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W HAT IS AN ADEQUATE RATE OF RETURN for an electrical utility?* Textbooks and tradition usually mention a figure of 6%-a nice round figure probably pulled out of the air at some time in the past. But is this mythical 6% adequate, or is it too much or too little? The purpose of this article is to develop a measure whereby the rate of return can be justified on more solid ground than heretofore. Although the results may not necessarily be precise, at least some sort of a yardstickperhaps with a bit of rubber in it-will have been established. It is our thesis that the rate of return should be related to the corporate-bond interest rate and should vary in the same direction as the interest rate. Utilities must compete with other enterprises for money, and the price of money is determined by the interest rate, with premiums being paid for risk. Therefore utilities must be allowed a return that not only is commensurate with the risks involved at the present (that is, on their sunk capital) but also will attract future financing on a competitive basis. A strict cost of capital approach is not advocated since, within limits, the higher the proportion of debt, the lower the rate of return required. Furthermore, in times of bear markets, stocks sell on a higher yield than in bull markets, and this could lead to the necessity for a higher rate of return in recessions than in good times. These are but two of the many arguments that may be made against the cost of capital approach.t

The advance that has been made in determining the economic value of education, since I last considered this problem,1 is impressive. Tlis symposium affords an opportunity to take stock with a view of re-examining this problem and of seeing where we have arrived. I shall comment, first, on the advantages of thinking in terms of the rate of return, provided allowance is made for the lack of efficiency prices in the capital market serving private investment in education and for omissions of particular forms of capital when planning for economic development. I shall, then, evaluate the new crop of estimates of earnings from education and of the costs of education. Mainly, however, I shall concentrate on the limits of the rate of return as a guide in allocating investment resources to education.

During the period of the late fifties and early sixties there was a considerable amount of discussion in the literature on the usefulness of the concept of the marginal efficiency of capital in the evaluation of alternative investment projects; see, for example, Masse (1962) and Merrett and Sykes (1962). There are basically two problems: multiplicity of roots for the solution of the marginal efficiency of capital, given in income stream and capital cost, and the different results obtained in ranking projects according to marginal efficiencies of capital and according to net present values. With respect to the former problem, some thought has been given to the economic meaning of the multiple roots and to the choice of root for ranking projects. The objectives of this paper are to show that the marginal efficiency of capital is not appropriate for ranking investment projects, as it is essentially an equilibrium concept; that the "internal rate of return" and the marginal efficiency of capital must be distinguished; and that, when the internal rate of return is appropriately defined, the ranking of projects by the internal rate of return and by net present value for projects with equal time spans is identical. Further, it is shown that the internal rate of return can always be calculated and has a unique value relative to the market interest rate. Finally, an economic interpretation is given to the multiple roots for the solution of the marginal efficiency of capital and to the case where there are no real roots.

IT IS WELL KNOWN that under certain circumstances the internal rate of return and the present value criteria for capital budgeting analysis can give conflicting recommendations as to the projects that should be included in the budget. When this occurs, the source of the difficulty can often be traced to the question of the reinvestment of cash flow receipts from the alternative investments. This note is intended to review and clarify this matter of the reinvestment of cash flows. The subject was correctly treated in the literature some 15 years ago, when several classic articles were published on the problems inherent in making "Ccorrect" capital budgeting decisions.2 In recent years, however, a number of elementary texts in corporate finance have contained a statement to the effect that "the present value approach assumes reinvestment of intermediate cash receipts at the discounting rate, while the internal rate-of-return approach assumes reinvestment at the internal rate."3 Taken at face value, this statement is incorrect, for neither approach to the selection of a "correct" set of investment projects from a larger set of opportunities makes any assumption whatever about the reinvestment of cash flows or the rate of return to be earned if reinvestment were to be considered. The point can be made clear by quoting the balance of the sentence by Renshaw (10) from which the quotation above was taken :4

THIS PAPER PRESENTS the results of an attempt to estimate the rate of return on capital by regression analysis of financial data. A model relating current profits to current and lagged inflows of long-term capital is considered and fitted to a set of data from the British Mechanical Engineering Industry. Both time-series and cross-section data are used. Acquisitions of long-term capital are measured by summing depreciation provisions, retained earnings and receipts from issues of ordinary shares and instruments of long-term debt. The motivation behind the exercise described in this paper is a feeling that micro-econometric analysis might provide useful information about financial performances in the industrial sector. The discounted cash-flow rate of return on capital is one of the most important dimensions of financial performance, and increasing emphasis is being placed on it in the literature on management decision-making.

As IS WELL KNOWN, regulatory agencies determine the dollar earnings of public utilities by fixing in rate decisions the rate base of the utilities and the rate of return that the utilities can earn on that rate base. Some regulatory agencies use original cost as their criterion in determining the rate base, others use reproduction cost as their criterion, and still others use a value, which for purposes of this paper will be called "fair value," somewhere between original cost and reproduction cost as their criterion.1 Since the reproduction cost of public utility assets has exceeded the original cost of these assets during the postwar period of increasing factor prices, the question naturally emerges of whether agencies using the original-cost ratebase criterion have tended to compensate for the lower rate base by allowing higher rates of return. This paper suggests an answer to this question, at least for the 15 Bell operating telephone companies in the country which operate within a single regulatory jurisdiction.2 The first part of the paper shows that in the case of these 15 telephone companies, those in original-cost rate-base jurisdictions have been permitted the highest rates of return on their rate bases and those in reproduction-cost jurisdictions have been permitted the

(1968). Cost of Capital—Rate of Return. Financial Analysts Journal: Vol. 24, No. 4, pp. 113-116.

PERIODS OF INFLATION have almost inevitably been accompanied by higher interest rates as a result of both borrower and lender discounting continuing inflationary conditions. These higher money costs have had obvious economic effects on both public and private sectors of the economy in terms of taxes and prices. Regulated industry, unfortunately, cannot look to higher rates for earnings relief except over the long term. In the interim, it is affected by unrecoverable lags in return for its investors. Informed regulatory agencies-operating with a degree of flexibility in recognizing the economic implications of higher interest costs are able to protect the investors and consumers from the vicissitudes of the economy. The purpose of this article is to explain fundamental problems for the investor and to point out major negative effects of doctrinaire regulation as it pertains to rate of return allowed utilities. The myriad of side issues entering rate investigations have been eliminated for ease in understanding the basic issues. The article points out serious deficiencies of a fixed rate of return as a measure of public utility operations under long-run inflationary conditions accompanied by higher costs of money.

(1965). Rate of Return as a Criterion for Investment Decisions. Financial Analysts Journal: Vol. 21, No. 4, pp. 109-113.

A rather extensive literature has developed that analyzes the behavior of the profit-maximizing regulated firm using the model introduced by H. Averch and L.L. Johnson (A-J). Taking the value of the fair rate of return as exogenously given, this set of papers has provided a rather complete and detailed analysis of the (absolute and relative) input levels chosen by such a regulated firm and the quantity of output produced by the company.

THE QUANTITY OF SCHOOLING embodied in the population and labor force of many countries has increased rapidly during the last generation. Some of this increase has been due to autonomous governmental action which makes schooling more accessible. But much of the pressure for more schooling comes from the population itself. While the reasons for this "social demand" may seem obvious, little is known about the dynamics by which the incentives to take more schooling are translated into increased demand. This study concerns itself with one particularly important incentive-monetary gain-and attempts to explain how the pecuniary yield to investment in schooling affects the increase in the amount of schooling taken. The private rate of return to investment in schooling and the private present value of additional schooling are both measures of the economic incentive for individuals to take more or less education.' In this paper, we estimate for a given year (1959) both rates of return and present values to taking additional schooling in Puerto Rico.2 We relate these rates and present values to the increase in schooling per male worker in broad occupational categories over the 20 years, 1940-1960. This yields a crude estimate of the relation between the rate of return (or present value) as a measure of economic incentive and the increase in average schooling in the labor force. Based on the 1960 rate of return estimates, we then make some hypothetical statements about the behavior of our incentive measures over time, and how this behavior would affect the demand for additional schooling in Puerto Rico. The results of the study show that the increase in the per capita stock of schooling has been rapid in the 20 year period covered-greater for females than for males, somewhat greater in absolute terms (but not relative) for urban males than for rural, and greater in both absolute and relative terms for rural females than for urban females (see Table 1). Similarly, per male worker in

The subject of this paper is a public utility's optimal dynamic response to the rate of return allowed by a regulatory commission. The problem is formulated in terms of the firm's capital-budgeting policy, and a dynamic analysis is made using modern control theory. This permits the utility's financial policies to be related directly to (a) the way the capital market values the utility and (b) the restriction on earnings imposed by rate-of-return regulation. The solution to the resulting nonlinear control problem provides a quantitative basis for analyzing the impact that small changes in the rate of return have on market valuation and the firm's investment policy. The results furnish one measure of what is commonly called "capital attraction capability," or the firm's ability to attract investment capital in a competitive capital market, and display the relation between that capability and the allowed rate of return.

The model presented assumes that public managers select investment projects hat maximize the net private benefits of their constituent pressure groups. This achieves increased agency size, which is more likely to increase managerial compensation than to maximize net social benefits, the assumed goal of the conventional public investment model. To increase agency size, managers must often resort to projects with low or negative return rates. The selection of such projects is possible because transactions costs are sufficiently large to bar successful opposition by disaffected taxpayers. The analysis as well as empirical evidence suggests that inefficient public projects are the rule rather than the exception.

THIS study is not meant to be a defense of or an attack upon the tobacco program. It began as an effort to understand the distributive process. The results conflict sharply with the beliefs of those who argue that labor has benefited from the program. Even though owner-operators supply the majority of the labor, it does not follow that opportunity returns to labor are therefore inseparable from returns to other factors. Nor is there any logical reason for a restriction of production to increase the demand for labor; and certainly nothing has been done under the program to reduce the supply of workers. North Carolina has more farmers than any other state, and many of them grow tobacco. The program clearly has helped the State, and some of its land owners, a great deal.' The main results of the study are summarized in Table 1. Independent estimates were obtained for the annual net revenue and the capitalized value of the right to produce a pound of flue-cured tobacco. Average values of these series, converted to constant dollars, were then calculated for approximately three decades, between 1934 and 1962. Net revenues were relatively constant during this period, increasing from 19.2 cents per * Published with the approval of the Director of Research, Agricultural Experiment Station, as Paper No. 265.3 of the journal series. The author is indebted to Richard C. Manning for the regression analysis of allotment values and for many of the ideas. He also wi-s es to thank Dale M. Hoover, Carnett L. Bradford, and J. S. Chappell for valuable suggestions. ' Agricultural economists have made a number of worthwhile studies of the tobacco program. These fall into roughly four categories: (a) explaining political forces and program alternatives; (b) social costs, including aggregate effects on exports; (C) JAMEs A. SEAGRIAVES is professor of economics at North Carolina State University. 320

