Answer to Question #285894 in Microeconomics for Fayee

Question

. A monopolist producing and selling cooking gas faces a demand curve,

Q = 100 – 0.2P. If Total Cost is TC=4000+ 50Q.

i. Determine the quantity of cooking gas she will produce and the price she will charge to maximize profits and determine her profit.

ii. Explain how her profits she will affected if regulators forced her to operate like a perfectly competitive firm.

iii. Illustrate and compute dead-weight loss and lost consumer surplus associated with her Monopoly operations.

a. Suppose the joint cost function of a firm producing two products X and Y IS given 

Answer 1

Solution:

i.). Quantity of cooking gas required to maximize profits is where: MR = MC

Derive MR from TR:

TR = P $\times$ Q

Get the inverse demand curve:

Q = 100 – 0.2P

P = 500 – 5Q

TR = (500 – 5Q) $\times$ Q = 500Q – 5Q²

TR = 500Q – 5Q²

MR = $\frac{\partial TR} {\partial Q}$ = 500 – 10Q

 

TC = 4000 + 50Q

MC = $\frac{\partial TC} {\partial Q}$ =50

 

Set MR = MC

500 – 10Q = 50

500 – 50 = 10Q

450 = 10Q

Q = 45

Quantity of cooking gas to produce = 45 pcs

Price = 500 – 5Q = 500 – 5(45) = 500 – 225 = 275

Price of cooking gas = 275

 

Profit = TR – TC

TR = P $\times$ Q = 275 $\times$ 45 = 12,375

TC = 4000 + 50Q = 4000 + 50(45) = 4000 + 2250 = 6,250

Profit = 12,375 – 6,250 = 6,125

Profit = 6,125

 

ii.). If the regulator forced her to operate as a perfectly competitive firm, she will earn zero economic profit.