RATIONAL EXPECTATIONS 317 because expectations of a single firm may still be subject to greater error than the theory It does not assert that the scratch work of entrepreneurs resembles the trepreneurs are perfect or that their expectations are all the samg ns of en- system of equations in any way; nor does it state that predictic For purposes of analysis, we shall use a specialized form of the hypothesis In particular, we assume 1. The random disturbances are normally distributed 2. Certainty equivalents exist for the variables to be predicte 3. The equations of the system, including the expectations formulas, are These assumptions are not quite so strong as may appear at first because any one of them virtually implies the other two 3. PRICE FLUCTUATIONS IN AN ISOLATED MARKET We can best explain what the hypothesis is all about by starting the analysis in a rather simple setting: short-period price variations in an isolated market with a fixed production lag of a commodity which cannot be stored. 5 The market equations take the form Ct=-Bpe (Demand) Pt= ypi +u Pe Market equilibrium where: Pt represents the number of units produced in a period lasting as long as the production lag Ct is the amount consumed pt is the market price in the tth period, is the market price expected to prevail during the tth period on the basis of information available through the(t-1)'st period, is an error term--representing, say, variations in yields due to weather Au the variables used are deviations from equilibrium values 4 As long as the variates have a finite variance, a linear regression function exists and only if the variates are normally distributed. (See Allen [2] and Ferguson [12]. The certainty-equivalence property follows from the linearity of the derivative of the appropriate quadratic profit or utility function. (See Simon [28] and Theil [32].) 5 It is possible to allow both short- and long-run supply relations on the basis of dynamic costs. See Holt et al. [17, esp. Chapters 2-4, 19]). More difficult are the supply effects of changes in the number of firms. The relevance of the cost effects has bee emphasized by Buchanan [7] and Akerman [1]. To include them at this point would however, take us away from the main objective of the paper.RATIONAL EXPECTATIONS 317 because expectations of a single firm may still be subject to greater error than the theory. It does not assert that the scratch work of entrepreneurs resembles the system of equations in any way; nor does it state that predictions of en￾trepreneurs are perfect or that their expectations are all the same. For purposes of analysis, we shall use a specialized form of the hypothesis. In particular, we assume: 1. The random disturbances are normally distributed. 2. Certainty equivalents exist for the variables to be predicted. 3. The equations of the system, including the expectations formulas, are linear. These assumptions are not quite so strong as may appear at first because any one of them virtually implies the other two.4 3. PRICE FLUCTUATIONS IN AN ISOLATED MARKET We can best explain what the hypothesis is all about by starting the analysis in a rather simple setting: short-period price variations in an isolated market with a fixed production lag of a commodity which cannot be stored.5 The market equations take the form Ct -AfiPt (Demand), (3. 1) P=t -yIP + ut, (Supply), Pt Ct (Market equilibrium), where: Pt represents the number of units produced in a period lasting as long as the production lag, Ct is the amount consumed, Pt is the market price in the tth period, pe is the market price expected to prevail during the tth period on the basis of information available through the (t -1)'st period, ut is an error term-representing, say, variations in yields due to weather. All the variables used are deviations from equilibrisui3 values. 4 As long as the variates have a finite variance, a linear regression function exists if and only if the variates are normally distributed. (See Allen [2] and Ferguson [12].) The certainty-equivalence property follows from the linearity of the derivative of the appropriate quadratic profit or utility function. (See Simon [28] and Theil [32].) 5 It is possible to allow both short- and long-run supply relations on the basis of dynamic costs. (See Holt et al. [17, esp. Chapters 2-4, 19]). More difficult are the supply effects of changes in the number of firms. The relevance of the cost effects has been emphasized by Buchanan [7] and Akerman [1]. To include them at this point would, however, take us away from the main objective of the paper