(Assume firms compete over quantity) Two identical firms are serving a market in
ID: 1206675 • Letter: #
Question
(Assume firms compete over quantity) Two identical firms are serving a market in which the inverse demand function is given by P = 400 - 2Q (P = 400 - 2 (q_1 + q_2). The marginal costs of each lirm arc $40 per unit. Calculate the Monopoly equilibrium. What is the Monopoly price. P^M? What is the Monopoly quantity (Q^M)? What Ls the total profit (^M)? Calculate the Cournot equilibrium. What is the Cournot price, P^C? What are the equilibrium quantities (q^C_1, q^C_2, Q^C )? What ore the total profits and profit furn (pi_1, pi_2, II^C)? Compare the Monopoly solution in part (a) to tin Cournot solution in pait (b). Provide intuition to explain the difference. (d) On a "Best Response graph, plot the solution to part (b). Then show and explain, how the Cournot quantities will change when cost of firm 1, c_1 falls to 30? You may skip the calculations for this part, but you must provide the basic intuition. (e) What is the Bertrand Nash equilibrium outcome? What is the price, P^B? What are the equilibrium quantities (q^B_1, q^B_2, Q^B)? What are the total profits and profit per firm (pi^B_1, pi^B_2, II^B)?Explanation / Answer
a) Inverse demand curve: P = 400-2Q
total revenue = P*Q = 400Q-2Q2
Marginal Revenue (MR) = dtr/dQ = 400-4Q
and MC = 40
Equating MR and MC
400-4Q = 40
Q = 360/4 = 90 units.
and P = 400 - 2(90) = 400-180 = 220.
Hence equilibrium Q = 90 units
and equilibrium P = $220 per unit.
Profit = tr - tc = 220*90 - 40*90 = $16200.
b) Under cournot market:
Best response functions are:
Firm 1: Profit = (400-2(q1+q2))q1 - 40q1 = 400q1-2q12-2q2q1-40q1
differentiating profit and equating to zero
dProfit/dq1 = 400-4q1-2q2-40 = 0
90-0.5q2 = q1 ... eq 1
and similarl, Firm 2: Profit = (400-2(q1+q2))q2 - 40q2 = 400q2-2q22-2q2q1-40q2
differentiating profit and equating to zero
dProfit/dq2 = 400-4q2-2q1-40 = 0
q1 = 180-2q2 .. eq 2
from eq 1 and 2
90-0.5q2 = 180-2q2
q2 = 60
and q1 = 180 - 120 = 60
hence q1 = q2 = 60 units.
and total Q = 60+60 = 120 units.
Price = 400 - 2(60+60) = $160.
Profit of each firm : 160*60 - 40*60 = $7200.
total profit = 7200+7200 = $14400.
c) When firm formed a cartel o have monopolo in market the profit was much more than under the cartel. Hence firms were earning more in earlier case. Price was higher and so the units.
d) When cost of firm 1 fall o $30, then it will become market leader and the other firm will become the market follower.
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