Question

Suppose the market demand function for a good is given by.
Q=-5p+1000
i. find the monopolist’s total revenue function
ii. Find maximum total revenue

Answer 1

Q = -5p + 1000 or p = 200 - 0.2Q.

i. The monopolist’s total revenue function is:

$TR = p*Q = 200Q - 0.2Q^2.$

ii. The total revenue is at its maximum if marginal revenue $MR = TR'(Q) = 0.$

So:

$200 - 0.4Q = 0,$

$Q = 500$ units.