Question

Suppose you own the only spa in a small college town. Everybody in town is either a student or a professor. Their demand functions for your Relaxing Healing Package (RHP) are: Qp = 175-P Qs = 125-P Where Qp and Qsis quantity demanded by professors and students, respectively. Your average variable costs are $50 per customer regardless of the quantity, and your fixed costs are $1000 per month. A) Suppose first that you only sell your product through coupons online, so you can only sell to everybody at the same price. Find the profit-maximizing quantity and price that you should offer. B) Calculate your profits in part A). C) What conditions would be necessary for you to use 3rd degree price discrimination in this market? D) If you manage to use 3rd degree price discrimination, what price should you charge to each group? And how much will you sell to each? E) Calculate your profits in part D).

Answer 1

A) Qp = 175-P Qs = 125 - P Total demand Q = Qptas Q = 175-P + 125-P Q = 300-QP 2p= 300-8 P = 150 - 0 MR = 150 - 21). MR = 150-2 FC = 1000 AUC= 50 TUC = TC = TC = Mc = MR = mc 150-0 =50 AUCXQ = 500 FC + TVC 1000+ 500 50 = 0=1007 P = 150 - P = 150-100 [P=100]

B) T = PO - TC 100X100 - 1000 - 50x100 10000 - 1000 - 5000 = 10000-6000 = 4000 () Necessary condition for 3rd degree price discrimination i) Firm must have monopoly power. ii) Maraet must be divided into different sub markets. i) Price elasticity of demand must be different in each sub market. Qp = P = MRP 175-P 175- OP = 175 - 20p mc = 50

62.5 175 - 20 p = 50 175 - 50 = 200 125 = 2OP = Op = P = 175- 62.5 P = 112.5 mRs = mc Qs = 125-P P= 125-ds MRs = 125-285 125 - 20s = 50 125 - 50 = 20 75 = 205 Qs = 37.5 P = 125- 37.5 P=87-5 E) Profit, n = = Pop + Psds - TC 112.5 X62.5+ 87.5% 37.5-1000 - 50 (62.5737.5) 7031.25+ 3281.25 - 1000 - 5000 10312.5 - 6000 - 4318-5 =