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 100P. Suppose that there are 100 shares of the stock outstanding. There are M optimists and each has a demand of 100+P. a) What is the price of the stock as a function of parameters N,M and ? b) Suppose N=M=50 and =20, are the rational traders long or short and by how much? c) Suppose N=M=50,=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