An industry has two companies (1 and 2). The cost function of enterprise i is C (qi) = 4qi, i = 1.2. The inverse demand function of the industry is p = 100 - 2q, where p is the price and q is the total quantity produced [ie. the sum of the quantities produced by 1 and 2 (q=q1 + q2)]. (i) Calculate the equilibrium according to Cournot. At what price will it be sold product and what will be the profits of each company? (ii) Assume that the two companies decide to form a cartel and each agree to produce ½ of the total amount of the cartel. Calculate the amount that maximizes the profits of the cartel as well as the profit of each business, assuming that both companies respect the terms of the partnership. (iii) Assume that (a) market conditions are expected to remain unchanged (no change is foreseen), (b) the quantity produced by each firm during a year is accurately disclosed to its competitor, but only at the end of it of the year, (c) if a business does not comply with the cartel agreement in the first year, then the other company never cooperates with it again after that year and therefore the companies decide independently on the quantity they will produce in each period. Assume that the interest rate is r = 5%. Do you believe? that the partnership is sustainable?