Question

You are a manager of company with market power, and your demand and cost functions are given by:

Q = 142,000 – 500P + 6M – 400P_R and

C(Q) = 500,000 + 200Q – 0.024Q² + 0.000006Q²

Where Q is the amount demanded, P is price, M is income, and P_R is the price of a related good. The estimated values for M and P_Rare $25,000 and $200, respectively.

a. What is the profit maximizing (or loss minimizing) output for this firm?

b. What is the firm’s profit maximizing (optimal) price?

c. What are the firm’s maximum profit (loss)?

d. Do you think this firm enjoy much market power? Why?

Answer 1

Q142000 - 50 p+ 6 M- 400 PR (1)

C(Q) 500000 + 200Q -0.024 + 0.000006

now M = 25000

PR = 200

put these values in equation 1

1 ) Q = 142000-500 P [phone](200)

Q = 142000-500 P +150000 - 80000

Q = 212000 - 500 P

500 P = 212000 -Q

P =

P = 424 - 0.002 Q equation 2

now TR = PQ

= (424- 0.002 Q)Q

= 424Q - 0.002

so profit maximizing

put   

224 = 0.043988 Q

Q =  

Q = 5092.29

so profit maximizing output is 5092.29

b) put this value in equation 2

P = 424 -0.002(5092.30)

P =  

so the profit maxi maximizing price is

c) now put the value of Q = 5092.30 in equation (3)

so firms profit is

d ) as profit is so heavy

so firm is njoying the market powers.