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Hurwicz, Luce-Raiffa, Savage, Wald and others have distinguished between decision making under conditions of certainty, risk, and uncertainty. But other than for discourses such as Knight's, which was concerned with comparing reality and theory, writings in the field of competition economics were centered on conditions of certainty, though, more recently, extended to include the state of risk. But what about uncertainty? If we assume that it is basic to certain economic markets, would it be possible to include it as part of general economic theory in much the same way that decision making theory includes uncertainty as part of its framework? We shall contend that it is, first by accepting a simple transformation which combines risk and uncertainty, then by formulating a general theory of maximum profits. Our initial task is the most elementary and hence easiest to fulfill. We need observe only the well established thought that risk differs from uncertainty in the sense that mathematical probabilities are assignable to the former but not the latter. It follows in the literature that when uncertainty prevails the decision maker must select some criterion which, in effect, enables him to apply his own a priori probabilities distinct from the statistical or analytic probabilities on which all may agree. He is able to do this on the basis of some criterion; e.g., the criterion of regret, or optimism, or, say, the Laplace criterion where each unknown is considered to be equally likely to happen and where, accordingly, the probabilities are equal and the given strategy takes the form 1/n (Payoff 1 + Payoff 2 + ..-+ Payoff n). For our purposes, we should note that once the criterion is given--a pre-condition establishable by the individual household or business unit-any payoff matrix will appear the same as that under risk. It follows further that the general theory of maximum profit which we will formulate-and which speaks in terms of probabilities-includes the statistical or analytic probability relevant to decision making under risk, or the probability selected under uncertainty on some personal basis, such as hunch, fear, or, let us say, reason. One more preliminary should be observed. We accept the premise that a general profit theory not only will have good use in pure economics, especially the kind in which a closer approximation to realism is fruitful' but also applied economics. In fact, to help form a framework for our theory, we will refer to an empirical study in economics which requires this particular kind of realism. Our approach (and objective) is to suggest the importance of a general theory of maximum profit, and, of course, to form this kind of theory.
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