Suppose that the inverse demand for rakomelo in Greece is given by P = 80 - 2Q, where P is the price per bottle (750ml) of rakomelo and Q is the total quantity, i.e., number of bottles, supplied in the market. There are two rakomelo manufacturers in Greece, A.H. and A.W., operating under similar cost conditions. Each manufacturer's cost function is C(q) = 2qi, i = 1,2, where qi the manufacturer's individual quantity produced and Q = 91 +92. (i) Based on demand conditions every year, they decide, independently of each other, the quantity of rakomelo that will be supplied, letting the market determine the price per bottle. Find the equilibrium price and each firm's profit in this market. (Mark: 0.5) (ii) Consider that the above two manufacturers form a cartel, agreeing to fix their total quantity in such a way that the market maintains a collusive price. For simplicity, the eventual cartel directory will determine the target total-quantity and price pair, and each firm will produce 1/2 of the total quantity decided by the directory. Find the total quantity that maximizes cartel profits, the price that the cartel directory fixes, and each firm's profit, assuming that both firms respect their cartel-imposed quota. (Mark: 0.5) (iii) Assume that i) market conditions are expected to infinitely remain the same (no change predicted), ii) the quantity a manufacturer has produced during a year is accurately revealed to its rival, but only at the end of that year (price-revision period of one year), iii) if a firm cheats on the cartel agreement it does so by setting a price that is 1 less than the monopoly price; in this case it serves the entire market at that price until the next price-revision period. Assume that the relevant interest rate is r = 3%. Do you think that the cartel agreement is sustainable? How does your answer change if r = 15%? (Approximate all calculations to three decimal points). Explain your findings. (Mark: 1.5)