Question 3 Jeju Spa offers a long massage (L), a medium massage (M), or a short massage (S). There are three different customer types numbering 100 in all. The number of each customer type, their values and the marginal cost for these services are given in the table below. L M S Type 1 20 $100 $70 $50 Type 2 30 $80 $60 $40 Type 3 40 $50 $40 $30 MC $30 $20 $10 Each customer buys at most one kind of massage, choosing the one which provides the highest consumer surplus. If the consumer surplus from two different kinds of massage is the same, the consumer prefers the longer massage. Jeju Spa chooses prices p. Py and ps targeting the long massage to type 1, the medium one to type 2, and the short one to type 3 customers. Calculate the optimal prices p, ', PM* and p,*. NB: These prices must be incentive compatible