Question

3. James is a producer in a monopoly industry. His demand curve, total revenue, curve, marginal revenue curve and total cost curve are given as follows:

Q=100-4P

TR=25Q-0.25Q²

MR=25-0.5Q

TC=6Q

MC=6

a. (4 points) How much output will James produce?

b. (4 points) What price will James charge per unit of output?

c. (4 points) How much profit will James make?

d. (8 points) If this was a competitive firm. Calculate the profit maximizing price and quantity and compare with price and quantity under monopoly.

e. (6 points) Calculate the amount of deadweight loss incurred because James is a monopolist and not perfectly competitive firm.

Answer 1

ANswer
a)
the firm produces at MR=MC
25-0.5Q=6
0.5Q=19
Q=38
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b)
from demand funtion
Q=100-4P
38=100-4P
4P=62
P=15.5
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c)
Profit =TR-TC
TR=25*38-0.25*38^2=589
TC=6*38=228
Profit=589-228=361
the profit is $361
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d)
the firm produces at MC=P
P=25-0.25Q from the demand curve
25-0.25Q=6
0.25Q=19
Q=76
P=6
the price decreases and quantity increases compared to moopoly
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e)

DWL=0.5*change in quantity *(monopoly price -monopoly MC)
=0.5*(76-38)*(15.5-6)
=180.5
the DWL is $180.5