equity in a ratio that depends on the tax rates and on the rate of inflation.]

This paper is concerned with tax policies designed to obtain an improved competitive allocation in the presence of consumption externalities. It is known that the full optimum can, in general, be attained only through the imposition of excise taxes at different levels for different individuals. Since these may be ruled out (possibly because of implementation costs), one is confined to consider second-best taxes. The common interpretation of the Pigouvian principle has called for taxes on the externality-creating commodities. With no relationships between the consumption of different commodities the Pigouvian principle is obviously impeccable. But the existence of substitutes or complements for an externality-causing commodity raises the possibility of indirect policies: treating the externality through the markets for related goods. Obviously, if the direct policy is not feasible, the indirect treatment may provide some partial remedy. We show, however, that even when direct policies are available, the overall optimum may involve only indirect policies. An example with such a result is provided in the paper. We also list a number of cases in which the traditional prescription is confirmed, and the overall optimum involves only direct policies.

Our tax system was designed for an economy with little or no inflation. The current paper shows that inflation causes capricious changes in the effective rate of tax on capital income and therefore in the real net rate of return that savers receive. This is not only a temporary disequilibrium effect but one which persists in steady-state equilibrium. Unlike earlier papers by Feldstein and by Green and Sheshinski, the current study recognizes that firms finance investment by both debt and equity in a ratio that depends on the tax rates and on the rate of inflation.