Journal Article Further Implications of Learning by Doing Get access David Levhari David Levhari Hebrew University, Jerusalem Search for other works by this author on: Oxford Academic Google Scholar The Review of Economic Studies, Volume 33, Issue 1, January 1966, Pages 31–38, https://doi.org/10.2307/2296638 Published: 01 January 1966

Journal Article Extensions of Arrow's "Learning by Doing" Get access David Levhari David Levhari The Hebrew University, Jerusalem Search for other works by this author on: Oxford Academic Google Scholar The Review of Economic Studies, Volume 33, Issue 2, April 1966, Pages 117–131, https://doi.org/10.2307/2974436 Published: 01 April 1966

Introduction, 98. — Samuelson's nonsubstitution theorem, 99. — Switching of techniques, 102.

ONE OF THE common problems facing an economist dealing with production functions is the problem of aggregation of factors. In a rather neglected paper, Houthakker advances an ingenious approach for explaining the possibility of finding a neoclassical production function for an industry even when production within each of the firms (or cells)3 is done according to a fixed coefficients production function. These fixed proportions vary in a regular way from one cell to another so that the overall input-output relationship takes the form of a regular neoclassical production function. As Solow notices in a survey article on production functions4 this paper has been forgotten and not followed in any direction. In this note we try to reverse Houthakker's procedure and to show how each neoclassical production function implies some density function or distribution function over the cells. We here do it for CES production functions, but it will be obvious that the same method applies to any production function. Following Houthakker we normalize the cells so that each of them is capable of producing one unit of output. Each cell has a requirement, say t, of the variable factor and this requirement varies from one cell to another. If the wage rate in terms of output produced is p then all the cells with tp < 1 will produce a unit of output, all others will be idle. Assume that we are given a density function of the various cells by g(t). Output produced will then be Q = f Pg(t)dt and the input used A f f'IP tg(t)dt. By eliminating i/p one gets a relationship between Q and A. In this way Houthakker has shown that a Pareto distribution implies a CobbDouglas production function. Notice that the relationship between Q and A the cumulated product and factor used-is the familiar Lorenz curve. Assume that the overall relationship between output and the variable factor follows a CES production function with elasticity of substitution (a) smaller than 1;

Journal Article On the Sensitivity of the Level of Output to Savings: Embodiment and Disembodiment Get access David Levhari, David Levhari The Hebrew University of Jerusalem Search for other works by this author on: Oxford Academic Google Scholar Eytan Sheshinski Eytan Sheshinski Harvard University Search for other works by this author on: Oxford Academic Google Scholar The Quarterly Journal of Economics, Volume 81, Issue 3, August 1967, Pages 524–528, https://doi.org/10.2307/1884816 Published: 01 August 1967

[Machines produce a constant flow of output when operating, and break down in a random process. The task of workers is to repair the broken machines. Servicing time is also a random process [2]. The limiting steady state probabilities and the relation between output and inputs are derived, and fitted to a Cobb-Douglas production function.]

T is an accepted proposition that there is a positive association between efficiency and experience in production. Yet, until quite recently, only industrial engineers tried to estimate and evaluate the contribution of experience to productivity, while economists have on the whole neglected this aspect of production. The growing interest in growth and the search for factors which can help to explain quantitatively the growth of production over and above the growth of the conventionally identified inputs have led economists to reconsider the problem. Arrow's pioneering article on the subject suggested that learning, which may be identified with cumulated experience, contributes to the growth of productivity.' In contrast to the engineer's approach, which usually concentrates on the effect of experience on efficiency in specific processes, the economist's approach is more general. Learning is not exclusively attributed to the individuals who make up a firm's labor force or to specific processes, though both are considered to be integral elements of the process. Rather, it is ascribed to the production unit as a multidimensional entity. It is therefore the modus operandi of the firm in each of its many facets entrepreneurial ability, technical expertise, the know-how of its labor force, layout, buying and selling, human relations, lines of command, all of them subject to continuous change which is the best testing ground of the empirical significance of the learning hypothesis. Since the acquisition of experience requires time, time or a proxy for it, such as cumulated investment and cumulated output, must obviously appear as an explicit variable in an empirical test of the hypothesis. Productionfunction analysis based on time series is therefore an obvious way of studying the quantitative effect of learning. Arrow's reference to the Swedish Horndal firm is a case in point.2 However, it is only rarely possible to find a similar example. This means that although empirical testing of the learning hypothesis can be carried out on the basis of time-series data,3 it strains the theoretical framework of the analysis. The use of cross-section data in estimating the contribution of experience to productivity is therefore an obvious alternative. Since the input and output figures necessarily refer to different firms, this way of tackling the problem is also constrained by the necessity of assuming that, except for random differences, the technologies applied by the firms concerned are identical. The requirement of intra-firm technological identity, or to put it more mildly, the similarityof-technology condition, can, in practice, be approximated under certain conditions. For example, a good approximation to the identical technology constraint can be obtained within a narrowly defined branch and for a group of firms located in a relatively small area, which maintain strong personal contact between managements so as to facilitate the inter-firm flow of information and whose labor forces are similar in background, attitude, and know-how. If the firms in such a group differ in their acquired experiences, and if these differences can be easily measured in terms of simple units, such a group may be a satisfactory testing ground for the learning hypothesis. These conditions obtain in the case of kibbutzim in Israel. They form a tightly organized group of collectives, relatively homogeneous in manpower, which has established effiReceived for publication December 6, 1971. Revision accepted for publication July 10, 1972. * This article makes use of data prepared for a comprehensive study on the Israeli kibbutz economy currently in preparation at the Falk Institute for Economic Research in Israel, and financed by the Falk Institute and the Twentieth Century Fund. The authors are indebted to Yoram Levin for his help in the preparation of the quantitative skeleton of this article. 1See Kenneth J. Arrow (1962), pp. 155-174. 2Production methods in this firm do not appear to have changed for about 15 years; productivity, however, increased continuously. 'Shifts in the production function cannot be ruled out if the period studied is long. For shorter periods, for which this objection may have less force, the number of observations may be too small to allow for statistically significant results.