3. A pharmaceutical firm faces the following monthly demands in the U.S. and Mex
ID: 1166794 • Letter: 3
Question
3. A pharmaceutical firm faces the following monthly demands in the U.S. and Mexican markets for one of its patented drugs: Qus-300,000-5,000Pus and Qx-240,000-8,000Px where quantities represent the number of prescriptions. Marginal cost is constant at $2 per prescription in both markets. Monthly fixed costs are $1 million in the United States and $500,000 in Mexico. Assume that the firm cannot prevent resale or arbitrage and is forced to set the same price in both markets. Find the price and profits for the firm. (10 points) Assume that resale or arbitrage among markets is impossible. Find the profit-maximizing prices and quantities. What are the firm's total profits? (15 points) Can the firm increase its profits by practicing price discrimination? (5 points) a. b. c.Explanation / Answer
(a) With single pricing, Market quantity (QM) = QUS + QX and Uniform price (P) = PUS = PX
QM = 300,000 - 5,000P + 240,000 - 8,000P
QM = 540,000 - 13,000P
13,000P = 540,000 - QM
P = (540,000 - QM) / 13,000
Total revenue (TR) = P x QM = (540,000QM - QM2) / 13,000
Marginal revenue (MR) = dTR/dQM = (540,000 - 2QM) / 13,000
Equating MR with MC,
(540,000 - 2QM) / 13,000 = 2
540,000 - 2QM = 26,000
2QM = 514,000
QM = 257,000
P = (540,000 - 257,000) / 13,000 = 283,000 / 13,000 = 21.77
Profit ($) = Revenue - Fixed cost - Variable cost = QM x (P - MC) - FC
= 257,000 x (21.77 - 2) - 1,000,000 = 257,000 x 19.77 - 1,000,000 = 5,080,890 - 1,000,000
= 4,080,890
(b) In absence of resale, profit is maximized when MRUS = MC and MRX = MC
For US,
QUS = 300,000 - 5,000PUS
5,000PUS = 300,000 - QUS
PUS = 60 - 0.0002QUS
Total revenue (TRUS) = PUS x QUS = 60QUS - 0.0002QUS2
Marginal revenue (MRUS) = dTRUS/dQUS = 60 - 0.0004QUS
Equating MRUS with MC,
60 - 0.0004QUS = 2
0.0004QUS = 58
QUS = 145,000
PUS = 60 - (0.0002 x 145,000) = 60 - 29 = $31
For Mexico,
QX = 240,000 - 8,000PX
8,000PX = 240,000 - QX
PX = 30 - 0.000125QX
TRX = PX.QX = 30QX - 0.000125QX
MRX = dTRX/dQX = 30 - 0.00025QX
Equating MRX with MC,
30 - 0.00025QX = 2
0.00025QX = 28
QX = 112,000
PX = 30 - (0.000125 x 112,000) = 30 - 14 = $16
Total profit ($) = (PUS x QUS) + (PX.QX) - MC x (QUS + QX) - Fixed cost
= (31 x 145,000) + (16 x 112,000) - 2 x (145,000 + 112,000) - 1,000,000
= 4,495,000 + 1,792,000 - (2 x 257,000) - 1,000,000 = 6,287,000 - 514,000 - 1,000,000 = 4,773,000
(c) Since profit is higher with price discrimination (Profit in part b > Profit in part a), the firm can increase profits by price discrimination.
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