The Fun-Land Amusement Park is a 40-acre fun park full of rides, shows, and shop

Question

The Fun-Land Amusement Park is a 40-acre fun park full of rides, shows, and shops. Fun-Land's marketing department segments its customer base into two parts: local patrons and tourists. Fun-Land assumes local patrons are more price sensitive than out-of-town tourists. Yearly demand and marginal revenue relations for overnight lodging services, Q, are as follows: Locals PL = $40 - $0.0005QL MRL = $40 - $0.001QL Tourists PT = $50 - $0.0004QT MRT= $50 - $0.0008QT Marginal cost is constant at $20 per unit. A) Assuming the company can discriminate in price between locals and tourists customers calculate the profit-maximizing price, output, and total profit contribution levels. B) Calculate point price elasticity of demand for each customer class at the activity levels identified in part A. C) Given a fixed cost of $150,000 what is the firm

Explanation / Answer

A.

With price discrimination, profits are maximized by setting MR = MC in each market, where MC = AVC = $20 (because AVC is constant).

Locals

MRL = MC

$40 - $0.001QL = $20

0.001QL = 20

QL = 20,000

PL = $40 - $0.0005(20,000)

= $30

Tourists

MRT = MC

$50 - $0.0008QT = $20

0.0008QT = 30

QT = 37,500

PT = $50 - $0.0004(37,500)

= $35

The profit contribution earned by the Fun-Land Amusement Park is:

p = PLQL + PTQT - AVC(QL + QT)

= $30(20,000) + $35(37,500) - $20(20,000 + 37,500)

= $762,500

B.

Yes, a higher price for Tourist customers is consistent with the lower degree of price elasticity observed in that market.

Locals

QL = 80,000 - 2,000PL

eP = ¶QL/¶PL PL/QL

= -2,000 ($30/20,000)

= -3

Tourists

QT = 125,000 - 2,500PT

eP = ¶QT/¶PT PT/QT

= -2,500 ($35/37,500)

= -2.3

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A.

With price discrimination, profits are maximized by setting MR = MC in each market, where MC = AVC = $20 (because AVC is constant).

Locals

MRL = MC

$40 - $0.001QL = $20

0.001QL = 20

QL = 20,000

PL = $40 - $0.0005(20,000)

= $30

Tourists

MRT = MC

$50 - $0.0008QT = $20

0.0008QT = 30

QT = 37,500

PT = $50 - $0.0004(37,500)

= $35

The profit contribution earned by the Fun-Land Amusement Park is:

p = PLQL + PTQT - AVC(QL + QT)

= $30(20,000) + $35(37,500) - $20(20,000 + 37,500)

= $762,500

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