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The inverse market demand in a homogeneous-product Cournot duopoly is P = 200 – 3(Q1 +...

The inverse market demand in a homogeneous-product Cournot duopoly is P = 200 – 3(Q1 + Q2) and costs are C1(Q1) = 26Q1 and C2(Q2) = 32Q2.

a. Determine the reaction function for each firm.

Firm 1: Q1 =  -  Q2

Firm 2: Q2 =  -  Q1


b. Calculate each firm’s equilibrium output.

Firm 1:

Firm 2:


c. Calculate the equilibrium market price.

$


d. Calculate the profit each firm earns in equilibrium.

Firm 1: $

Firm 2: $

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Answer #1

Demand is P = 200 – 3(Q1 + Q2) and marginal costs are MC1 = 26 MC2 = 32

a. Use MR1 = MC1 and MR2 = MC2

200 - 6Q1 - 3Q2 = 26 and 200 - 6Q2 - 3Q1 = 32

Q1 = 29 - 0.5Q2 and Q2 = 28 - 0.5Q1

Hence the reaction functions are

Firm 1: Q1 = 29 - 0.5Q2

Firm 2: Q2 = 28 - 0.5Q1

b. Use these functions to get

Q1 = 29 - 0.5*(28 - 0.5Q1)

Q1 = 15 + 0.25Q1

Q1 = 20 units and Q2 = 18 units

Firm 1: 20 units

Firm 2: 18 units

c. Equilibrium market price = 200 - 3*(20 + 18) = $86

d. Firm 1: $1200

Firm 2: $972

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