24. Cournot duopolists face a
24. Cournot duopolists face a market demand curve given by P =90 – Q where Q is total market demand. Each firm can produce outputat a constant marginal cost of 30 per unit. There are no fixedcosts. Determine the (1) equilibrium price, (2) quantity, and (3)economic profits for the total market, (4) the consumer surplus,and (5) dead weight loss.
25. If the duopolists in question 24 behave according to theStackelberg Leader-Follower model, determine the (1) equilibriumprice, (2) quantity, and (3) economic profits for the total marketand (4) the consumer surplus, and (5) dead weight loss.
26. If the duopolists in question 24 behave, instead, accordingto the Bertrand model, determine the (1) equilibrium price, (2)quantity, and (3) economic profits for the total market and (4) theconsumer surplus, and (5) dead weight loss.
27. If the duopolists in question 24 behave as a sharedmonopoly, determine the (1) equilibrium price, (2) quantity, and(3) economic profits for the total market and (4) the consumersurplus, and (5) dead weight loss.
Answer:
24. Each firm’s marginal cost function is MC = 30 and the marketdemand function is P = 90 – (q1 + q2) where Q is the sum of eachfirm’s output q1 and q2.
Find the best response functions for both firms:
Revenue for firm 1
R1 = P*q1 = (90 – (q1 +q2))*q1 = 90q1 –q12 – q1q2.
Firm 1 has the following marginal revenue and marginal costfunctions:
MR1 = 90 – 2q1 – q2
MC1 = 30
Profit maximization implies:
MR1 = MC1
90 – 2q1 – q2 = 30
which gives the best response function:
q1 = 30 – 0.5q2.
By symmetry, Firm 2’s best response function is:
q2 = 30 – 0.5q1.
Cournot equilibrium is determined at the intersection of thesetwo best response functions:
q1 = 30 – 0.5(30 – 0.5q1)
q1 = 15 + 0.25q1
This gives q1 = q2 = 20 units This theCournot solution. Price is (90 – 40) = $50 . Profit to each firm =(50 – 30)*20 = $400 or 800 in total. CS = 0.5*(90 – 50)*40 = $800.DWL = 0.5*(50 – 30)*(60 – 40) = $200.
"Our Prices Start at $11.99. As Our First Client, Use Coupon Code GET15 to claim 15% Discount This Month!!"
