Question

Cal Health Club and Spa offers two types of membership services: A Fitness Gym and a Pool/Spa. Let’s say that customers Abby, Bea, and Chewy have willingness to pays for each service as below. Both the Fitness Gym and Spa have constant marginal cost at $20 per month to supply a membership. And customers decide whether to purchase a membership for the Fitness Gym and/or Spa, and Cal Health Club decides the type of membership and price to offer.

Abby Bea Chewy

Willingness to Pay (per month) Fitness Gym Spa membership membership

$60 $50 $50 $125 $25 $140

a. If Cal wants to sell each customer separate memberships to each service, what prices should be charged? What would be firm’s producer surplus?

b. Caldecidestobundletheservices–thatis,sellamembershipthatallowsaccesstoboththe Fitness Gym and the Spa. What price should be charged for the bundled membership if it wants to sell the bundled membership to all three consumers? Explain. What is the producer surplus?

c. Now Cal considers offering options to purchase only a Fitness membership for $60, or only Spa membership for $140, or a membership package that includes both for $175. Which option will each customer choose? What is the producer surplus?

3. (5 points) G-Blast Gaming members pay a monthly fee that allows unlimited hours of online gaming. G-Blast hires you to consult on the best membership pricing scheme. You estimate its typical user’s inverse demand for streaming gaming as P = 600 – 20Q, where Q is hours of streaming. The company can supply an additional hour of streaming to another member at zero marginal cost. What is the highest price that G-Blast should charge for a membership fee?

Answer 1

ANSWER a) seperate memberships FOR FITNESS GYM: Suppose if P= 25, and All 3 buy's TT= (25-20 X = 5x3=15 = 30x2=60 It p=50; All 2 buy's T = (50-20 X2 > If P=60; only abby buys T (60-20 x1 = 40 Hence charge P=50, TT= PS = 60 Producer surplus = 60 for SPA - It p=50 All 3 will buy, then edhe fu T= (50-20)x3 = 90 thes > If p= 125 ; TT= (125-20) x2 DOO Jesenn an 10542 T-210 If = 140; then then T= (140-20) X1 T= 120 Hence P=125 charge producer susplus = TT=PS= 210 And Total producer surplus = PS = 60+20 = 270.

Bundle sale is here the bundle paces which is loual to sum of witp = 110, 175, 165 If P=110, All 3 buys bundle 20+20=40. Then bundle cost = TT= (110-40) x3 = 70x3 T = 210 If p=165, T = (165-40) X2 T= 125 x 2 T = 250 If p=175, then T=1175-40) 135 T = Hence charge P=165 and Producer surplus is PS=250 CjAs bundle popce = 175, Bea will purchause bundle. » Pf=60 - Abby will purchase fitness gym membership chewy PS=140 will buy SPA S Total = (175-40) + (60-20) + (140-20 135 +40+120 Producer = 295. surplus

200 = 6ooP Q = 600-P120 Q = 30- Plzo i MC-O at P=o Q=30 Highest membership fee = Consumer Surplus at P-o. ==x (600-0) X30 = 600 x 30 30X30 I $900. -