Comparative static properties of optimal nonlinear income taxes are obtained for a finite population version o f the Mirrlees income-tax model with a weighted utilitarian social we lfare function and quasilinear preferences. The parameters which are varied are the weights in the welfare function, the slope of the prod uction constraint, and a parameter in the utility function. The endog enous variables are the consumers' consumption levels, pretax incomes (labor supplies in efficiency units), utility levels, and marginal t ax rates.
This paper presents a finite-horizon search model that is econometrically implemented using all of the restrictions impli ed by the theory. Following a sample of male high school graduates fr om the youth cohort of the National Longitudinal Surveys from graduat ion to employment, search parameters are estimated. Reservation wages and offer probabilities are estimated to be quite low. Simulations a re performed of the impact of changing the parameters on the expected duration of unemployment.
We consider the problem of providing incentives over time for an agent with constant absolute risk aversion. The optimal compensation scheme is found to be a linear function of a vector of N accounts which count the number of times that each of the N kinds of observable events occurs. The number N is independent of the number of time periods, so the accounts may entail substantial aggregation. In a continuous time version of the problem, the agent controls the drift rate of a vector of accounts that is subject to frequent, small random fluctuations. The solution is as if the problem were the static one in which the agent controls only the mean of a multivariate normal distribution and the principal is constrained to use a linear compensation rule. If the principal can observe only coarser linear aggregates, such as revenues, costs, or profits, the optimal compensation scheme is then a linear function of those aggregates. The combination of exponential utility, normal distributions, and linear compensation schemes makes computations and comparative statics easy to do, as we illustrate. We interpret our linearity results as deriving in part from the richness of the agent's strategy space, which makes it possible for the agent to undermine and exploit complicated, nonlinear functions of the accounting aggregates.
We study Hotelling's two-stage model of spatial competition, in which two firms first simultaneously choose locations in the unit interval, then simultaneously choose prices. Under Hotelling's assumptions (uniform distribution of consumers, travel cost proportional to distance, inelastic demand of one unit by each consumer) the price-setting subgames possess equilibria in pure strategies for only a limited set of location pairs. Because of this problem (pointed out independently by Vickrey (1964) and d'Aspremont et al. (1979)), Hotelling's claim that there is an equilibrium of the two-stage game in which the firms locate close to each other is incorrect. A result of Dasgupta and Maskin (1986) guarantees that each price-setting subgame has an equilibrium in mixed strategies. We first study these mixed strategy equilibria. We are unable to provide a complete characterization of them, although we show that for a subset of location pairs all equilibria are of a certain type. We reduce the problem of finding an equilibrium of this type to that of solving three or fewer highly nonlinear equations. At each of a large number of location pairs we have computed approximate solutions to the system of equations. Next, we use our analytical results and computations to study the equilibrium location choices of the firms. There is a unique (up to symmetry) subgame perfect equilibrium in which the location choices of the firms are pure; in it, the firms locate 0.27 from the ends of the market. At this equilibrium, the support of the subgame equilibrium price strategy is the union of two short intervals. Most of the probability weight is in the upper interval, so that this strategy is reminiscent of occasional sales by the firms. We also find a subgame perfect equilibrium in which each firm uses a mixed strategy in locations. In fact, in the class of strategy pairs in which the firms use the same mixed strategy over locations, and this strategy is symmetric about 0.5, there is a single equilibrium. In this equilibrium most of the probability weight of the common strategy is between 0.2 and 0.4, and between 0.6 and 0.8. There is a wide range of pure Nash (as opposed to subgame perfect) equilibrium location pairs: the subgame strategies in which each firm threatens to charge a price of zero in response to a deviation support all but those location pairs in which the firms are very close.
In an economy with one public and one private good, egalitarian-equivalent cost sharing consists of finding the highest public good level, x*, such that consuming x* for free yields a feasible utility distribution. The corresponding feasible allocation (typically unique), called egalitarian-equivalent, is in the core of the economy. Conversely, any cost sharing method satisfying Pareto optimality, cost monotonicity (nobody suffers a utility loss if the production technology improves upon, ceteris paribus), and individual rationality (no single-agent coalition objects) or no private transfers (no agent receives a positive amount of private good), must select an egalitarian-equivalent allocation in every economy.
This paper studies the random walk, in a general time series setting that allows for weakly dependent and heterogeneously distributed innovations. It is shown that simple least squares regression consistently estimates a unit root under very general conditions in spite of the presence of autocorrelated errors. The limiting distribution of the standardized estimator and the associated regression t statistic are found using functional central limit theory. New tests of the random walk hypothesis are developed which permit a wide class of dependent and heterogeneous innovation sequences. A new limiting distribution theory is constructed based on the concept of continuous data recording. This theory, together with an asymptotic expansion that is developed in the paper for the unit root case, explain many of the interesting experimental results recently reported in Evans and Savin (1981, 1984).
This paper demonstrates how time consistency of the Ramsey policy–the optimal fiscal and monetary policy under commitment–can be achieved. Each government should leave its successor with a unique maturity structure for the nominal and indexed debt, such that the marginal benefit of a surprise inflation exactly balances the marginal cost. Unlike in earlier papers on the topic, the result holds for quite general Ramsey policies, including timevarying polices with positive inflation and positive nominal interest rates. We compare our results with
This study undertakes a systematic analysis of several theoretic and statistical assumption s used in many empirical models of female labor supply. Using a singl e data set (PSID 1975 labor supply data) the author is able to replic ate most of the range of estimated income and substitution effects fo und in previous studies in this field. He undertakes extensive specif ication tests and finds that most of this range should be rejected du e to statistical and model misspecifications. The two most important assumptions appear to be the Tobit assumption used to control for sel f-selection into the labor force and exogeneity assumptions on the wi fe's wage rate and her labor market experience.