Knowledge that Transforms

We consider a model of capital accumulation and prove the existence of a support price path for the optimal path of capital accumulation. The considered model is a continuous time model of infinite horizon. Our problem is the so-called convex problem of optimal control without differentiability. We adopt the overtaking optimality criterion and prove the existence of a dual price path which supports the value function as well as the Hamiltonian function.

We investigate the stochastic relation between income and consumption (specifically, consumption of food) within a panel of about 2,000 households. Our major findings are: 1. Consumption responds much more strongly to permanent than to transitory movements of income. 2. The response to transitory income is nonetheless clearly positive. 3. A simple test, independent of our model of consumption, rejects a central implication of the pure life cycle-permanent income hypothesis. The observed covariation of income and consumption is compatible with pure life cycle-permanent income behavior on the part of80 percent of families and simple proportionality of consumption and income among the remaining 20 percent. As a general matter, our findings support the view that families respond differently to different sources of income variations. In particular, temporary income tax policies have smaller effects on consumption than do other, more permanent changes in income of the same magnitude.

Inflation,

Limit pricing involves charging prices below the monopoly price to make new entry appear unattractive.If the entrant is a rational decision maker with complete information, pre-entry prices will not influence its entry decision, so the established firm has no incentive to practice limit pricing.However, if the established firm has private, payoff relevant information (e.g., about costs), then prices can signal that information, so limit pricing can arise in equilibrium.The probability that entry actually occurs in such an equilibrium, however, can be lower, the same, or even higher than in a regime of complete information (where no limit pricing would occur).'Much of the work reported here first appeared in [11].This work has been presented at a large number of conferences, meetings, and seminars, and we would like to thank our audiences at each of these events for their comments.We are particularly indebted to Eric Maskin, Roger Myerson, Steve Salop, Robert Wilson, and two referees for their helpful suggestions, to David Besanko for his excellent research assistance,

This paper considers the problem of testing statistical hypotheses in linear regression models with inequality constraints on the regression coefficients. The Kuhn-Tucker multiplier test statistic is defined and its relationships with the likelihood ratio test and the Wald test are examined. It is shown, in particular, that these relationships are the same as in the equality constrained case. It is emphasized, however, that their common asymptotic distribution is a mixture of chi-square distributions under the null hypothesis.

THIS PAPER REPRESENTS an attempt to make Aaron and McGuire's [1] approach to incidence operational.2 The tax paid by any individual is interpreted by Aaron and McGuire as the sum of two components. The first is a Lindahl tax equal to the individual's marginal rate of substitution between the public good and income times the amount of the public good provided. The second component is a negative or positive transfer equal to the Lindahl tax minus the tax the individual has actually paid. This second component is used to measure the incidence or redistributional impact of a particular budget program. Empirically, Aaron and McGuire found that the computation of Lindahl taxes is highly sensitive to the choice of individual utility functions. Under certain assumptions that sensitivity is reflected in the value of a coefficient related to the marginal rate of substitution between the public good and income. Maital [16], later on, used three separate identical estimates of this coefficient to reduce the ambiguity in the computation of Lindahl taxes. This paper offers an alternative computational approach to Aaron and McGuire's. The key information on Lindahl tax prices or marginal rates of substitution is obtained from individual demand curves for public goods which are estimated using the median voter model (see [5]). An advantage of this approach over Aaron and McGuire's is that it does not assume separability of the public good and income in taxpayers' preferences. The present approach also permits the study of the incidence of a budget policy on groups defined by socio-demographic characteristics other than income. On the other hand, and because of empirical reasons which will become apparent below, the present approach is useful for the study of incidence at the local level only. Section 1 of the paper restates the measure for the simultaneous incidence of taxes and one public good, henceforth called fiscal incidence, in the context of a formalized political process. This section also discusses some of the theoretical difficulties involved in extending the case with one public good to the multi

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Treble correct when he states that the integral representing consumer surplus is increasing in D(, where Do stands for market radius for the firm. But he incorrect in his speculation that the CV solution under L6schian competition according/v yields an increasingly smaller consumer surplus in the aggregate. Note that the decreasing surplus with decreasing Do created by each one of the individual firms which are increasing in number under free entrv. The aggregate consumer surplus therefore not necessarily greater under spatial monopoly than it under conditions of spatial competition. In fact, it can readily be shown to be increased, not decreased, with an increasing entry under the CV model. To prove our contention consider the average consumer surplus a la W. Holahan [3] which given below by evaluating Treble's integral S in [4, p. 1328] and in turn dividing both sides of the resulting equation by Do: