The Class of Homothetic Isoquant Production Functions Get access S. Clemhout S. Clemhout University of California, Berkeley Search for other works by this author on: Oxford Academic Google Scholar The Review of Economic Studies, Volume 35, Issue 1, January 1968, Pages 91–104, https://doi.org/10.2307/2974410 Published: 01 January 1968

Journal Article Optimal Growth and Continual Planning Revision Get access S. M. Goldman S. M. Goldman University of California, Berkeley Search for other works by this author on: Oxford Academic Google Scholar The Review of Economic Studies, Volume 35, Issue 2, April 1968, Pages 145–154, https://doi.org/10.2307/2296544 Published: 01 April 1968

I. Introduction, 419. — II. Elasticity of supply of savings, 420. — III. Analysis under uncertainty, 427. — IV. Implications, 434.

EMPIRICAL studies of the investment decision have been restrained by the lack of data to the examination of investment expenditures anticipated or realized. A consequence of this empirical bias may be the diversion of attention away from the complete decision-making process and to the misleading impression that the investment decision is primarily and essentially one of timing and financing investment outlays. (See, however [2, 5, 6, 12-14].) The underlying hypothesis of this paper is that there are two investment decisions: The first, reflecting long-run plans and expectations, is whether or not to invest at all; the second, chronologically, is when to make and how to finance the actual expenditures. The latter is likely to be a function of the actual market conditions faced or the short-term expectations of those market conditions. While the need to include plans and expectations into the analysis may be fairly obvious, the necessary algebra remains elusive. However, objective data can capture most of what we need to know about expectations, leaving the algebra to be uncovered by empirical research. All that is needed are data that can be deemed to embody expectations without necessarily specifying their origin. Accordingly, a rather general model will be developed using capital appropriations data and initial conditions, which will illustrate the method proposed. In this paper, only the first decision, the formal commitment to invest, will be examined further. Given the capital appropriation, the question is what constitutes the set of relevant initial conditions and how much of the capital appropriations can be accounted for by reference to it. If the hypothesis of two investment decisions is correct, then there is a subset of initial conditions influencing this first investment decision and another subset which does not. This is essentially an empirical question. To examine the relationship between capital appropriations and initial conditions, cross-section data are used. They are generally regarded as reflecting long-run tendencies, and since the first decision is more or less a stock one, variables which vary over time and thus more appropriate for the flow decision prices, interest rates are eliminated. Two years have been selected for study 1956 and 1961-which are the best years available in the basic data. These years exhibit roughly the same movements in the business cycle and are far enough apart so that structural changes are permitted. The initial approach to the data and the immediate task for the present is to determine: (a) What the relationship is between capital appropriations and various selected variables for selected industries in each of the two years; (b) Whether the structure of expectations the same variables dominating was the same for each industry in 1956 as in 1961; (c) Whether there are significant differences among industries in the variables which are important. The data used were supplied by the National Industrial Conference Board (NICB) which since 1953 has conducted a quarterly survey of capital appropriations for the top corporations in the United States. These are large corporations and account for a sizeable proportion of investment expenditures. For a more detailed description of the data see Cohen [13]. Out of seventeen industrial groups of NICB, seven were selected for study: Primary Iron and Steel, Primary Nonferrous Metals, Machinery (except electrical), Fabricated Metals, Food and Beverages, Textiles Mill Products, and Paper and Allied Products. These industries were selected for their possible differing structure of expectations and because they rep* The author is an Assistant Professor of Economics at the University of Vermont. Parts of this paper are based on his Ph.D. dissertation, Expectations and The Investment Function (Rutgers The State University, Jan. 1966). He is indebted to Rutgers The State University for grants received, and to The Bureau of Economic Research at Rutgers University for additional financial support. The author is also indebted to K. K. Kurihara and M. Dutta for many helpful suggestions.

CONSIDERABLE attention has recently I ~~been given to the theory of foreign exchange operations and its implications for government policy. Central to this is the analysis of forward exchange speculation.' Although the essence of speculative behavior is the balancing of uncertainty and expected gain, the analysis of uncertainty in the current theory of forward exchange speculation has generally been less rigorous than other parts of that theory. The purpose of this paper is to present a more explicit theory of the role of uncertainty in forward exchange speculation in the framework of von Neumann-Morgenstern expected utility maximization and to explore its implications for speculator behavior and government policy. Section I is a brief review of the contemporary analysis of foreign exchange speculation. Section II presents the expected utility maximization theory and derives a mean-variance framework for analyzing speculator behavior. The effects of changes in the mean and variance of anticipated gain is discussed in section III, with speculation assumed to occur only in terms of one currency. The theory is extended to multiple currency speculation in section IV. Some policy implications are discussed in section V. Finally, section VI provides a brief summary.

can take all the Sj and try to minimize the variance of vj via factor analysis. We could then find S and also see which Sj was most closely correlated with S. Unfortunately this technique requires that the Sj does not have common measurement error. Since none of the Sj are completely independent of all others (some common source of data is used), common error can creep in. In principle, if one data sourcebut not another -gave answers unacceptable in terms of the a priori considerations dictated by economics, we could eliminate the series. In the present instance, the only possibility would be the significance of NTW1 in the Sggc equations but not in the SOBi}B forms. The differences in cyclical behavior between series are disturbing. But none of the responses violate all saving theories especially since the more recent theoretical innovations, such as permanent income and the ratchet effect define saving to include purchases net of depreciation. Finally the relative quality of the data could be judged by a detailed examination of the primary data sources and subsequent manipulations. This cannot be done now since the last time the SEC and the OBE published detailed descriptions of their sources and manipulations was more than a decade ago and those descriptions in [3, 5] are out of date. Besides, the number of primary data sources used is quite large and diverse. Only a group of individuals familiar with the separate parts could hope to do a competent study. The conclusion, thus, is quite pessimistic. For the saving function, one of the most basic elements of macro-economics, the dynamic and cyclical characterization depends upon our choice of measurement of a given concept and we do not know which measurement is correct.

Corporations tender for their own shares for a variety of reasons. Some stock tenders are made for strategic purposes—to prevent a take-over, to raise the market price of the stock, or simply because the stock represents ‘a good investment.’ For discussion of tendering in these situations, see the articles of Ellis [2] and Guthart [1]. In addition, there may be tactical reasons for a stock tender; one such reason is to reduce bookkeeping and shareholder servicing costs. In this instance, the argument runs roughly as follows: “The annual cost of servicing a holding is independent of the number of shares; consequently, the cost per share of servicing small holdings is relatively great. Let us reduce these high per-share costs by buying up small holdings.” Typical procedure is to then mail out an offer to buy holdings of less than a certain size directly, thus permitting the shareholder to dispose of his holding without paying the usual brokerage and odd-lot fees. Frequently no premium is offered except for the avoidance of brokerage fees. If one were to consider the premium offered as a controllable variable, it would be surprising to discover that its optimal value were exactly zero. One also recognizes that the maximum shareholding tendered for may be another decision variable available for optimization. See the appendix for data on tenders of this sort made in recent years. The variety of policies seems to indicate an almost complete absence of systematic application of the ideas presented here.

E. S. Phelps, R. A. Pollak; On Second-Best National Saving and Game-Equilibrium Growth1, The Review of Economic Studies, Volume 35, Issue 2, 1 April 1968,