Showing papers by "Kenneth J. Arrow published in 1972"

Economic Welfare and the Allocation of Resources for Invention

Abstract: Invention is here interpreted broadly as the production of knowledge. From the viewpoint of welfare economics, the determination of optimal resource allocation for invention will depend on the technological characteristics of the invention process and the nature of the market for knowledge.

A Production Function for the Repairman Problem'2

Abstract: In this paper we consider the repairmen problem from the point of view of production theory. This problem, which has a large literature,3 can be described as follows. There are m identical machines which operate independently and which normally require no human care. However, at any time a machine may break down and call for service, according to an exponential failure distribution. Furthermore, it is assumed that there are r repairmen, each capable of repairing one machine at a time. The time required for servicing a machine is again taken as a random variable with an exponential distribution. If fewer than r machines are being repaired a failed machine is immediately serviced. On the other hand, if r or more machines are being repaired, the failed machine joins a queue and waits for service. The queue discipline assumes that all repairmen are working if a machine is waiting, but it is otherwise arbitrary. If we let x(t) be the total output produced at time t, then x(t) is proportional to the number of machines operating at time t, n(t), which follows a stochastic birth and death process. Our purpose in this paper is to study the limiting behaviour of x(t) over time and, in particular, the behaviour of the expected value of x(t) as m and r become large. We here prove that as the number of machines and repairmen increases, expected output becomes, in a way to be specified below, proportional to the number of repairmen or to the number of machines, depending upon whether the ratio of repairmen to machines is below or above a certain value. It has previously been shown, by means of numerical calculations [4], that the production function relating expected output to the number of machines and to the number of repairmen exhibits smooth isoquants (with continuous marginal rates of substitution). It seemed, therefore, that the random character of the production process had introduced smoothing effects into an otherwise fixed-coefficients technology.4 But, as is proved here, for a large number of machines, the production function is of the fixed-coefficients type. In Figure 1, the isoquant relating the inputs per unit of output is seen to approach an L shape as m becomes large. The critical value (the ray OA) depends on the parameters of the stochastic process, i.e. the average failure time and the average repair time. More generally, it can be shown that the sequence of output processes, properly translated and scaled, tends to be a limiting diffusion process, the well-known OrnsteinUhlenbeck process.

Problems of resource allocation in United States medical care.

Abstract: Medical care in the United States has been and in many ways still is directed by the free play of the market. Individual patients use their incomes as they choose to buy medical services; physicians derive their incomes from these fees and freely decide how much medical services to offer, how to specialize, and where to locate. These decisions may be made for all sorts of reasons, but certainly income is not irrelevant. Such a system for the allocation of medical resources has been largely abandoned in most other leading countries and is undergoing progressive modification in the United States. The state and local governments have always intervened to some extent in providing medical services to the poor; the spread of medical insurance, even though nominally private, has sensibly modified the earlier financial arrangements and motivations; and more recently the Federal government has intervened massively to finance medical services to the aged and to greatly increase those for the poor. Now it is clear that the country is on the way to some form of national health insurance. The only question is what form it will take. We may expect several years of vigorous debate among the contesting proposals emanating from all sides. But when a Republican administration comes forth to urge a definite permanent role for the Federal government in the provision of medical care to the entire population, the issue of principle has been resolved.

General Economic Equilibrium: Purpose, Analytic Techniques, Collective Choice

Abstract: : The lecture is designed to survey modern development of the theory of general equilibrium in a competitive economy and its role in the allocation of resources. A survey is given of the state of the theory as developed by J.R. Hicks, P.A. Samuelson, and their predecessors as of about 1945, followed by an evaluation of the needs for further development. The differing general equilibrium tradition in the German-language literature is summarized.