t) What is the consumer surplus at ( (g) What is the deadweight loss at (P*,Q\")
ID: 1103511 • Letter: T
Question
t) What is the consumer surplus at ( (g) What is the deadweight loss at (P*,Q")? 2. Assume that a monopolists sells a product in the short- run with a total cost function 103+26Q1Q2 Q>0 100 STC(Q) = The market demand curve is given by the equation P(Q) = 50-2Q. (a) Find the marginal cost for the firm. (b) Find the profit-maximizing output and price (c) What are the monopolists profits? (d) Does the monopolist want to stay in business? 3. Assume that a monopolist has TC 3+ 26Q +1Q2 and the market demand is P(Q) = 50-2Q.Explanation / Answer
(a)
When Q = 0, STC = 0 and MC = 0
When Q > 0, STC = 103 + 26Q + Q2
MC = dSTC / dQ = 26 + 2Q
Therefore,
MC = 0 When Q = 0
= 26 + 2Q When Q > 0
(b) P = 50 - 2Q
Total revenue (TR) = P x Q = 50Q - 2Q2
Marginal revenue (MR) = dTR / dQ = 50 - 4Q
Profit is maximized by equating MR and MC (Assuming Q > 0):
50 - 4Q = 26 + 2Q
6Q = 24
Q* = 4
P* = 50 - (2 x 4) = 50 - 8 = 42
(c) When Q = 4,
STC = 103 + (26 x 4) + (4 x 4) = 103 + 104 + 16 = 223
TR = 42 x 4 = 168
Profit = TR - STC = 168 - 223 = 55
(d) Since profit is negative for monopolist, it will not want to stay in business in long run.
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