Two firms compete in selling identical widgets. They choose their output levels
ID: 1189085 • Letter: T
Question
Two firms compete in selling identical widgets. They choose their output levels Q1 and Q2 simultaneously and face the demand curve P = 30 - Q
where Q = Q1 + Q2. Until recently, both firms had zero marginal costs. Recent environmental regulations have increased Firm 2’s marginal cost to $15. Firm 1’s marginal cost remains constant at zero.
TRUE-FALSE: Is the following statement true of false? ”As a result, the market price will rise to the monopoly level.” Solve for the Cournot equilibrium and write a convincing explanation of your answer.
Explanation / Answer
TRUE.
P = 30 - Q = 30 - Q1 - Q2
Total Revenue of Firm 1, TR1 = P x Q1 = 30Q1 - Q12 - Q1Q2
Marginal Revenue of Firm 1, MR1 = dTR1 / dQ1 = 30 - 2Q1 - Q2
Total Revenue of Firm 2, TR2 = P x Q2 = 30Q2 - Q1Q2 – Q22
Marginal Revenue of Firm 2, MR2 = dTR2 / dQ2 = 30 - Q1 - 2Q2
In Cournot equilibrium, each firm will equate its MR with MC.
(Case 1) Each firm’s MC is 0: MC1 = MC2 = 0
For Firm 1,
MR1 = 0
30 - 2Q1 - Q2 = 0
2Q1 + Q2 = 30 (1) [Firm 1’s response function]
For Firm 2,
MR2 = 0
30 – Q1 – 2Q2 = 0
Q1 + 2Q2 = 30 (2) [Firm 2’s response function]
Multiplying (2) with 2,
2Q1 + 4Q2 = 60 (3) And
2Q1 + Q2 = 30 (1)
(3) – (1) gives,
3Q2 = 30
Q2 = 10
Q1 = 30 – 2Q2 = 30 – 20 = 10
Market price, P = 30 – Q1 – Q2 = 10
(Case 2) MC1 = 0 & MC2 = 15
Firm 1’s response function remains the same. Firm 2 equates its (Unchanged) MR with (New) MC:
MR2 = MC2
30 - Q1 - 2Q2 = 15
Q1 + 2Q2 = 15 (4)
2Q1 + Q2 = 30 (1)
(4) x 2 gives us:
2Q1 + 4Q2 = 30 (5)
(5) – (1) gives
3Q2 = 0
Q2 = 0
Q1 = 15 – 4Q2 [From (4)]
= 15 – 0 = 15
Market Price, P = 30 – Q1 [Since Q2 = 0]
P = 30 – 15 = 15
Which is a monopoly market structure, since there is only one firm in the market producing any positive output (Firm 1).
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