Steven Slutsky

A voting model for the allocation of public goods: Existence of an equilibrium☆

Abstract It is well known that equilibria may not exist for majority voting over multidimensional policy spaces. This paper shows that certain institutional constraints can be imposed upon the voting process to ensure existence of a restricted equilibrium. A restricted equilibrium point must defeat only those points connected to it by one of an exogenously given set of linearly independent voting vectors. Using this procedure in a general equilibrium model to determine demands for public goods, existence of a general political equilibrium is proven. The equilibrium need not be Pareto optimal and may be manipulated by changing the vectors.

DYNAMIC OPTIMAL INCOME TAXATION WITH GOVERNMENT COMMITMENT

The optimal income taxation problem has been extensively studied in one-period models. This paper analyzes optimal income taxation when consumers work for many periods. We also analyze what information, if any, that the government learns about abilities in one period can be used in later periods to attain more redistribution than in a one-period world. When the government must commit itself to future tax schedules, intertemporal nonstationarity of tax schedules could relax the self-selection constraints and lead to Pareto improvements. The effect of nonstationarity is analogous to that of randomization in one-period models. The use of information is limited since only a single lifetime self-selection constraint for each type of consumer exists. These results hold when individuals and the government have the same discount rates. The planner can make additional use of the information when individual and social rates of time discounting differ. In this case, the limiting tax schedule is a nondistorting one if the government has a lower discount rate than individuals.

Multi-agent equilibria with market share and ranking objectives

A model of nonprice unidimentional spatial competition between firms or between political candidates is studied. Typically in such models agents are assumed to maximize their shares of customers (as a proxy for profits) by firms, or of voters by candidates. This paper derives conditions for the existence, and characterization, of equilibrium outcomes when there are more than two agents, all of whom are assumed to minimize their rank as well as maximize their shares. The rank of an agent is defined as the sum of the number of agents with greater shares and a fraction of the number of agents with equal shares. It is shown that rank minimization tends to require more symmetry in location than share maximization, that the greater the weight on agents with equal shares in defining rank, the more extreme are the requirements for equilibrium until, for weights greater than 1/3, no equilibrium exists for more than three competing agents, and that when agents care about both rank and shares, the relative weights put on each is irrelevant in determining the equilibrium locations.

Quantity Competition in a Spatial Model

The authors analyze a duopoly model where firms first choose locations on a line segment and then choose quantities in the second stage. Pure strategy quantity equilibria fail to exist for locations close together. For low transport costs, near agglomeration occurs and the firms choose locations where pure strategy quantity equilibria exist. As transport costs rise, firms become less direct competitors as they move away from the center of the market. Coauthors are James F. Klein, Eytan Sheshinski, and Steven M. Slutsky. We analyse a duopoly model where firms first choose locations on a line segment and then choose quantities in the second stage. Pure strategy quantity equilibria fail to exist for locations close together. For low transport costs, near agglomeration occurs and the firms choose locations where pure strategy quantity equilibria exist. As transport costs rise, firms become less direct competitors as they move away from the centre of the market. Coauthors are James F. Klein, Eytan Sheshinski, and Stephen M. Slutsky.

The value of explicit randomization in the tax code

Abstract Consider individuals who draw income from the same random distribution but who differ in their risk aversion and who decide whether or not to report their income truthfully. The government chooses the tax structure including a random tax option, audit probabilities, and penalties on detected evaders to maximize expected ex post social welfare. High income individuals who do not evade then choose to pay either a given amount or draw from a random tax schedule. This schedule ensures that everyone complies with more risk averse individuals choosing the deterministic schedule and less risk averse ones choosing the random tax option.

Endogenizing the order of moves in matrix games

Players often have flexibility in when they move and thus whether a game is played simultaneously or sequentially may be endogenously determined. For 2 × 2 games, we analyze this using an extended game. In a stage prior to actual play, players choose in which of two periods to move. A player moving at the first opportunity knows when his opponent will move. A player moving at the second turn learns the first movers action. If both select the same turn, they play a simultaneous move subgame.If both players have dominant strategies in the basic game, equilibrium payoffs in the basic and extended games are identical. If only one player has a dominant strategy or if the unique equilibrium in the basic game is in mixed strategies, then the extended game equilibrium payoffs differ if and only if some pair of pure strategies Pareto dominates the basic game simultaneous play payoffs. If so, sequential play attains the Pareto dominating payoffs. The mixed strategy equilibrium occurs only when it is not Pareto dominated by some pair of pure strategies.In an alternative extended game, players cannot observe delay by opponents at the first turn. Results for 2×2 games are essentially the same as with observable delay, differing only when only one player has a dominant strategy.

Neutrality and the private provision of public goods with incomplete information

Abstract In this paper we introduce incomplete information about income into a standard model of private provision of public goods. Generally, one obtains neutrality results similar in nature to those obtained in the complete information model. However, with incomplete information, several additional difficulties exist in attaining neutrality. For neutrality to hold, (i) positive contributions have to be made by all individual types, (ii) any redistribution of income must not convey information to the individuals, and (iii) any redistribution must not depreciate the private information individuals have.

Private provision of public goods under price uncertainty

In this paper, price uncertainty is introduced into the model of voluntary provision of public goods. The analysis is carried out depending upon whether individuals make real or nominal contributions. We highlight the significant factors that determine the complex effects of changes in uncertainty on the level of provision, the level of welfare, and the gaps between equilibrium and optimal values of these variables. In particular, we show that in some situations it would be desirable to introduce artificial randomness in prices in order to alleviate the free rider problem and to increase welfare.

Production efficiency and optimal pricing in intermediate-good regulated industries

Abstract This paper reconsiders the relationship that exists between the production efficiency result of Diamond and Mirrlees and the Ramsey Rule. Specifically, the paper considers a general equilibrium hierarchical structure of production. One industry sells at least some of its output to another regulated industry. A single regulatory agency must balance the budgets of all regulated industries in the aggregate so as to maximize the utility of a representative individual. The Ramsey Rule always holds. Pricing rules, however, are far more complex. The optimum may have some negative price-cost margins and may not involve production efficiency.

Optimal nonlinear income taxation with a finite population

Abstract In the standard optimal income taxation problem, tax payments depend only on each consumers own actions. Piketty [J. Econ. Theory 61 (1993) 23–41] shows that, if one individuals tax schedule depends on others’ actions and the government knows the exact ability distribution, it can implement any undistorted allocation as the unique revelation game outcome. If some individuals misreveal their types, Pikettys mechanism may assign infeasible allocations. We require that tax schedules must balance the government budget for every possible vector of revelations. When individuals reveal their type by simple announcements, all undistorted allocations can be still implemented, even with off-equilibrium feasibility constraints.