[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.]

Tlis article was written independently of Solow's [13] but is closely related to it. Under some plausible assumptions the author discusses various stability properties of a dynamic input-output system wNith a spectrum of techniques. Those economists who are interested in game theory, linear programming and input-output analysis may be charmed by Mrs. Robinson's model [9], a bor(derline model between von Neumann's theory of growth [8] and Marx's theory of reproduction. It is shown that her solution of a golden age is a particular solution of the dynamic Leontief model. INTERINDUSTRY ANALYSIS of the Leontief type is concerned with systems in whiclh the products of economic factors (materials, machines, labour, etc.) are themselves used as factors to produce further goods. Dynamic Leontief models include at least one good entering production repeatedly in more than one period (capital good), whereas static models comprise only goods which cease to exist once they are used up in further production (current goods). This paper deals with a dynamic Leontief model, i.e., the length of life of at least one good is assumed to be greater than unit time. In Sections 1 and 2 we discuss the time paths of prices and outputs, and we reach the following main results: (1) the long-run equilibrium prices have global stability; (2) the stationary solutions for outputs are necessarily unstable; (3) there is a balanced growth solution for the deviations of outputs from the stationary state; and (4) this balanced growth solution is unstable

Abstract : The most important characteristics of capital goods are durability and non-transferability. When time goes on, the number of periods during which a capital good can survive decreases, and it becomes less productive. The other problem relates to the fact that no capital good can be transferred to another industry once it has been installed in some industry. This paper re-examines the dynamic input-output model of Leontief's type from this point of view, and shows how it has to be altered, on the assumptions that there is no technical change and that prices are so flexible as to establish the long-run equilibrium price conditions instantaneously. The authors begin by proving the dynamic substitution theorem, assuming the existence of differentiable general neo-classical production functions, taking vintages of capital goods into explicit account. Then the existence of the golden equilibrium of the model is discussed. (Author)