The inverse market demand in a homogeneous-product Cournot duopoly is P = 200 - 3(Q1 + Q2) and costs are C1(Q1) = 26Q1 andC2(Q2) = 32Q2.

a. Determine the reaction function for each firm.

b. Calculate each firm's equilibrium output.

c. Calculate the equilibrium market price.

d. Calculate the profit each firm earns in equilibrium.

a. Solve for Q1

P= 200 - 3(Q1+Q2)

P = 200 - 3Q1 - 3Q2

3Q1 = 200 - P - 3Q2

Q1 = 200/3 - P/3 - Q2

Solve for Q2

P= 200 - 3(Q1+Q2)

P = 200 - 3Q1 - 3Q2

3Q2 = 200 - P - 3Q1

Q2 = 200/3 - P/3 - Q1

b. Find MR for Q1

TRQ1 = P * Q1 = 200Q1 - 3Q1^2 - 3Q2*Q1

MRQ1 = 200 - 6Q1 - 3Q2

MCQ1 = 26

Set MR = MC

26 = 200 - 6Q1 - 3Q2

6Q1 = 174 - 3Q2

Q1 = 29 - 0.5Q2

find MR for Q2

TRQ2 = P * Q2 = 200Q2 - 3Q1*Q2 - 3Q2^2

MRQ2 = 200 - 3Q1 - 6Q2

MCQ2 = 32

Set MR = MC

32 = 200 - 3Q1 - 6Q2

6Q2 = 168 - 3Q1

Q2 = 28 - 0.5Q1

Q1 = 29 - 0.5(28 - 0.5Q1)

Q1 = 29 - 14 + 0.25Q1

0.75Q1 = 15

Q1 = 20

Q2 = 28 - 0.5(20)

Q2 = 20 - 10 = 10

Q2 = 10

c. P = 200 - 3(20 + 10)

P = 200 - 3(30)

P = 200 - 90

P = 110

The equilibrium price is 110, the equilibrium quantity for good 1 is 20 and the equilibrium quantity for good 2 is 10.

d.

TRQ1 = 110 * 20 = 2200

TRQ2 = 110 * 10 = 1100

TCQ1 = 26 * 20 = 520

TCQ2 = 32 * 10 = 320

Profit Q1 = 2200 - 520 = 1680

Profit Q2 = 1100 - 320 = 780