Knowledge that Transforms

qi yj + (xjpjyj). Pi Stone, who applied this model in several papers (1954, 1964, 1965), suggested the parameters could either be given a time trend or allowed to depend on the past history of the branch of demand to which they relate. We want to explore the second suggestion and to see what happens when the y's are explained by past choices. In doing so, our approach will be close to the one followed by R. A. Pollak in (1970). Pollak redefines the y's as linear functions of consumption in the previous period, while we redefine these as linear functions of current values of state variables representing stocks of durable goods or habits. This has the advantage of bringing durable goods into the picture and in particular permits the introduction of a depreciation rate. Our approach is different from Pollak's in another respect: short-run behavior will be shown to be a partial adjustment to long-run equilibrium, thus permitting estimation of a reaction coefficient for each commodity. To a large extent, we follow the line of thought suggested by Houthakker and Taylor in the second edition of Consumer Demand in the U.S. (1970, chap. 5) in dynamizing the quadratic utl1it3 function. Improvements include the ex, ici t formulation of the partial adjustment procl. ;s implied in the maximization behavior anu specific consideration of the covariance structure of the error term.

PpTHE application of duality in economic analysis was initiated by Hotelling (1932) and Roy (1942) in the area of consumer demand. Subsequently, Shephard (1953) in his pioneering work on cost and production functions extended the duality concepts to the theory of production and derived many of the fundamental results, including the basic duality theorems and Shephard's (1953) Lemma, which asserts that the gradient of the dual function is equal to the supply and demand correspondences. More recently McFadden (1972) generalized the duality concepts in production theory to include profit and revenue functions. The profit function is a function of the output and input prices which gives the value of the maximized profit of a profit-maximizing and pricetaking firm endowed with a given technology. Because of Shephard's (1953) Lemma, the partial derivatives of the profit function with respect to the output and input prices give the supply and demand functions. Thus, the econometric analysis of the behavior and technology of the profit-maximizing and price-taking firms is greatly facilitated.' In this paper we are concerned with the properties of the profit functions of technologies with multiple inputs and outputs. Several theorems which relate the properties of the transformation functions to the properties of the profit functions and vice versa are proved. The specific properties considered are: (1) homogeneity, (2) separability, and (3) nonjointness. The properties of the profit function have been studied by McFadden (1972), Diewert (1969), and Jorgenson, Christensen and Lau (1970), among others. In addition, Hall (1972) has approached the problem of multi-output, multi-input firms from the point of view of joint cost functions.

IN recent years, the American public has become greatly alarmed over an apparent shortage of physicians, a shortage which is expected to reach crisis proportions within the next decade. The predicted shortage stems, in part, from the nation's current efforts to make health care accessible to all income classes and from past neglect of medical-school facilities. However, there is also some evidence that the shortage is further aggravated by widespread inefficiency in the use of medical manpower. It is a matter which is increasingly attracting the attention of health-manpower specialists, but one on which opinions still differ widely. Somne students of the health-care sector have argued, as early as a decade ago, that it would be techniically imnpossible to add to the already hea\y patient load carried by American physicians.' In contrast, Rashi Fein's recent book The Doctor Shortage (1967) concludes with the assertion that physicians could increase their productivity still further, either by joining large-scale group practices or by delegating more of their workload to auxiliary personnel. Fein admits, however, that in the absence of more research, one cannot be certain whether the gains from group-practice formation and from increased reliance on paramedical aides will be large or more modest. (p. 144) His argument therefore rests on essentially intuitive grounds. Fein's call for more research on the production of physicians' services is entirely justified. For, in spite of the crucial role played by physicians in the production and delivery of health services, there exists very little enmpirical information on the technical and economic determinants of the physician's productivity. This paper is an attempt to contribute to our understanding of this important parameter. Using a simnple model of physician behavior and a nationwide cross-section sample of physicians, the study seeks to identify the effects of auxiliary persoi)nel and of the mode of practice (solo or group) on the physician's rate of output. Our analysis leads to the conclusion that the average American physician could profitably employ roughly twice the number of aides he currently employs and thus increase his hourly rate of output by about 25 per cent above its current level. This figure takes on added meaning when it is recalled that a mere increase of 4 per cent in average physician productivity in the United States would add more to the aggregate supply of medical services than would the entire current graduating class froin American medical schools. Looked at in another way, our results suggest that, in choosing his combination of practice inputs, the average physician in our sample appears to have priced out his own time at a value much below that implicit in his medical fees. On either interpretation, the results therefore support the thesis that American physicians tend to be wasteful in the use of their scarcest and most expensive resource.

