Economics - Profit, Marginal Revenue - Hw Help!?

Question

Assume there are only two producers of tennis rackets: Wilson and Prince. The market demand for tennis rackets is depicted by the algebraic formula P = 100 - Q, where P stands for price and Q stands for quantity of rackets. If the market were monopolized, the resulting formula for the monopolist's marginal revenue would be MR = 100 - 2Q, where MR stands for marginal revenue. Assume that both producers face a constant marginal cost of $40 and that there are no fixed costs.

3.6. When both firms decide to cheat and to produce one more racket than specified in their collusive agreement, how much profit (in dollars) does each firm earn?

Answer 1

Maximal profit under fair collusion:

Profit=TR-TC

MR=MC

TR=P*Q=100Q-Q^2

MR=(TR)'=100-2Q

TC=40Q

MC=40

100-2Q=40

60=2Q

Q=30

Cheating condition: Q=30+1+1=32

TR=100*32-32^2=2176

TC=40*32=1280

TotalProfit=2176-1280=896

Each firm profit=896/2=448