Answer to Question #286148 in Microeconomics for Sooo me

Question

a. Suppose you are a manager of a County government project that is meant to provide rent-regulated housing units in low-income settlements. Using your knowledge of equilibrium, advice the Governor whether this policy will be a success.

b. A Monopolist producing and supplying cooking gas to Mombasa city faces the demand function.

Q = 8800 – 20P. Its cost function is given by TC = 20Q + 0.05Q2.

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.

Answer 1

Solution:

a.). The policy will be successful since it will increase the demand for rent-regulated houses by low-income earners. The role of the policy is to make houses affordable for low-income earners by building cheaper houses that are government regulated. The demand for such houses will increase as people seek them. 

b.). 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.