Question

Two firms compete in a market to sell a homogeneous product with inverse demand function: P = 400 – 2Q. Each firm produces at a constant marginal cost of $50 and has no fixed costs -- both firms have a cost function C(Q) = 50Q.

If this market is defined as a Cournot Oligopoly, what is the optimal amount for firm 1 to produce? (Round to the nearest whole number)

Refer to the information above.

If this market is defined as a Cournot Oligopoly, what is the optimal amount for firm 2 to produce? (Round to the nearest whole number)

If this market is defined as a Cournot Oligopoly, what is the market price? (Round to the nearest whole number)

Using your answers above, what are firm 1's profits? (Round to the nearest whole number)

Using your answers above, what are firm 2's profits? (Round to the nearest whole number)

Answer 1

We should reaction functions of both firms.

$TP1 = PQ1 - C(Q1) = 400Q1 - 2Q1^2 - 2Q1×Q2 - 50Q1 = 350Q1 - 2Q1^2 - 2Q1×Q2.$

$TP'(Q1) = 350 - 4Q1 - 2Q2 = 0,$

Q1 = 87.5 - 0.5Q2.

Similarly Q2 = 87.5 - 0.5Q1.

Q1 = 87.5 - 0.5×(87.5 - 0.5Q1),

0.75Q1 = 43.75,

Q1 = Q2 = 58.33.

P = 400 - 2(Q1 + Q2) = 283.33.

Profits of both firms TP1 = TP2 = 283.33×58.33 - 50×58.33 = 13,610.33.