The market demand for a monopoly firm is estimated to be: Q= 100,000 - 500P+2M+5
ID: 1188521 • Letter: T
Question
The market demand for a monopoly firm is estimated to be:
Q= 100,000 - 500P+2M+5000PR
Where Q is quantity demanded, P is the price, M is income, and PR is the price of a related good. The manager has forecasted the values of M and OR will be $50,000 and $20 respectively, in 2014.
The average variable cost function is estimated to be:
AVC=520-0.03Q+0.000001Q^2
Total fixed cos in 2014 is expected to be $4 million.
Please show all work for the following answers
a. Determine the profit maximizing choice of output.
b. What price should the firm charge?
c. What will be the firm's expected profit?
Explanation / Answer
Q= 100,000 - 500P+2M+5000PR
M=50000
PR=20
=>Q= 100,000 - 500P+100,000+5000*20=300000-500P
=>P=(300000-Q)/500
AVC=520-0.03Q+0.000001Q^2
TFC=4000000
Profit=Q*P-AVC-TFC
=>Q*(-Q+300,000)/500-(520-0.03Q+0.000001Q^2)-4000000
=-Q^2/500+600Q-500+0.03Q-0.000001Q^2-4000000
A)
for max profit dPr/dQ=0
=>d(-Q^2/500+600Q-500+0.03Q-0.000001Q^2-4000000)/dQ=0
=>-Q/250+600+0.03-0.000002*Q=0
=>Q=149933
B)P=(-Q+30000)/500=$250.1
C)Profit=Q*(-Q+300,000)/500-(520-0.03Q+0.000001Q^2)-4000000=$3,347,974.1
Related Questions
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.