Knowledge that Transforms

IN THE GROWTH model of Kemeny-Morgenstern-Thompson [2, pp. 115-135], the production space is a closed convex and polyhedral cone in R2, with some further properties. In the growth model of Gale [1, pp. 285-303], the production space has to fulfil the same assumptions except that the cone need not be polyhedral. Therefore the model of Gale can be regarded as a generalization of the KMT-model. In this paper it will be shown that in contradiction to a central theorem of Gale, the existence of an optimal price vector cannot be guaranteed in this generalized production space. To describe the difficulty in the growth model of Gale, we enumerate the properties of the production space and the basic definitions given by him. The technological possibilities of production are described by the production space

The paper discusses the allocation of output among consumption and two types of capital with different gestation periods. Along an optimal path, we show that the imputed prices of capital goods, from the time they start production, do not exceed the prices of output, which are not less than the marginal instantaneous utility of consumption. A simple numerical example helps to illustrate some further implications of the model. RECENT PAPERS on optimal growth consider models of allocation of resources between consumption and investment. It is invariably assumed that investment results in an instantaneous increase in the stock of capital. Such assumptions obscure differences in the gestation periods among various capital goods. In [1] we discuss how a growth problem with time lags can be formulated and interpreted and explain the derivation of the necessary conditions for optimization. In this note we study the effects of differences in gestation periods on optimal investment plans for a growth problem including depreciation and population growth. Consider an economy where two capital goods and labor are used in the production of a single commodity. The per capita output at time t is given by the production function: f (kl, k2), where k, is the per capita stock of capital of type one, and k2 is the per capita stock of capital of type two. From now on, all variables will be per capita and we drop the designation. We assume the following:

[This paper is concerned with the introduction of input or output targets in decentralized planning processes. The process which is studied is that of Dantzig-Wolf-Malinvaud. All the properties of a "good" scheme are present when the central board designates a neighborhood of a point of the production set (instead of an exact output target) where each firm or sector is constrained to maximize an index.]

[The multi-period control problem analyzed assumes the data are generated by the simple regression model with an unknown slope coefficient. There is a tradeoff between stabilization and experimentation to learn more about the unknown coefficient. When parameter uncertainty is large, experimentation becomes an important consideration.]

[The "price-specie-flow" mechanism depends on a mechanical application of the quantity theory of money, i.e., it assumes that the price level of a country is solely determined by that country's money supply, which is incorrect in an open economy. Two alternative interpretations of the equation of exchange are offered, namely, the aggregate expenditure approach and the demand for money approach; and it is shown that, in general, the Marshall-Lerner condition is neither necessary nor sufficient for the stability of the classical system.]