Question

An investor discovered that there is no oil change service available in the small town that he has recently moved to and decides to open a shop offering this service. The estimated market demand for the oil change service is given by P=400-10Q. The total cost of the oil change service is TC=150Q²+200 and the marginal cost is MC=30Q

a) If the investor engages in perfect price discrimination, how many oil change services will he offer? What would be his producer surplus?

b) What will be will be the profit maximizing price and quantity if the investor is not allowed to price discriminate, and is forced to charge a uniform price to all the customers? What will be the profits, consumer surplus and deadweight loss?

c) Calculate the price point - elasticity of demand when the price is 100. Is the demand elastic, inelastic or unitary elastic? Explain.

Answer 1

a) perfect price discrimination:

PS  = $500
Quantity= 10

His quantity will be where demand = MC.

400 - 10Q = 30Q So, Q = 10

Quantity= 10

PS = ½*(Y-intercept - MC) 8 quantity
MC = 30Q = 30* 10 = 300; Y-intercept = 400 (P = 400-10Q; when Q=0)

PS = ½*100*10 = $500

b) Uniform price:

profit = $ 15,800
consumer surplus = $320
Deadweight loss = $80

calculation: His MR = MC; MR = 400 - 20Q (double slope of demand curve)

400- 20Q = 30Q SO, Q = 8; P = 320 (400 - 10*8)

Profit = TR - TC ; TR = P*Q

So, profit = (320*80) - (150*8²+200) = 25,600 - 9,800 = 15,800

consumer surplus = ½*(y-intercept - price) * qunatity = ½(400-320)*8 = $320

Deadweight loss = ½*(Price - MC) * lost quantity = ½*(320 - 240) * (10-8) = ½*80*2 = $80

c) Ed = -1.11 Demand is elastic (Ed is greater than 1)

calculation: Point price elasicity = (Q2-Q1)/(Q2+Q1)/2  ÷ (P2-P1)/(P2+P1)/2

where Q1 = 30(400 - 10Q when pricee = 100); Q2 = 8; P1 = 100; P2 = 320

Ed = -22/19 ÷ (220/ 210) Ed = -1.11 Demand is elastic (Ed is greater than 1)