Economics 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.

If Wilson and Prince form a cartel and each agrees to produce one half of the monopolist's profit-maximizing output, how many rackets would each manufacturer produce

Answer 1

1)

40=100-2Q

2Q=100-40=60

Q=30

Answer: both will produce 30 t-rackets and each will produce 15 t-rackets.

2)

P=100-30=70

Answ: To maximize profits price would be $70

3)

Q=31

P=100-31=69

Prince profit=TR-TC=69*15-40*15 =29*15=$435

Wilson profit=69*16-40*16 =29*16=$464