Swedish lottery bonds offer a unique opportunity to study ex-day effects in an environment where cash distributions are tax-advantaged relative to capital gains. Thus, in the lottery bond market, we observe a reversal of the preference for capital gains that researchers have cited as an explanation for the ex-day behavior of U.S. equities. Further, in this market there are barriers to short-term arbitrage when prices do reflect the tax preferences of individual investors. We find the bonds are priced around the ex-day to reflect differential tax rates on income and capital gains consistent with the prevailing tax regimes. The bonds consistently experience negative returns over the coupon payment period, and in fact often sell at negative yields prior to the cash distribution, as one would expect given tax-motivated trading between high-tax investors, who buy prior to the distribution, and low-tax investors, who buy after the distribution.

[The core is the set of all unblocked allocations. Implicit in this definition is the idea that if an allocation is proposed which could be blocked, some coalition will form and issue a counterproposal which it can enforce. A process of successive counterproposals based on this idea is shown to converge in a finite period of time (amost surely) to the core.]

[The existence of an equilibrium is proven for a two-period model in which there are spot transactions and futures transactions in the first period and spot markets in the second period. Prices at that date are viewed with subjective uncertainty by all traders. This introduces the possibility of speculation. Conditions for the existence of a competitive equilibrium include restriction on the nature of price expectations.]

I. Introduction, 138. — II. Outline of Arrow's model and results, 138. — III. Public goods, 139. — IV. Expenditures as produced commodities, 140. — V. Examples, 142. — VI. Conclusion, 144.

This paper formulates the notion of stochastic equilibria as invariant probability distributions consistent with the behavior patterns of individuals and the disequilibrium adjustment mechanism of the economy. Conditions for existence, uniqueness, and stability of such equilibria are examined. WE CONSIDER A CLASS of problems in this paper in which the economic environment is stochastic. We will be concerned primarily with developing an equilibrium concept for general equilibrium models of this type. However the essential ideas can be carried over directly to partial equilibrium applications. The choice of the specific general equilibrium model used results primarily from a desire to facilitate comparisons with earlier work on alternative equilibrium concepts for this model (see Hildenbrand [9] and Majumdar and Bhattacharya [2 and 3]). Randomness can arise from several sources. We will be considering, for concreteness, a simple exchange economy in which the basic data are the preferences and endowments of the economic agents. Either of these can be random. Typically, randomness of endowments can be allowed for by creating contingent markets in which case the Arrow-Debreu deterministic equilibrium suffices. It is conceptually much more difficult to create markets contingent on tastes due to the difficulties of discovering the true taste pattern of an individual, difficulties which do not arise in the case of endowment vectors which can be observed directly. We will be considering an economy without markets for every future contingency and thus there will remain some randomness. This residual uncertainty in the economy necessitates equilibrium concepts other than the Arrow-Debreu system of market clearing prices. 2. NOTATION

In a principal-agent model with adverse selection, we study the implementation of social choice functions when the agent's message space is a correspondence which depends on this true characteristic. We characterize such correspondence for which the Revelation Principle is valid.

When a decision rule is implemented using a Bayesian incentive compatible mechanism in which the messages are publically obser vable, the players' information is augmented by their observation of each others' strategies. In this paper the authors study the set of Bayesian implementable decision rules which have the further property that the information c onveyed in the process of thier implementation does not invalidate the optimality of the players' strategies. Such rules are called posterior implementable. The authors concentrate on a two-person problem with two possible decisions and, for this problem, they obtain a complete characterization of the set of posterior implementable decision rules. Copyright 1987 by The Econometric Society.

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.