Question

Two identical firms compete as a Cournot duopoly. The inverse market demand they face is P = 128 - 4Q. The total cost function for each firm is TC(Q) = 8Q. The price charged in this market will be

Answer 1

Answer: 48

Step-by-step explanation:

Since TC(Q) = 8Q, the marginal cost(MC) will be = dC/dQ = 8

P = 128 - 4Q.

P = 128 - 4Q1 - 4Q2

For firm 1, the Total revenue will be:

= 128Q1 - 4Q1²- 4Q1Q2

MR1 = 128 - 8Q1 - 4Q2

Then, we'll set MR1 = MC1,

128 - 8Q1 - 4Q2 = 8

Collect like terms

8Q1 + 4Q2 = 120 .........(1)

For firm 2,

TR2 = 128Q2 - 4Q1Q2 - 4Q2²

MR2 = 128 - 4Q1 - 8Q2

Then we'll set MR2 = MC2,

128 - 4Q1 - 8Q2 = 8

4Q1 + 8Q2 = 120..........(2)

Thenz we'll multiply equation (2) by 2 and this will be:

8Q1 + 16Q2 = 240 ........(3)

8Q1 + 4Q2 = 120.........(1)

Equation (3) - equation (1) will give:

12Q2 = 120

Q2 = 120/12

Q2 = 10

Since the cost function for both firms is identical, then Q1 = 10 as well.

Q = Q1 + Q2

Q = 10 + 10

Q = 20

P = 128 - 4Q

P = 128 - (4 x 20)

P = 128 - 80

P = 48

The price charged in the market is 48.