Answer to Question #286073 in Microeconomics for Frank

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 will be to make houses more cheaper to the low-income earners by making cheaper houses that are government regulated. The demand for such houses will increase as people seek for them.

 

b.). i.). Profit maximizing quantity is where: MR = MC

TR = P $\times$ Q  

P = 440 – $\frac{Q} {20}$

TR = (440 – $\frac{Q} {20}$ ) $\times$ Q = 440Q – $\frac{Q^{2} } {20}$

MR = $\frac{\partial TR} {\partial Q}$ = 440 – $\frac{Q} {10}$

TC = 20Q + 0.05Q²

MC = $\frac{\partial TC} {\partial Q}$ = 20 – 0.1Q

 

Set: MR = MC

440 – $\frac{Q} {10}$ = 0.1Q + 20

Q = 2,100

The quantity of cooking gas she will produce = 2,100 pcs

P = 440 – $\frac{Q} {20}$ = 440 – $\frac{2100} {20}$ = 440 – 105 = 335

Price = 335

The price she will charge to maximize profits = 335

 

Profit = TR – TC

TR = P $\times$ Q = 335 $\times$ 2100 = 703,500

TC = 20Q + 0.05Q² = 20(2100) + 0.05(2100²) = 42,000 + 220,500 = 262,500

Profit = 703,500 – 262,500 = 441,000

Profit = 441,000

 

ii.). If the regulators forced her to operate as a perfectly competitive firm, her economic profits will be affected greatly as she will now earn zero economic profits.