In an industry there are three firms, R, R and R3, producing differentiated products. They all have constant marginal costs c = C = 20, C3= c. The demand functions of their respective products are D1(P1, P2, P3) = D2(P1, P2, P3) = D3(P1, P2, P3) = 80 -2p1 + P2 + P3 80+p12p2 + P3 80+ P1+ P22p3 (i) Set up the profit functions of the three firms. [5 marks] (ii) The three firms are in a two stage price setting competition. In the first stage firms R and R set their prices p and p2 simultaneously. In the second stage, firm R3 once it observes the prices set by R and R sets its price p3. Compute the equilibrium prices in this two stage game, as a function of the cost parameter c. [20 marks] (iii) Suppose that the game is repeated over time periods t = 1,2,.... You have an invention that can reduce the cost parameter c over time, according to the equation 3 1 Ct = ct-1+8, co = s where s=1+the fourth digit of your student number. (a) Compute the time path of the equilibrium price of firm R3. (b) Compute the long run equilibrium prices in this market as t 0.