Knowledge that Transforms

SOME FIFTEEN YEARS have passed since Phillips [15] first showed that the application of certain types of stabilization policies to multiplier-accelerator macroeconomic models could result in undesired oscillations or instabilities. It has become clear from this and other analyses of macroeconomic policy [1, 3, 5, 16] that, because of the dynamic structure of the economy, well-intentioned policies may have unexpected and counterintuitive results. In recent years a number of economists have demonstrated the potential application of the mathematical techniques of optimal control theory to economic policy formulation for stabilization [6, 20, 22] as well as long-run growth and development [7, 8, 12, 13, 21]. While much of this work has been successful in showing how optimal control could be applied to policy problems, there has been little attempt made to actually apply it to a realistic policy problem, particularly in the area of short-run stabilization. A goal of this paper is to show that if one is willing to work with a linear or linearized economic model and quadratic cost criteria, optimal control theory can provide a viable tool for both analyzing and understanding the dynamic properties of the model, and for formulating stabilization policies based on the model. In this paper economic stabilization will be approached as a dual tracking problem in optimal control. The problem that is defined and solved involves tracking nominal state and nominal policy trajectories, subject to a quadratic cost function and the constraint of a linear system. This is actually quite general and will enable us to penalize for variations in, as well as the levels of, the state variables and control variables. Moreover, this lets us structure the problem as one without absolute limitations on the sets of allowable controls and allowable states; any restrictions that are to be imposed on the motion of control or state variables are expressed by assigning higher costs to their deviations. We will also

IN THIS PAPER we examine the concept of irreducibility in the von Neumann model, as defined by Gale [2, Ch. 9]. Since this property corresponds to a condition on the types of production in the model, we term it technological irreducibility. We show that there is a dual concept, which we call economic irreducibility, involving a condition on the price structure. The wellknown von Neumann indecomposability assumption is shown to have a very simple relationship to the property of economic irreducibility. We also show how to generalize certain results from the Perron-Frobenius theory of irreducible non-negative square matrices to the case of an irreducible von Neumann model.

The paper provides several axiomatizations of the concept of "path independence" as applied to choice functions defined over finite sets. The axioms are discussed in terms of their relationship to "rationality" postulates and their meaning with respect to social choice models.

[The effect of economic constraints upon fertility are analyzed within the theory of household production and allocation of time. The interaction of individual components of family income and the direct economic costs of children are shown to have an increasingly large impact upon Swedish fertility as industrialization proceeds.]

How should rule-of-thumb priorities be assigned for the rationing of intermediate goods in an economy marked by shortages and non-scarcity prices? A method is developed for setting these priorities in an optimal way, and the method is applied to Soviet data as an illustration. 1.

[This paper develops an iterative procedure for estimating "specific" and "income" consumer unit scales in Engel curve analysis. The proposed procedure is essentially a modification of the Prais and Houthakker method and is illustrated by means of a numerical example based on the Indian National Sample Survey data.]

[The properties of systems of investment equations derived under the hypothesis of present value maximization are investigated. The possibility that either the optimal time rate of change in some factor or the stationary level of some stock may increase with its own rental rate is shown to be consistent with the hypothesis in the case of more than one factor. A condition necessary for this result is that marginal products depend on the rates of which factor levels are justified.]

[This paper is concerned with showing differentiability and measure theoretic properties on demand functions. The main results are roughly as follows. (i) Demand is differentiable and the Slutsky equation holds for almost all prices if demand satisfies a Lipschitz condition in income (except possibly for a closed cone of prices of measure zero) and utility is concave. This includes the homothetic case which is given special attention in Section 4. (ii) For the Slutsky equation to indicate demand behavior in the large, it is sufficient that along any given indifference curve the ratio of changes in price to changes in quantity be bounded from zero (Section 5). (iii) Even with almost everywhere differentiable demand derived from continuously differentiable utility, most change in demand does not necessarily take place where the Slutsky equation is valid (Section 5). (iv) By way of proof of Theorems 1-3, it is shown that the maximand in a Lagrange problem is differentiable under appropriate conditions on the function being maximized (Theorem 6, Section 3, and Appendix). (v) For preferences as in (ii) and for almost all wealths, equilibrium is locally unique (Section 6).]