Question

You are the manager of a golf course. A typical member’s inverse demand function for weekly visits (Q) is known to you and is given as P = 100 – 20Q, where P is the fee charged for each visit. Your cost function is C = 20Q.
i. If you operate your business as a single price monopolist, what fee you will charge for each visit and what profit you will earn?
ii. Acting as a single-price monopolist (as above), calculate your monopoly power in the market by computing the Lerner’s Index. What is the price elasticity of demand? How much deadweight loss you cause to the society?
iii. If instead, you adopt a two-part pricing strategy, what profit you will make and how will you do your pricing? What will be the deadweight loss now?

Answer 1

Solution:-

Given that

a)

A single price monopolist uses MR = MC

100 - 4Q = 20

80 = 40Q

Q = 2 visits

P = 100 - 20 * 2 = $ 60 per visit

Profit = revenue - cost

= 2*60 * 20*2

= $ 80

As a single price monopolist, it will charge a fee of $ 60 per visit and its profit will be $ 80.

b)

Lerner index = (P-MC)/P

= (60-20)/60

= 0.67

Elasticity = -1/Lerner index

= -1 / 0.67

= -1.5

DWL = 0.5 * (60-20) * (4-2)

= $ 40

Hence Lerner index is 0.67 and price elasticity is -1.5 and deadweight loss is $ 40

c)

There is no deadweight loss in two-part pricing. The first price is the marginal cost and it will be $ 20 per visit. The second price is the admission fee and it is equal to the consumer surplus at P = MC

Fee = 0.5 * (100 - 20) * 4

= $ 160

Profit is the consumer surplus extracted and it is $ 160

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