Certainty Case Research Articles

The effect of production uncertainty on the labor-managed firm

The effects of production uncertainty on the behavior of the labor-managed, cooperative firm are examined and it is shown that they generally differ from the case of certainty and the case of the entrepreneurial, profit-maximizing firm. In particular, it is shown that the risk-averse (risk-seeking) cooperative will have a larger (smaller) ratio of labor to nonlabor input employed in production than the risk-neutral cooperative.

Production theory, uncertain prices and investment portfolios

AbstractThis paper examines the allocative decisions of a competitive firm where input and output prices are uncertain and where the capital asset pricing model prevails. The firm behaves much as a profit maximizer under certainty, except that certainty equivalent prices formally replace the known prices. These certainty equivalent prices are composed of the expected price, the covariance of the price with the market (a measure of systematic risk) and a measure of risk aversion in the economy. Both static and comparative static propositions emerge in a natural way as extensions of standard, competitive and profit maximizing behavior. In addition, the model contains both the certainty case and the risk‐neutral case as limiting examples.

Financial Theory and Corporate Policy.

I. FINANCIAL THEORY. 1. Introduction to Capital Markets, Consumption and Investment. 2. Investment Decisions: The Certainty Case. 3. Theory of Choice Under Uncertainty: Utility Theory. 4. State-Preference Theory. 5. Objects of Choice. 6. Market Equilibrium: CAPM and APT. 7. Pricing Contingent Claims: Option Price Theory and Evidence. 8. Futures Contracts and Markets - Term Structure - Cox, Ingersoll, Ross. 9. Multiperiod Aspects of Financial Theory - Real Options - Investment. 10. Efficient Capital Markets: Theory. 11. Efficient Capital Market: Evidence. 12. Information Asymmetry: Agency Cost Theory and Signaling. II. CORPORATE POLICY. 13. The Role of the CFO and Performance Measurement. 14. Valuation and Tax Policy. 15. Capital Structure. 16. Dividend Policy. 17. Applied Issues in Corporate Finance. 18. External Investment Decisions. 19. International Finance: Theory and Evidence. 20. Open-Ended Issues for Research.

On the Measurement of Welfare Cost under Uncertainty

Welfare cost measurement under various sorts of uncertainty (essentially all welfare cost measurement) has proceeded with ad hoc and unsatisfactory methods. Generally, either uncertainty is suppressed entirely, with social surplus computed at the point of mean values of the random variables, or expected social surplus is used. While a natural evolution from the certainty case, neither procedure has a justification except as an approximation to some undefined true measure, and either can lead to gross miscalculations of benefit. This paper offers a rigorous and operational alternative by defining an appropriate concept of compensation under uncertainty and developing an approximation to it. Most dead weight loss analysis of tax changes involves pure planner uncertainty about preferences and thus about the price and income changes due to the tax changes. Each consumer is assumed to know his own tastes with certainty, but planners know them only probabilistically. This creates a forecast problem for prices and incomes. The universal procedure is to suppress randomness entirely and use mean values of demand slopes, intercepts, and induced price and income changes as if they were certain. With price and income uncertainty for both consumers and planners the focus, a number of authors have studied the effects of price stabilization using expected social surplus. Brown, [2], Hueth and Schmitz, [4], and others have followed the lead of Waugh, [11], and Oi, [8], in this procedure. AndersonRiley, [1], criticize expected social surplus for ignoring the variation in the marginal utility of income which lies at the heart of welfare issues under uncertainty.' In fact, it is shown that when prices are stabilized at the mean, the signs of expected welfare change and expected social surplus can differ.

The Stock Market, the Objective Function of the Firm, and Intertemporal Pareto Efficiency-the Certainty Case

An extensive literature has recently dealt with problems concerning the stock market and the objective function of the firm, under conditions of uncertainty. This paper deals with the certainty case and develops a two-date production economy with a stock market, distinguished from the corresponding Arrow-Debreu model by a different market structure. Even in this simple set-up, different objective functions of the firm can be examined. Maximizing the market value of shares does not lead to Pareto efficiency, unless there are very many firms. By contrast, maximizing the rate of return on stockholders' investments, when taking the value of shares as given, does lead to Pareto efficiency.

An Asymptotic Theory of Growth Under Uncertainty

The neoclassical theory of capital accumulation and growth under certainty for both positive and optimal savings functions has received extensive study in the literature for almost two decades. However, the study of capital accumulation under uncertainty began much later and these analyses for the most part confined themselves to linear technologies. In his pioneering work, Phelps [19] and, later, Levhari and Srinivisan [10] ,Hahn [5] and Leland [23], examine the optimal consumption-saving decision under uncertainty with a given linear production technology. Hakansson [6], Leland [9] and Samuelson [21] in discrete time and Merton [12, 13] in continuous time, along with a host of other authors, have studied the combined consumption-saving-portfolio problem where the production functions are linear, but where there is a choice among alternative technologies. There have been a few notable exceptions to this concentration on linear technologies. In a seminal paper, Mirrlees [17] tackled the stochastic Ramsey problem in a continuoustime neoclassical one-sector model subject to uncertainty about technical progress. Later, in [18], he expanded his analysis to other types of technologies. Mirman [16] for positive savings functions and Brock and Mirman [1] for optimal savings functions, using a discrete-time, neoclassical one-sector model, proved the existence, uniqueness and stability of a steady-state (or asymptotic) distribution for the capital-labour ratio. These steadystate distributions are the natural generalizations under uncertainty to the golden-age/ golden-rule levels of the capital-labour ratio as deduced in the certainty case. While these papers are important contributions with respect to existence and uniqueness, they have little to say about the specific structure of these asymptotic distributions or about the biases (in an expected-value sense) induced by assuming a certainty model when, in fact, outcomes are uncertain. The basic model used in this paper is a one-sector neoclassical growth model of the Solow-type where the dynamics of the capital-labour ratio can be described by a diffusiontype stochastic process. The particular source of uncertainty chosen is the population size although the analysis would be equally applicable to technological or other sources of uncertainties. The first part of the paper analyses the stochastic processes and asymptotic distributions for various economic variables, for an exogeneously given savings function, and deduces a number of first-moment relationships which will obtain in the steady-state. In addition, the special case of a Cobb-Douglas production function with a constant savings function is examined in detail and the steady-state distributions for

Competitive Firm and the Theory of Input Demand under Price Uncertainty

In this paper, we examine the behavior of the competitive firm faced with making input-hiring decisions under conditions of price uncertainty. Unlike Sandmo and Baron, among others, we show categorically that a marginal increase in uncertainty stimulates a decline in the firm's output, provided the absolute risk aversion is decreasing. Furthermore, the implications of a change in expected price remain unchanged, but those of a change in input price need not be the same as in the certainty case. Specifically, the input demand function is downward sloping only if the production function is well behaved.

Long- and Short-Term Rates of Interest.

The object of this paper is to discuss the main principles underlying the pattern of interest rates on government securities in this country. It does not attempt to examine the place in the yield structure of those stocks which may possess special characteristics of term or provision for repayment, etc.; and because of its concentration on general principles the complex effects of taxation have been relegated to the background. The subject is approached by the following stages: (1) The pattern in the hypothetical case of complete certainty. (2) The idea of a ‘normal’ pattern, i.e. in conditions of complete uncertainty. (3) The changing pattern in conditions of varied and fluid expectations.