How many homes should be built in a new residential area. The firm has some mono

Question

How many homes should be built in a new residential area. The firm has some monopoly power in
its local market. Its demand is estimated to be Q = 10 - 1/6 P

Its cost function is C = 70 + 8Q + 1/2 Q2 (Price is in tens of thousands, quantity is in units.)

a. What is the revenue-maximizing price and quantity? Explain.

b. What is the profit-maximizing price and quantity? Explain.

c. Can you recommend any pricing strategy that would further improve profit beyond
the profit-maximizing level? Explain such strategy and its implementation.

Explanation / Answer

a.

Demand is Q = 10 - 1/6P

Cost, C = 70 + 8Q + 1/2Q2

P = 60 - 6Q

Profit = Total Revenue - Total Cost

Total Revenue(TR) = P*Q = (60 - 6Q)*Q

Total Cost(C) = 70 + 8Q + 1/2Q2

Revenue maximising condition is dTR/dQ = 0

MR = 0

MR = 60 - 12Q = 0

Q = 60/12 = 5

P = 60 - 6(5) = 30

Revenue maximizing price is 30 units and quantity is 5 units.

b.

Profit maximising condition is Marginal Rvenue = Marginal Cost

MR = 60 - 12Q

MC = 8 + Q

Equating the equations, 60 - 12Q = 8 + Q

13Q = 52

Q = 4

P = 60 - 6(4) = 36

Profit maximizing price is 36 units and quantity is 4 units.

c.

Price discrimination can help the firm to increase its profit. Price discrimination is basically charging different prices from different consumers. If the firm can charge different prices for houses to different consumers then the firm will increase its profit by taking a bite of the consumer surplus. First degree price discrimination i.e. where the firm can charge different price to each and every consumer can help the firm to increase its profit by taking away the whole consumer surplus.

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