Question

The Kennedy Center is launching a membership campaign to raise funds. The 100 prospective members are of two types: 60% are ordinary, 40% are generous. Memberships can be of two types: sustainer, with ordinary benefits, and golden circle, with more generous benefits. The cost of providing benefits to each type of members, and the members’ willingness to pay are summarized in the following table (measured in dollars):

Cost Willingness to Pay Ordinary Generous 280 450 350 600 Sustainer Membership Type pe Golden Circle 200 300

a) How much does the Kennedy Center collect by selling golden circle memberships to generous donors and sustainer memberships to ordinary donors?

b) Assume not that the Kennedy Center cannot identify the customers’ types. What happens if they follow the same pricing policy as of point A?

c) Find the membership-pricing mechanism that the Kennedy Center should follow to separate types of prospective members.

d) Assume now that the share of generous members grows to 50%. What kind of membership-pricing mechanism would ensure higher revenues to the Kennedy Center?

Answer 1

a. According to probabilities, out of 100 customers, there are 60 ordinary and 40 generous customers.

Revenue = 60*280 + 40*600 = 40,800

b. If Kennedy Centre can identify customers, then it would able to maiximise the benefits by selling the sustainer membership to ordinary customer at 280 and golden circle membership to generous customers at 600. This would maximise the centre's revenue.

c. In order to seperate the customers, it could charge such that the amount earned over the cost is maximised. For ordinary customers, 80 (280-200) is profit above the cost for sustainer membership and 50 (350-300) is profit above the cost for golden circle membership. It is beneficical for the centre to get the ordinary customers pay for sustainer membership. For generous customers, 250 (450-200) is profit above the cost for sustainer membership and 300 (600-300) is profit above the cost for golden circle membership. It is beneficical for the centre to get the generous customers pay for golden circle membership. But if the centre charges 280 for sustainer membership, then even generous customers would want to go for sustainer membership because of higher benefit for them. If price is 280 and their willingness is 450 for sustainer, then there is a benefit of 170 over the price. So, the centre could charge 429 (600 - 170-1) for golden circle membership such that generous customers would be indifferent between two types of membership at price 430 and would chose golden circle membership for price 429. This way the centre could maximise its revenue and seperate the customers.

d. Even if the generous customers rise to 50%, the optimal startergy for the centre would be to chose the stratergy mentioned in part c.