One of the most important concepts in economic theory is the “invisible hand,” introduced by Adam Smith in the following terms:

Every individual intends only his own gain, and he is in this, as in many other cases, led by an invisible hand to promote an end, which was no part of his intention. Nor is it always the worse for the society that it was no part of it. By pursuing his own interest, he frequently promotes that of the society more effectually than when he really intends to promote it.

One of the problems which has plagued microeconomic theory is the difficulty in achieving close correspondence between formal models and practical market situations. The most widely accepted models envisage the firm set in a static mold with the implication that profits will be maximized in every period. The model is more generally acceptable in the case of perfect competition, for then the market results are most likely to be “as if” the firms acted marginally to maximize profits. Only the profit maximizers will survive. While such a scheme may lead to realistic results in the case of perfect competition, this condition does not bulk large in the United States economy.

A number of studies have recently attempted to explain cross sectional variations in selected characteristics of commercial bank operations through least squares regression analysis.1 Generally, whether the particular study objective was to explain inter bank differences in costs, revenues, profits, or loan rates, several explanatory variables were isolated which varied systematically among banks, and which at least partially explained differences in the dependent variable. The explanatory variables which were shown to be theoretically relevant, and statistically significant, were then interpreted literally and designated as having causal characteristics.

The determination of the term structure of interest rates, a subject of much controversy in recent years, has emphasized two principal viewpoints: the expectations hypothesis stresses the importance of expectations of future yields as determining the present term structure of interest rates; and the liquidity hypothesis emphasizes the greater “moneyness” of short-term debt as opposed to long-term debt. These main theories provide certain unique insights into the term structure; the acceptance of one need not require the rejection of the other. And the factors they stress at least hold the possibility of simultaneously influencing the term structure of interest rates.

The concept of profit sharing—whereby a company provides employees with a contribution above and beyond their regular wages based upon business profits—is very old indeed. Implementation of this concept is witnessed by the many profit sharing plans of all kinds in existence today. However, even though the concept is old and the use widespread, there is a complete void in published literature on the nature of optimal profit sharing plans. It is the purpose of this paper to investigate this subject.

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.

J. M. Keynes' theory of portfolio management (modified and refined by Tobin)occupied an important role in his analysis of the demand for money. According to this theory, financial investors were thought to vary the composition of their portfolios between money and securities on the basis of expected yields on securities. When yields were expected to rise, investors would shift out of securities and into money. Conversely, when yields were expected to fall, investors would shift out of money and into securities. Hence, the asset, or portfolio, demand for money was argued to be negatively related to the expected yields on securities.