Journal Article A Note on the Transactions Demand for Cash Get access Russell D. Morris Russell D. Morris Board of Governors of the Federal Reserve System Search for other works by this author on: Oxford Academic Google Scholar The Quarterly Journal of Economics, Volume 85, Issue 3, August 1971, Pages 546–547, https://doi.org/10.2307/1885942 Published: 01 August 1971

In recent years, several studies have appeared which provide some support for an inverse relationship between earnings variability and share price.' That is, increased variability in reported earnings, other things equal, appears to reduce the price of a firm's shares. A rationale for this behavioral phenomenon has been suggested by several accounting writers. Almost two decades ago Hepworth contended that :2

Careful examination of the behavior of financial variables over time uncovers an important distinction: variables expressed in dollars, such as earnings per share, behave very differently from percentage changes in those same variables. Similarly, financial ratios, such as the price/earnings ratio, behave quite differently from percentage changes in financial ratios. Variables expressed in dollars and financial ratios appear comparatively stable and predictable over time. Successive values are fair approximations of one another. Percentage changes in dollar and financial ratio variables-i.e., growth variables on the other hand, tend to be erratic, volatile, and unpredictable over time. Successive values bear little relation to one another. This distinction between dollar and ratio variables, on the one hand, and percentage changes in these variables-i.e., growth variables-on the other, serves as a useful basis for a financial model.

[In this study, a dynamic initial investment-borrowing model involving nonconvex investment effects and borrowing limitations is formulated as a discrete-time control problem. In the model, the firm's objective is to maximize, subject to constraints, the net worth of the firm over a finite decision-making period. Initial investment and borrowing are control parameters; and the scale of capacity use is the control variable. Investment costs, which reflect the "six-tenths" rule in particular, are nonconvex. Special considerations are thus involved in deriving the investment and borrowing rules. It is shown that the optimum must be at one of the following three points: (i) no investment and no borrowing, (ii) investment of just the endowment, and (iii) investment of the maximum amount possible. This result is especially important computationally, because the problem is convex at the points described by (ii) and (iii), and trivial at the origin. Therefore, the optimum may be computed by the use of published algorithms.]

In this paper, a continuous time model for a monopoly firm of the Evans' type, encompassing operations, investments, and output prices, is formulated as an optimal control problem. In the model the objective of the firm is to maximize, subject to various constraints, the integral of production profits less interest and investment costs over a finite decision-making interval, plus the value of the capacity at the end of the period. The state variables are capacity, debt, and output price; the controls are the scale of operation, rate of purchase of new capacity, and rate of change of the output price. Final capacity, price, and debt are control parameters. There are several inequality constraints. Using results in control theory, the optimal controls are characterized for a model basically linear in structure. It shows that the one case suggested by Evans for further analysis is a trivial problem. These results are interpreted using the properties of the value equation. In addition, the control model is formulated alternatively as a mathematical programming problem. Solutions may then be computed by published algorithms.