Price-level accounting, Price levels, Utility function

Journal Article The Efficient Capital Programme for a Maintainable Utility Level Get access H. Atsumi H. Atsumi Osaka University Search for other works by this author on: Oxford Academic Google Scholar The Review of Economic Studies, Volume 36, Issue 3, July 1969, Pages 263–287, https://doi.org/10.2307/2296427 Published: 01 July 1969 Article history Received: 15 December 1967 Received: 15 December 1968 Published: 01 July 1969

Consider an economy consisting of individuals and firms with the following characteristics: all individuals are rational in the von Neumann- Morgenstern sense and non-neutral toward risk; the dividend streams of some firms are certain, while the dividend streams of the other firms are uncertain; and the economy is equipped with perfect financial markets. In this economy, as we show in the present paper, the value of each firm with a certain dividend stream depends only on the dividend stream itself and the set of future interest rates—i.e., the market value of such firms is independent of the attitudes toward risk and the level of wealth of any individual. However, the value of each firm with an uncertain dividend is, with one exception, not independent of anything: it depends not only on the firm's own dividend stream, the set of future interest rates, and (all) individuals' risk attitudes, but also on the wealth levels of these individuals and on the dividend streams of all other firms with uncertain dividends even when these streams are stochastically independent. The exception occurs when the individuals have exponential utility functions of money. In this case, the market value of each firm with uncertain dividends is independent of other dividend streams and of individual wealth levels if these variables are statistically independent of the firm's dividends. Exponential utility functions of money, of course, are not considered empirically plausible.

Until very recently, in most work on normative models for capital investment planning, it has been assumed that availability of capital is unconstrained; i.e., that money may be freely borrowed or lent at a single market rate of interest, and that no other constraints affect the proper choice of available productive investment projects to be undertaken. Since practical situations almost universally do involve such constraints, the traditional theories have, for the most part, been an unsatisfactory guide to achievement of optimal capital investment behavior in the real world.

This article examines some aspects of the portfolio selection problem when the “no-easy-money-condition” holds and the investor is constrained to stay solvent. The possible presence of a non-capital income is also taken into consideration.

When we combine assumptions that the utility function is additive and that one commodity is an inferior good (defined as one for which purchases decrease as income increases), we produce a case in which there are n-i inferior goods, each of which has diminishing marginal utility, and one normal commodity (defined as one for which purchases increase as money income increases), which has increasing marginal utility. This result is of considerable general interest. It provides an analytical method of evaluating the results of empirical studies of demand based upon additive utility functions written for blocks of commodities [2] [4] [7]. Unless such empirical studies produce a result in which all income elasticities are positive, they must produce a result in which there are n-i negative income elasticities and one positive income elasticity. In addition to the general demonstration mentioned above, this paper also presents what is apparently the first published specific utility function, together with its associated demand functions to illustrate the case of a commodity with a negatively sloping income consumption curve. This specific (additive) utility function can be subjected to a monotonic transformation by squaring it; such a transformation leaves the demand functions unchanged and, in our case, will produce an illustration of the case of an inferior good based on an assumption of dependence of the marginal utilities. I turn first to the general demonstration that the combined assumptions: (1) that the utility function is additive, and (2) that one good is inferior, imply that there are n-1 inferior goods (all with diminishing marginal utility) and one normal commodity (with increasing marginal utility). Assume the existence of a consumer with a utility function of the form:

This paper is concerned with the use of spectral analysis to analyze data generated by computer simulation experiments with models of economic systems. An example model serves to illustrate two different applications of spectral analysis. First, spectral analysis is used to construct confidence bands and to test hypotheses for the purpose of comparing the results of the use of two or more alternative economic policies. Second, spectral analysis is employed as a technique for validating an econometric model.