Knowledge that Transforms

the assumption of equality of variances of error terms between two separate sample regimes. It is shown that the test is well behaved when there are variations of variances if at least one of two sample sizes is very large. However, if two samples are of small size, even moderate heteroscedasticity has considerable effect on the level of significance of the test. In what follows, it is assumed that T1 samples belong to the first regime and T2 samples to the second regime; subcripts 1 and 2 denote the first and the second regimes, respectively. Consider the regression model

In a classical optimal control problem the terminal time, either prescribed a priori or not, is always a real number. In many dynamic optimization problems in economics one is lead to consider optimal control problems in which the terminal time is the extended real number + infinity. These are the so called optimal control problems with infinite horizon. In the paper the author gives a precise formulation for a standard problem of that type and establishes a necessary condition for that problem. (Author)

[A consistent theory of demand is possible without the transitivity axiom. Here it is shown that a class of nontransitive orderings can be represented by a continuous numerical function, in such a way that an individual's demand function may be found by solving a constrained maximum problem.]

[There are two types of mathematical economists, one who applies existing mathematics to economic problems (the best example is Court) and the other who anticipates new mathematical problems within economics. Taking Marx as the second type of economist (Section 1), I discuss two of his problems: the fundamental Marxian theorem (Section 2) and the transformation problem (Section 3). In Section 2 I propose a generalisation of the theorem to the effect that the theorem does not need the labour theory of value and hence is independent of any criticisms of that theory. In Section 3 it is seen that the transformation problem is formally identical with the Markov chain process transforming the initial position to the ergodic position.]

It is the purpose of this paper to show first that in a competitive system satisfying a generalized Wairas' law all principal minors of order less than n of the Jacobian determinant of the system of excess supply functions will ordinarily change sign somewhere on the domain of all positive prices whether demand is bounded or not. Conditions for uniqueness of equilibrium are proposed for the case of bounded demand which allow minors of the Jacobian to change signs. Unbounded demand was treated in Part I. Existence of equilibrium is proved under a generalized Walras law.

R. L. Basmann, D. H. Richardson, R. J. Rohr, Finite Sample Distributions Associated with Stochastic Difference Equations--Some Experimental Evidence, Econometrica, Vol. 42, No. 5 (Sep., 1974), pp. 825-839

This paper develops a dynamic model of oligopoly and discusses the existence and characteristics of optimal policies for firms in such a model. The firms are assumed to face a random demand so they hold inventories which fluctuate from one period to the next. This necessitates a dynamic model rather than a static one. Our extension of the equilibrium concept to the oligopoly model is founded on recent generalizations of Shapley's stochastic game. We show the existence of equilibrium price-quantity strategies for the firms and also (i) an equilibrium strategy may be found by solving an appropriate static game and (ii) the quantity part of the strategy is often a constant (time invariant).

[The paper presents maximum likelihood methods for estimating four types of disequilibrium models. In each case the model includes three equations: the demand equation, the supply equation, and the condition that quantity observed is the minimum of quantity demanded and quantity supplied. The first model consists of just these equations. In the second model one knows whether one is on the demand function or the supply function by looking at the direction of the change in price. In the third model the price change is assumed to be proportional to excess demand. In the fourth model the price change is a stochastic function of excess demand and possibly other exogenous variables. Some illustrative calculations are presented using the housing starts model considered by Fair and Jaffee in an earlier issue of this journal.]

An infinite horizon consumption model is considered where the labor part of income is random. An upper bound on optimal consumption is obtained by considering the expected value of the optimal return function in the deterministic labor income case. This upper bound on consumption is easily shown to be lower than the value of optimal consumption in the case where the random labor income is replaced by its mean.