386 The Journal of Finance limited only by period 3 dividend risk.The demand of a rational speculator is given by D5=④-P四=a0-p, 2ya号 (2) where we set a =(yo2)for notational convenience. A passive investor's period 2 demand is also negatively related to price: D5=a(④=p2) (3) where we assume that a is the same as in equation(2).We make the slope of passive investors'demands and rational speculators'period 2 demands equal and set the numbers of rational speculators and passive investors equal to u and 1- u,respectively.This allows us to examine the consequences of introducing informed rational speculators without changing the risk-bearing capacity of the market,since changes in u keep the risk-bearing capacity of the economy constant. In the absence of passive investors,an increase in the number of informed rational investors has two opposite effects:it destabilizes prices because it enhances the stimulus of rational investors'purchases to positive-feedback trading,and it stabilizes prices because it increases the risk-bearing capacity of the market.The second role of rational speculators has been stressed by Friedman (1953)and Stein(1987).In this paper,however,we abstract from this effect and to this end include passive investors in the model.'If we perform the experiment of simply adding rational speculators,there are cases in which the risk-sharing stabilizing effect is less important than the destabilizing effect of anticipatory purchases. For the model to have stable solutions,we require &B. (4) Because rational speculation makes period 1 prices rise one-for-one with expected period 2 prices,unless a>B the model will have no stable equilibrium:for high correctly anticipated values of p2,demand will exceed supply. Period 1 In period 1,informed rational speculators receive a signal e∈{-中，0，p}about period 2 fundamental news We consider two different assumptions about the signal e.First,the signal could be noiseless:e=.Second,the signal could be a noisy signal that satisfies: Prob(e=中，Φ=)=.25， Prob(c=中，Φ=0)=.25， (5) Prob(e=-中，Φ=-)=，25， Prob(e=-中，重=0)=.25 In the case of a noisy signal,when the speculators'signal e is o,the expectation Passive investors are not simply uninformed rational speculators.Since the price in period 1 reveals what rational speculators have learned,any rational investor can infer the period 1 signal from prices.Such a rational investor would then want to get into the speculative game as well. Passive investors,by contrast,neither receive the period 1 signal nor infer this signal from prices. Copvriaht O 2001 All Riahts Reserved