Two organic emu ranchers, Bill and Ted, serve a small metropolitan market. Bill
ID: 2495893 • Letter: T
Question
Two organic emu ranchers, Bill and Ted, serve a small metropolitan market. Bill and Ted are Cournot competitors, making a conscious decision each year regarding how many emus to breed. The price they can charge depends on how many emus they collectively raise, and demand in this market is given by Q = 150 P . Bill raises emus at a constant marginal and average total cost of $10; Ted raises emus at a constant marginal and average total cost of $20. (a) Find the Cournot equilibrium price, quantity (total and for each rancher), profits (for both ranchers), and consumer surplus. (b) Suppose that Ted breeds his emus earlier in the year than Bill, and is a first-mover in the market. Find the Stackelberg equilibrium price, quantity (total and for each rancher), and profits (for both ranchers). Does your answer coincide with the first-mover advantage? (c) Suppose that Bill and Ted merge, and become a monopoly provider of emus. Further, suppose that Ted adopts Bill’s production techniques. Find the monopoly price, quantity, total profits, and consumer surplus. (d) Has the combination of the two ranches discussed above been good for society or bad for society? Discuss how the forces of monopoly power and increased efficiency tend to push social well-being in opposite directions
Explanation / Answer
Q = 150 P
Q = q1 + q2
P =150 -q1 -q2
where q1 = Bill's Demand
and q2 = Ted's Demand
MC of Bill =10
MC of TED = 20
Profit function of Bill PB= TR -TC = P.q1 - MC.q1
= (150 - q1 -q2) .q1 -10.q1
Finding dPB/dq1 and putting equal to 0
dPB/dq1 = 150 - 2q1 -q2 -10 = 0
q1 = 70 - q2/2
Similary for q2
Profit function of Ted PB= TR -TC = P.q1 - MC.q1
= (150 - q1 -q2) .q2 -20.q2
Finding dPB/dq1 and putting equal to 0
dPB/dq1 = 150 - 2q2 -q1 -20 = 0
q2 = 65 - q1/2
Solving these we get
q1 = 140/3
q2 = 130/3
Q = q1 +q2 = 270/3 = 90
P = 150 -Q = 60
Profit of bill = 60*140/3 - 10*140/3 = 2,333.33
Profit of ted = 60*130/3 - 20*130/3 =1,733.33
Total Profit = Profit of bill + profit of ted = 4066.66
Consumer surplus = 1/2(vertical intercept of demand curve - price)*quantity
= 1/2(150 -60)*90
= 4050
Stackelberg Equilibrium
Step 1,
Follower firm(i.e Ted) BRF2 = =65 - q1/2 (same as counot)
Step -2
Leader firm1 residual demand
P = 150 –q1 –q2 = 150 – q1 - (65 - q1/2)
Hence , the MR associated with residual demand is
MR = 85 – 2q1 + q1
Putting MR =MC
85 - q1 = 10
q1 = 75
q2 = 65 - 75/2 = 27.5
Q = q1 +q2 = 102.5
P = 47.5
Profit of bill = 47.5*75 - 10*75 = 2,812.5
Profit of ted = 47.5*27.5 - 20*27.5 = 756.25
Total profit = 2,812.5 +756.25 = 3,568.75
c.
For monopoly
MR = MC
150 - 2Q = 10
Q = 70
P =150 - Q = 80
Profits combined = P.Q = 80*70 = 5600
Consumer Surplus = 1/2(vertical intercept of demand curve - price)*quantity
= 1/2(150 -80)*70
= 2450
The combination is bad for society as consumer surplus reduced due to the merger.
As in monopoly, a firm produces at a point where MR=MC , so it reduces the inefficiency that existed in duopoly but the gains of that plus the part of consumer surplus are all been observed by the producer.
I tried to be clear , but still have any doubts you can comment , i will be more than willing to revert back.:)
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