Consider the following model of a stock market. There are two groups of traders: rational traders and optimists. There are N rational traders and each has a demand for the stock of 100−P. Suppose that there are 100 shares of the stock outstanding. There are M optimists and each has a demand of 100 +δ−P.
a) What is the price of the stock as a function of parameters N,M and δ?
b) Suppose N=M= 50 andδ= 20, are the rational traders long or short and by how much?
c) Suppose N=M= 50,δ= 20, and there are 100 shares outstanding, again. Also,suppose the rational traders cannot short at all for institutional reasons. For example,they might work for mutual funds: most mutual funds do not allow shorting. Calculate the equilibrium price and the positions of the rational traders and the optimists in this scenario
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