IN this paper I have esitimated the amount United States cigarette consumption has been affected by cigarette advertising and by the health scare over smoking. During 19531970 the health scare depressed cigarette consumption considerably more than cigarette advertising boosted it. Section I presents econometric estimations of the demand function for cigarettes, incorporating econometric corrections for multicollinearity. Section II gauges the comparative effects of advertising and the health scare. On these results, section III evaluates whether the recent Congressional ban of broadcast advertising of cigarettes will promote public health by reducing cigarette consumption. Although the advertising elasticity of demand was positive, it was quite small. More importantly, however, the ban also eliminated the health-scare-oriented antismoking commercials, which the Federal Communications Commission had forced broadcasters to air in proportion to cigarette commercials. Since the health scare has been the relatively stronger influence, the net effect of the ban may be to increase consumption, not decrease it. Ban advocates disregarded the interconnection of cigarette and antismoking commercials; the United States cigarette manufacturers apparently were not confused about the interconnection. Finally, the probable anti-competitive effects of the ban are noted in section IV.

THIS paper examines the effect of market on the rate of return of selected firms operating in different market environments. It will be shown that the effect of on profiltability depends on the degree of concentration and rate of growth in the industries in which the firm competes, and on the absolute size of the firm. One of the most important propositions of micro-economic theory is that under competitive conditions, rates of return tend toward equality. A casual look at the data will reveal that rates of return are not equal and that differences in rates of return often persist over time. Many studies have utilized industry concentration as a measure of market power and have analyzed the effect of concentration on industry profitability (a sizeable list may be found in Weiss (1971)). Three recent studies have looked at the effect of concentration on profitability using the firm as the unit of analysis (Federal Trade Commission (FTC), Hall and Weiss (1967), and Shepherd (1972)). Although data is not generally available for most firms, the FTC study does examine the effect of relative market share (market divided by the big four firm concentration ratio) on profitability in food manufacturing firms, while the Shepherd paper examines the effect of market for a sample of large, nondiversified firms. The more recent of the above studies emphasize additive multiple regression models. While these models attempt to control for the effects of some dimensions of market structure when focusing on the effect of a particular structure variable, they do not capture the interaction effects of structure variables on profitability. Two independent variables are said to interact if the effect of one independent variable on the dependent variable depends on the level of the other independent variable. Interaction effects may be analyzed in the following three ways (1) specifying an interaction model, (2) including interaction variables in an additive model, or (3) by estimating the parameters of an additive model for subgroups of the total sample. A version of the third method is employed in this study and will be discussed in section I. To illustrate this subgrouping method, suppose we divide our sample into two subsamples (A) firms in highly concentrated industries and (B) firms in lowly concentrated industries. As will be explained below, we expect that the slope coefficient from a regression of profitability on in the high concentration subgroup will be much higher and more significant than the slope coefficient from the low concentration subsample. The primary goal of this paper is to develop and test a theory of the effect of firm on profitability under various competitive situations. We have tried to integrate, formulate, and extend some elements of oligopoly theory and to test the resulting hypotheses. The hypothesis and finding that affects rate of return is greatly strengthened by the more complex interaction hypotheses and findings.1 In carrying out this major goal we also examine the effects of both firm and industry growth on profits, develop new evidence on leverage as a measure of risk, comment on the controversy over the correct measure of profitability, and introduce the concept of market as a so;urce of product differentiation. The paper contains four major sections. The first section develops the theoretical relationship between and profitability. This discussion focuses on the interaction effects on profitability of and the market environReceived for publication September 30, 1971. Revision accepted for publication June 21, 1972. * I am indebted to Ronald G. Ehrenberg, Kenneth Gordon, Marshall C. Howard, James K. Kindahl, Thomas Muench, and George Treyz and two referees for comments and suggestions on an earlier draft of this paper and to Patricia M. Anderson for programming services and comments. ' The interaction findings, especially the growth interaction, support the case for interpreting the data in this cross-section study as representing the effect of on profitability. An examination of the dynamic process by which firms alter their market positions would require time-series data. (See Gale, 1972.)

PROBABLY more than half of capital expenditures involve in one sense or another the replacement of existing stock. Among competing hypotheses as to the timing and determinants of replacement expenditures are: (1) they are a fairly constant proportion of capital; (2) they substitute for expansion expenditures, thus stabilizing the annual rate of investment, falling when expansion rises and rising when expansion decreases; (3) they are tied closely or are essentially equal to depreciation charges; (4) they vary with the current rate of profit or flow of funds; (5) they are positively related to the age of capital stock. McGraw-Hill capital expenditure survey data and collateral statistics offer a unique opportunity to test these and related hypotheses. In a recent article, Feldstein and Foot (1971) have utilized McGraw-Hill aggregative reports, along with series from the Department of Commerce on planned capital expenditures. and from the Federal Trade Commission and Securities Exchange Commission on flow of funds, in an analysis of replacement expenditures. This paper offers a partly parallel analysis of both replacement and expansion expenditures on the basis of individual firm data. Key to the analysis is a question which has been included in the McGraw-Hill spring surveys in the years 1952 through 1955 and 1957 to date: Of the total amount you now plan to invest in new plants and equipment in [the current year] how much is for: expansion %; replacement and modernization % ? By applying the indicated proportions to anticipated and actual capital expenditures, estimates have been obtained of expenditures for replacement and modernization and expenditures for expansion. For actual expenditures these estimates related to from 112 to 254 firms in each of the fourteen years from 1954 to 1968, excluding 1956; 1 estimates of anticipated expenditures were available for approximately the same firms. The basic data, price-deflated and otherwise processed as previously reported,2 are as follows:

