A pharmaceutical firm faces the following monthly demands in the U.S. and Mexica

Question

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 Statesand $500,000 in Mexico. Assume that the firm cannot prevent resale or arbitrage and is forced to set the same pricein both markets. Find the price and profits for the firm.

Explanation / Answer

ANS.

In us market

QUS = 300,000 - 5,000PUS

PUS = 300,000 / 5,000 - ( QUS / 5,000 ) = 60 - (QUS / 5000)

MC = $2

TR = P*Q = 60QUS - Q2/5,000

by differentiaing w.r.t Q, we get MR

MR = 60 - 2Q/5000

At profit maximization MR = MC  

therefore, 60 -2Q / 5000 = 2

300000 -2Q = 10000

290,000/2 = Q

Q*US = 145000

PUS = 60 - QUS / 5000 = 60 - 145,000 / 5000

P*US = 60 -29 = $31

profit in US market = TR - TC, where TR = P*Q

profit = 31*145,000 - 1,000,000

profit in US = 4,495,000 - 1,000,000 = $3,495,000

In mexican market

QX = 240,000 - 8,000PX

PX = 30 - Qx / 8000

MC= 2

TR = P*Q = 30Q - Q2/ 8000

MR = 30 - 2Q/ 8000

At profit maximization MR = MC

30 -2Q/8000 = 2

240,000 - 2Q = 16,000

224,000 = 2Q

Q*X = 112,000

P*X = 30 - Q / 8000

P*X = 30 - 112,000/ 8000 = 30 -14 =$16

Profit in mexican market = TR - Tc

profit = 16*112,000 - 500,000 = 1,792,000 - 500,000 = $1,292,000

So total price of firm = P*US + P*X = 31 +16 = $ 47

total profit of firm = profit of US market + profit of Mexican market

Total Profit of firm = 3,495,000 + 1,292,000 = 4,787,000

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.