Price-level accounting, Price levels, Utility function

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.

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.

1. SUMMARY IN two previous papers [1] [12], a family of normative models of the individual's economic decision problem under risk were presented. At the same time certain implications of these models with respect to individual behavior were deduced for a class of utility functions. In a separate article [7], it was demonstrated that these models also give rise to an induced theory of the formation and operation of firms under risk for the aforementioned class of utility functions. In the present paper, it will be shown that the same models, developed with the individual in mind, have as further off-spring an induced theory of accounting for all firms so formed. In Section 2, the basic approach of the present study to the development of normative accounting theory is discussed. This section also considers some of the relationships of the present paper to other studies concerned with the development of prescriptive theories of accounting. In Section 3, the various components of the basic decision model used in the present paper are constructed. The individual's objective is postulated to be the maximization of expected utility from consumption as long as he lives and from the bequest left upon his death; his lifetime is presumed to be a random variable. The individual's resources are assumed to consist of an initial capital position (which may be negative) and a noncapital income stream. The latter, which may possess any time-shape, is assumed to be known with certainty and to terminate upon his death. In addition to insurance available at a "fair" rate, the individual faces both financial opportunities (borrowing and lending) and an arbitrary number of productive investment opportunities. The interest rate is presumed to be known but may have any time-shape. The returns from the productive opportunities are assumed to be random variables, whose probability distributions may differ from period to period but are assumed to satisfy the...