A monopolist faces the following demand curve: P = 100 - 3Q, its total cost is g
ID: 1220258 • Letter: A
Question
A monopolist faces the following demand curve: P = 100 - 3Q, its total cost is given by: TC = 100 + Q2 and its marginal cost is given by: MC = 2Q. (a) If it is a single price monopolist, what is its profit maximizing price and quantity? Show your work. How much is the profit? How much are consumer surplus and producer surplus? (b) Suppose it is a first degree price discriminator instead of a single price monopolist. What is the lowest price that the monopolist will charge? How much will be the profit (loss) of the firm? Show your work. How much are consumer surplus and producer surplus?
Explanation / Answer
Answer:
Given the information is:
The demand curve: P = 100 - 3Q
The Total Cost = TC = 100 + Q2
Marginal Cost = 2Q
(a) The profit maximizing price and quantity exist at MC = MR
MR = 100 - 3Q and MC = 2Q
100 - 3Q = 2Q
Q = 100/5
Q = 20 units
P = 100 – 3(20)
P = $40
Now, TC = 100 + (20)2
TC = $500
TR = Price * Quantity
TR = $40 * 20
TR = $800
Profit = TR – TC
= $800 - $500
= $300
The consumer surplus is:
= ½($100 - $40)(20)
C.S. = $600
The producer surplus is:
= ($40 - $40)(20)
P.S. = $20