Journal Article The Accelerator and Technical Progress Get access A. A. Walters A. A. Walters Birmingham Search for other works by this author on: Oxford Academic Google Scholar The Review of Economic Studies, Volume 30, Issue 1, February 1963, Pages 1–15, https://doi.org/10.2307/2296025 Published: 01 February 1963

Journal Article Economies of Scale; Some Statistical Evidence: Comment Get access Alan A. Walters Alan A. Walters Northwestern University and University of Birmingham, England Search for other works by this author on: Oxford Academic Google Scholar The Quarterly Journal of Economics, Volume 74, Issue 1, February 1960, Pages 154–157, https://doi.org/10.2307/1884139 Published: 01 February 1960

Статья представляет собой несложный обзор различных подходов к построению производственных функций и обсуждение связанных с этим проблем (агрегирование и т. п.). Функции затрат рассматриваются как заменитель производственной функции, так как первые намного легче оценить на практике. Во второй части статьи автор рассматривает все наиболее значимые попытки статистического исследования произвосдтвенных функций и функций затрат.

1. The theoretical foundations of the aggregate production function give one grounds for doubting whether the concept is at all useful. Nevertheless, the temptation to discuss movements in indices of input and output in terms of such a function is difficult to resist. And there is no doubt that it is useful to rationalize the data along these lines. In his analysis of the aggregate production function in the United States, Solow derived many useful results.1 These findings, however, depended on the assumption of constant returns to scale in the aggregate production function. This assumption simplified the analysis considerably. Solow found the capital coefficient a, in the Cobb-Douglas, from the proportion of income going to capital; then, by subtracting from output per unit of capital (X/K) the product of (1 a) and capital per

M ETHODS used to fit cost functions either to time series or cross-section data have been extensively criticized.' In a recent article Johnston2 has reexamined some of these criticisms and has to some extent succeeded in reestablishing the validity of the two major findings, i.e., (i) constant marginal cost, (2) decreasing long-run average cost. There are, however, criticisms made by Friedman (and Stigler) which Johnston is less successful in countering. The first which we shall consider here is a version of the classical regression fallacy. Friedman expresses this as follows: a firm produces a product the demand for which has a known two year cycle, so that it plans to produce ioo units in year one, 200 in year two, ioo in year three, etc. Suppose also that the best way to do this is by an arrangement that involves identical outlays for hired factors in each year (no 'variable' costs). If outlays are regarded as total costs, average cost per unit will obviously be twice as large when is ioo as when it is 200. If, instead of years one and two, we substitute firms one and two, a cross section study would show sharply declining average costs. When firms are classified by actual output, essentially this kind of bias arises. The firms with the largest outputs are unlikely to be producing at an unusually low level; on the average they are clearly likely to be producing at an unusually high level, and conversely for those that have the lowest output (page 236). And Stigler says: that three firms on average (over say a decade) produce ioo units each per year at an average cost of $io. In any one year because of weather, catastrophe, illness or death of a salesman, regional differences in business, etc. ('chance fluctuations') the firms will have sales (outputs) above or below the decade average of i0o. Suppose firm A sells only 8o units in a given year, firm B, Ioo units and firm C, I20 units. Suppose further that for each firm costs include (I) $500 of fixed costs plus (2) $5 of variable costs per unit of output. Tabulating the results:

The time series of consumption is explained as a consequence of expenditure. The quantity theory hypothesis relates the level of consumption in money terms to the nominal quantity of money. This is, of course, a variant of the normal quantity theory where the level of money income is determined by the amount of money. By subtracting investment from the dependent variable, one makes the quantity theory formulation directly comparable to its Keynesian rival. Money exerts its influence on consumption directly or via elements of expenditure such as investment. With a different definition of autonomous expenditure, we get rather different results for United Kingdom data. Specifically, the monetary hypothesis is more successful for our early period up to the First World War, while the inter-war years are a strongly Keynesian period. After the Second World War, neither model has very high explanatory power, while for the overall period, there is a slightly better fit with expenditure. Exogeneity of Money