T HIS paper presents the results of an empirical study of the distinguishing characteristics of United States manufacturing corporations with foreign subsidiaries. My conclusions are drawn from two sets of data: the first covers 1191 manufacturing corporations, 576 of which owned a majority interest in a Canadian subsidiary in 1967. My second set of data, a subset of the first, covers Fortune's 500 largest industrial corporations, 187 of which qualified for the designation of the Harvard Business School.' I hope to draw some basic inferences about the direct investment process by comparing the characteristics of those firms investing in Canada with those not doing so, of those which are multinational with those which are not, and those which are multinational with those investing in Canada, if not in, six other countries. In order to put the contribution of this paper into proper historical perspective, let me comment briefly on the existing literature on why firms invest abroad. Earlier research has tended to fall into one of two categories: studies of the characteristics of the industries in which foreign investing is comparatively heavy, or studies of the characteristics of the individual firms investing abroad. The industrial studies are far more common (owing largely, one suspects, to the easier access to industry data) and have been thoroughly surveyed in a recent paper by Richard Caves. His conclusions in a nutshell were:

HE field of industrial organization has acT quired an abundance of hypotheses about what comprises market structure.1 Neoclassical analysis was premised on the firm's market share, atomistic or pure monopoly. Then came the Chamberlinian group of the 1930's, Bain's entry barriers of the 1950's, and firm size and advertising in the 1960's. This abundance yields vitality, but it has also left uncertain the relative importance and interrelations of the individual structural elements. Empirical analyses, relying mainly on partial tests relating one or two elements with a dimension of behavior, have not resolved the patterns. This paper attempts to compose these differences by fitting models of structure to recent data on large United States industrial corporations. Section I prepares testable models of the elements, both in static and in comparativestatic contexts. Data on a panel of 231 large United States industrial firms during 19601969 are described in section II. Section III presents the empirical analysis, and the results are summarized in section IV.

M OST of the measures of income inequality are derived from the Lorenz curve; indeed Morgan (1962) states that the Gini index is the best single measure of inequality. The present article reviews some of the theoretical properties of the Lorenz curve, relates them to characteristics of the frequency function underlying the income distribution and develops methods for obtaining accurate bounds on the Gini index which do not depend on curve fitting. In the process we should also like to lay to rest some myths concerning the Gini index such as: (a) its relative insensitivity (Rltet6 and Frigyes, 1968), (b) difficulty in computation (1968), and (c) problems related to the inclusion of negative incomes (Budd, 1970). The basic idea of our approach is to obtain upper and lower bounds to the Gini index from data which are grouped in intervals and the mean income in each interval is known. The usual method (Morgan, 1962) of estimating the Gini index yields a lower bound by assuming that all incomes in any interval equal the average income. We derive an upper bound to the grouping correction (Goldsmith, et al., 1954, p. 10) and hence to the Gini index by distributing the income to maximize the spread within each group. On the 1967 Internal Revenue Service tax data, the difference between our bounds is less than 0.006. As most income distributions come from a frequency function (density) which decreases in the large income range, we develop improved bounds for the Gini index based on this assumption. Fortunately, this assumption can be checked from the data so that we can use the sharper bounds only for the appropriate intervals. Using this second method the difference between our bounds is ? .002. Because Soltow (1965) detects a change in the Gini index of 0.8 of one per cent or about 0.003 or 0.004, our bound seems quite adequate. In section VI we extend our method to obtain upper and lower curves for the Lorenz curve. After reviewing the basic properties of the Lorenz curve we proceed to derive bounds on the mean difference and Gini index. In section IV we analyze an actual sample and show that the method used by the Census Bureau (1967) often leads to estimates which are outside the mathematically possible bounds we derived. Finally, in an appendix we show that the Pareto law does not give a good fit to current United States tax data.

Journal Article CES Production Functions a la Samuelson Get access Ashok Guha Ashok Guha Jawaharlal Nehru University Search for other works by this author on: Oxford Academic Google Scholar The Review of Economic Studies, Volume 39, Issue 4, September 1972, Pages 501–503, https://doi.org/10.2307/2296519 Published: 01 September 1972