Suppose the demand curve for a monopolist is
QD = 500 − P, and the marginal revenue function
is MR = 500 − 2Q. The monopolist has a constant
marginal and average total cost of $50 per unit.
a.Find the monopolist’s profit-maximizing output
and price.
b. Calculate the monopolist’s profit.
c. What is the Lerner Index for this industry?
3 answers
I am not sure about the answer but I think that for profit maximizing output . MR = MC , therefore 500-2Q=50 ( MC = 50 per unit ) , after calculating , we get the output of 275 and the price of 225. The profit is 48,125.
This is what I got for the lender index:
L = (P- MC) / P
L = (225 - 50) /225
L = (175) / 225
L = 0.77
L = (P- MC) / P
L = (225 - 50) /225
L = (175) / 225
L = 0.77
These are my final responses:
a) Find the monopolist’s profit-maximizing output and price.
Output is 225 and price is 50
MR = 500 − 2Q
50 =500 – 2Q
-450 = -2Q
225 = Q (Profit maximizing quantity)
P = 500 − 2Q
P = 500 – 2(225)
P = 500 – 450
(Profit Price) P = 50
b) Calculate the monopolist’s profit.
TR = P *Q
TR = 50 * 225
TR = 11,250
TC = 500 + (50*225)
TC = 500+11250
TC = 11,750
Profit = TR – TC
Profit = 11250 – 11750
Profit = -500
c) What is the Lerner Index for this industry?
L = (P- MC) / P
L = (50 - 50) /50
L = (0) / 50
L = 0
I saw a Youtube video by Marginal Revolution University called "Office Hours: Calculating Monopoly Profit"
a) Find the monopolist’s profit-maximizing output and price.
Output is 225 and price is 50
MR = 500 − 2Q
50 =500 – 2Q
-450 = -2Q
225 = Q (Profit maximizing quantity)
P = 500 − 2Q
P = 500 – 2(225)
P = 500 – 450
(Profit Price) P = 50
b) Calculate the monopolist’s profit.
TR = P *Q
TR = 50 * 225
TR = 11,250
TC = 500 + (50*225)
TC = 500+11250
TC = 11,750
Profit = TR – TC
Profit = 11250 – 11750
Profit = -500
c) What is the Lerner Index for this industry?
L = (P- MC) / P
L = (50 - 50) /50
L = (0) / 50
L = 0
I saw a Youtube video by Marginal Revolution University called "Office Hours: Calculating Monopoly Profit"
3 answers