Consider a market that contains 2 identical firms, each of which produces an identical product. The inverse demand for this product is P = 1000 2Q; where P is price and Q is aggregate output. The production costs for each of these firms are identical and given by TC,-(qi) = 100qi,i = 1,2. 1. Assume that the firms each choose their outputs to maximize profits (a) Write down the profit function for firms 1 and 2. (b) Calculate the firms' reaction functions by expressing their optimal outputs as function of the outputs of their respective rival. (c) Calculate the one-period CournotNash equilibrium outputs, the market price, and the profits of each firm. 2. Now assume that the two firms form a cartel that produces the monopoly output for this market. The firms agree that they will share the cartel output and profit equally. (a) What aggregate output will the cartel agree upon? (b) What will be the market price, the outputs, and the profits of the cartel firms? (c) Determine the Social Welfare, resulting from the cartel, and com pa re this measure with the social welfare in the duopolistic market structure under 1