THE AMERICAN ECONOMIC REVIEW JUNE 1980 will depend only on P, but we shall assume which the informed can gain relative to the that they have rational expectations; they uninformed-is reduced learn the relationship between the distribu (b)Even if the above effect did not tion of return and the price, and use this in occur, the increase in the ratio of informed r dema If to uninformed means that the relative gains x denotes the supply of the risky asset, an of the informed, on a per capita basis, in equilibrium when a given percentage, A, of trading with the uninformed will be smaller. ders are informed, is thus a We summarize the above characterization P(8, x)such that, when demands are for- of the equilibrium of the economy in the mulated in the way described, demand following two conjectures equals supply. We assume that uninformed Conjecture 1: The more individuals who traders do not observe x. Uninformed are informed, the more informative is the traders are prevented from learning 6 via price system observations of Pa(0, x) because they can Conjecture 2: The more individuals who not distinguish variations in price due to are informed, the lower the ratio of expected changes in the informed trader's informa- utility of the informed to the uninformed tion from variations in price due to changes Conjecture I obviously requires a defini- in aggregate supply. Clearly, P(e, x) reveals tion of"more informative"; this is given in some of the informed trader's information the next section and in fn. 7.) to the uninformed trade The equilibrium number of informed We can calculate the expected utility of uninformed individuals in the economy will the informed and the expected utility of the depend on a number of critical parameters uninformed. If the former is greater than the the cost of information, how informative the latter (taking account of the cost of infor- price system is(how much noise there is to mation), some individuals switch from being interfere with the information conveyed by uninformed to being informed(and con- the price system), and how informative versely). An overall equilibrium requires the information obtained by an informed indi two to have the same expected utility. As vidual is more individuals become informed. the ex- Conjecture 3: The higher the cost of pected utility of the informed falls relative information, the smaller will be the equi- to the uninformed for two reasons librium percentage of individuals who are (a) The price system becomes more in- informed formative because variations in have a Conjecture 4: If the quality of the greater effect on aggregate demand and thus formed trader's information increases, the on price when more traders observe 8. Thus, more their demands will vary with their more of the information of the informed is information and thus the more prices will available to the uninformed. Moreover, the vary with 0. Hence, the price system be informed gain more from trade with the comes more informative. The equilibrium uninformed than do the uninformed. th proportion of informed to uninformed may informed, on average, buy securities when be either increased or decreased, because they are"underpriced"and sell them when even though the value of being informed has they are overpriced"(relative to what increased due to the increased quality of 0, they would have been if information were the value of being uninformed has also in equalized). As the price system becomes creased because the price system becomes more informative, the difference in their in- more informative formation-and hence the magnitude by Conjecture 5: The greater the magn tude of noise the less informative will the price system be, and hence the lower the 2The framework described herein does not explicitly expected utility of uninformed individuals of variations of futures markets and Hence, in equilibrium the greater the magni- ativeness of the price tude of noise, the larger the proportion of formed individuals OR Terms and Conditions394 THE AMERICAN ECONOMIC REVIEW JUNE 1980 will depend only on P, but we shall assume that they have rational expectations; they learn the relationship between the distribu￾tion of return and the price, and use this in deriving their demand for the risky assets. If x denotes the supply of the risky asset, an equilibrium when a given percentage, X, of traders are informed, is thus a price function PA(O,x) such that, when demands are for￾mulated in the way described, demand equals supply. We assume that uninformed traders do not observe x. Uninformed traders are prevented from learning 9 via observations of PA(O,x) because they can￾not distinguish variations in price due to changes in the informed trader's informa￾tion from variations in price due to changes in aggregate supply. Clearly, PA(O,x) reveals some of the informed trader's information to the uninformed traders. We can calculate the expected utility of the informed and the expected utility of the uninformed. If the former is greater than the latter (taking account of the cost of infor￾mation), some individuals switch from being uninformed to being informed (and con￾versely). An overall equilibrium requires the two to have the same expected utility. As more individuals become informed, the ex￾pected utility of the informed falls relative to the uninformed for two reasons: (a) The price system becomes more in￾formative because variations in 9 have a greater effect on aggregate demand and thus on price when more traders observe 9. Thus, more of the information of the informed is available to the uninformed. Moreover, the informed gain more from trade with the uninformed than do the uninformed. The informed, on average, buy securities when they are "underpriced" and sell them when they are "overpriced" (relative to what they would have been if information were equalized).2 As the price system becomes more informative, the difference in their in￾formation-and hence the magnitude by which the informed can gain relative to the uninformed-is reduced. (b) Even if the above effect did not occur, the increase in the ratio of informed to uninformed means that the relative gains of the informed, on a per capita basis, in trading with the uninformed will be smaller. We summarize the above characterization of the equilibrium of the economy in the following two conjectures: Conjecture 1: The more individuals who are informed, the more informative is the price system. Conjecture 2: The more individuals who are informed, the lower the ratio of expected utility of the informed to the uninformed. (Conjecture 1 obviously requires a defini￾tion of "more informative"; this is given in the next section and in fn. 7.) The equilibrium number of informed and uninformed individuals in the economy will depend on a number of critical parameters: the cost of information, how informative the price system is (how much noise there is to interfere with the information conveyed by the price system), and how informative the information obtained by an informed indi￾vidual is. Conjecture 3: The higher the cost of information, the smaller will be the equi￾librium percentage of individuals who are informed. Conjecture 4: If the quality of the in￾formed trader's information increases, the more their demands will vary with their information and thus the more prices will vary with 9. Hence, the price system be￾comes more informative. The equilibrium proportion of informed to uninformed may be either increased or decreased, because even though the value of being informed has increased due to the increased quality of 9, the value of being uninformed has also in￾creased because the price system becomes more informative. Conjecture 5: The greater the magni￾tude of noise, the less informative will the price system be, and hence the lower the expected utility of uninformed individuals. Hence, in equilibrium the greater the magni￾tude of noise, the larger the proportion of informed individuals. 2The framework described herein does not explicitly model the effect of variations in supply, i.e., x on commodity storage. The effect of futures markets and storage capabilities on the informativeness of the price system was studied by Grossman (1975, 1977). This content downloaded from 202.115.118.13 on Wed, 11 Sep 2013 03:12:49 AM All use subject to JSTOR Terms and Conditions