Question

Marvel Cleaning Service, Inc. is a firm that specializes in cleaning business offices, and Marvel enjoys a monopoly position because it is the only firm allowed to provide cleaning service at the TechCenter industrial office park - the monopoly is believed to enhance security. There are 25 equal-sized offices in TechCenter, each one leased to a different company. TechCenter is closed 45 days a year (Sundays plus official federal holidays), which limits the demand for Marvel's cleaning services to a maximum of 320 cleanings per year for each one of the 25 companies leasing offices. Marvel believes it faces an identical demand by each one of the 25 businesses in TechCenter. This demand function is given as P = 80 -0.25Q. Marvel's costs are constant and equal to $30 per office cleaning. The owner of Marvel Cleaning Service is considering uniform pricing

4.1. If Marvel practices uniform pricing, it will charge ________ for an office cleaning and will face a quantity demanded from each of the 25 identical firms of __________ cleanings per year.

4.2. At TechCenter, Marvel's total profit per year is __________ (i.e., the sum of the profits from the 25 businesses in TechCenter). Each one of the businesses enjoys ____________ of consumer surplus under uniform pricing.

4.3. If Marvel Cleaning is able to practice perfect price discrimination, what is the firm’ total profit?

Answer 1

Demand -- 80 - 0.25Q, So, MR = 80 - 0.5Q (double slope)

MC = 30

4.1 If Marvel practices uniform pricing, it will charge $55 for an office cleaning and will face a quantity demanded from each of the 25 identical firms of 100 cleanings per year.

calculation: A monopolist chooses quantity where MR = MC

80 - 0.5Q = 30 So, Q = 100; Plugging inthe value of Q in demand function for price:

80 - 0.25*100 = 55 So, P = 55

4.2. At TechCenter, Marvel's total profit per year is 625,000  (i.e., the sum of the profits from the 25 businesses in TechCenter). Each one of the businesses enjoys $1250 of consumer surplus under uniform pricing.

calculation:

Profit = total revenue (TR) - Total cost (TC)

TR = price * quantity = 55 * 100 = 5500

TC = MC * quantity = 30 * 100 =3000

SO, profit = 5500 - 3000 = 2500 (per business)

2500 * 25 = 62,500 (for 25 businesses)

Consumer surplus = ½ * (highest willingness to pay - price) * quantity

= ½ * (80 - 55) * 100 = ½ * 25 * 100 = 1250

4.3. If Marvel Cleaning is able to practice perfect price discrimination, what is the firm’ total profit?

$125,000

calculation:

He would get the whole area above price upto highest willingness to pay as his profit.

Minimum price would be $30 (competitive price = MC),

Quanitty would be 200 (plug in the value of P = 30 in demand function: 30 = 80 - 0.25Q; so Q = 200)

Profit = ½ * (80 - 30) * 200 =½ * 50 * 200 = 5000 (per business)

For 25 bsinesses, profit = 5000 * 25 = 125,000