A monopoly firm faces the following estimated demand and average variable cost functions:Qd = 39,000...

Question

A monopoly firm faces the following estimated demand and average variable cost functions:
Qd = 39,000 — 500P + 0.4M-- 8,000B.R Avc = 30 — 0.005Q + 0.0000005Q2
(totoO0 Qt 2
Where Q is output, P is price (dollars per unit), M is income, and PR is the price of the related good (dollars per unit). The firm forecasts income to be $40,000 and PR to be $2. Total fixed cost is $100,000. ,.¦=iner
As a manager of this firm, determine the profit max'inlizingjavethf_output, the price you will charge, and the expected profits for the firm.

005_znas9jk-4l1pom15.pdf

David · Accepted Answer

Q5
Q = 39000-500P +.4*40000 -2*8000 = 39000-500P
P = ( 39000-Q)/500
TR = P*Q =Q* ( 39000-Q)/500
MR = (39000 -2Q)/ 500
 MC= dTVC/dQ
TVC= AVC*q = 30Q -.005Q^2 +.0000005Q3
MC = 30-0.01Q +0.0000015Q^2
Equate MR with MC to get 
(39000 -2Q)/ 500 = 30-0.01Q +0.0000015Q^2
0.00075Q^2 -3Q -24000= 0 
Q= 8000
P = (39000-8000)/500= 62
Profits = 8000*62  - 30*8000 +.005*64000000 - .

A monopoly firm faces the following estimated demand and average variable cost functions: Qd = 39,000 — 500P + 0.4M-- 8,000B.R Avc = 30 — 0.005Q + 0.0000005Q2 (totoO0 Qt 2 Where Q is output, P is...

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