problem in the theory of regulation. In this paper, we develop a simple but general concept of fair return based on an equilibrium model of production under uncertainty. We propose regulatory behavior which will induce firms to make efficient input choices, while at the same time guaranteeing fair returns. * Regulation is a common phenomenon in "natural monopolies," those industries with decreasing average costs. Optimal resource use in such industries dictates that output be provided by a single firm, but this easily leads to inefficient monopolistic practices by firms in the absence of regulation. Effective regulation, however, requires that meaningful regulatory objectives be specified and rules devised for their implementation. While economic theory provides appropriate objectives and behavioral rules when there is no uncertainty, the presence of uncertainty is central to the knottiest problems of regulation. And until recently, economic theory had little to say about optimal production in the presence of uncertainty. A particularly crucial problem facing regulatory agencies is an appropriate definition of a "fair" rate of return. The legal guideline for regulation, based on the Hope decision, requires that regulatory policies provide a return to the equity holder "commensurate with returns on investments with corresponding risks."' Under certainty, this guideline is well-defined: equity holders should receive the riskless rate of return which prevails throughout the economy. Under uncertainty, the guideline is much less clear. Often corresponding risks are not present. And if they are present, they usually are associated with other regulated firms, leaving a simul

THE PRINCIPAL OBJECTIVE of this study is to investigate theoretically and empirically the relation between saving in the private sector of the United States and the rate of return on capital. A model of household behavior is developed in which the supply of labor is simultaneously determined with consumption and saving in a utility-maximizing framework. Previous studies have assumed that individuals could adjust their consumption time-path but not the pattern of labor services offered; the implicit assumption is that a labor-leisure decision precedes the consumption-saving decision. Allowing these decisions to be made simultaneously is more realistic. This is accomplished by introducing leisure into the household utility function. The utility function thus depends on consumption and leisure in the present and all future time periods. The functional forms that are used to represent the utility function have separability properties which allow the maximization of utility to be partitioned into a two-stage process. In the first stage total wealth is allocated between the present and all future periods, while the second stage distributes each period's allocation to the individual commodities, consumption and leisure. The time constraint combines with this result to yield the supply of labor and hence current wage income. A simple but restrictive specification for the welfare function is the nested CobbDouglas, where each single-period utility index is a Cobb-Douglas function of consumption and leisure, and the overall index is a Cobb-Douglas function of all the single-period indices. The allocation of wealth resulting from such a function is independent of the relative prices of consumption and leisure and of the rate of return. The Cobb-Douglas function has two well-known generalizations which can be used to relax the implied proportionality. The first is the Stone-Geary utility function which introduces nonhomogeneity parameters into the single-period utility indices. These are usually interpreted as committed amounts of consumption and (in this case) leisure. Allocation is still proportional at the margin but not proportional overall. The price level, the wage rate, and the rate of interest, however, still do not affect the allocation. The second generalization of the Cobb-Douglas function is the constant-elasticity-of-substitution (CES) function. In this case prices and the rate of return have a role to play in the allocation provided the elasticities of substitution are different from unity. Of course, both generalizations could be made simultaneously, yielding a nested CES function with nonhomogeneity parameters. Demand functions for consumption and leisure are derived for the various utilityfunction specifications. The demand functions corresponding to the generalized utility functions all have proportionality (Cobb-Douglas) as special cases. Thus with appropriate econometric specifications and time-series data the empirical relevance of the generalizations can be assessed. Even though the behavioral relations of the household sector are of primary interest, the observed variables entering these relations are jointly determined with other macro-variables in the economy. Feedback from the rest of the economy raises the possibility of stimultaneous-equations bias. Thus a complete, though simplified

This article illustrates a simple experimental approach, used in increasing the rate of return in mail surveys.

THIS paper examines the effect of market share on the rate of return of selected firms operating in different market environments. It will be shown that the effect of share 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 share data is not generally available for most firms, the FTC study does examine the effect of "relative market share" (market share divided by the big four firm concentration ratio) on profitability in food manufacturing firms, while the Shepherd paper examines the effect of market share 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 share 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 share 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 share 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 share as a so;urce of product differentiation. The paper contains four major sections. The first section develops the theoretical relationship between share and profitability. This discussion focuses on the interaction effects on profitability of share 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 share on profitability. An examination of the dynamic process by which firms alter their market share positions would require time-series data. (See Gale, 1972.)