Answer to Question #107455 in Economics for Dee

Question

A monopolist has the cost function, c=100+6q+1/2q^2
(i) If the demand curve is given by q=24 - 1/4p. compute the price-output combination that minimizes profits. Also, calculate total profits at this price-output combination.

(ii)Assume that it becomes possible to sell in a separate second market with demand determined by q=84 - 3/4p.

calculate the prices which will be set in the two markets and the change in total output and profits from case

(iii) Now suppose the firm still has access to both markets, but is prevented from discriminating between them. What will be the result?

Answer 1

(i) If the demand curve is given by q = 24 - 1/4p, then p = 96 - 4q.

The output for which profits are maximized (or losses minimized) is:

MR = MC,

MR = TR'(q) = 96 - 8q,

MC = C'(q) = 6 + q,

96 - 8q = 6 + q,

9q = 90,

q = 10 units,

p = 96 - 4×10 = 56.

Total profits at this price-output combination are:

$TP = TR - C = 56×10 - (100 + 6×10 + 0.5×10^2) = 350.$

(ii) If in a separate second market demand is determined by q = 84 - 3/4p, then the monopolist will set different

prices ans different quantities in the two markets, so the total output and profits will increase.

(iii) If the firm still has access to both markets, but is prevented from discriminating between them, then the firm will return to the same price and quantity for both groups.