261 0 Ferdinand Sludge has just written a disgusting new boo

26.1 (0) Ferdinand Sludge has just written a disgusting new book, Orgy in the Piggery. His publisher, Graw McSwill, estimates that the demand for this book in the United States is Q₁ = 50,000 2,000P₁, where P₁ is the price in the U.S. measured in U.S. dollars. The demand for Sludge\'s opus in England is Q₂ = 10, 000 500P₂, where P₂is its price in England measured in U. S. dollars. His publisher has a cost function C(Q) = $50,000 + $2Q, where Q is the total number of copies of Orgy that it produces.

(a) If McSwill must charge the same price in both countries, how many copies should it sell? What price should it charge to maximize its profits __________   How much will those profits be? __________

(b) If McSwill can charge a different price in each country and wants to maximize profits, how many copies should it sell in the United States? __________ How many copies should it sell in England? __________ What price should it charge in England? __________ How much will its total profits be? __________

Solution

(a) Q=Q1+Q2

Q= 50000-2000P+10000-500P

Q=60000-2500P

P=24-Q/2500

R = P*Q = 24Q-Q²/2500

MR=dR/dQ=24-Q/1250

C=50000+2Q

MC=dC/dQ = 2

FOR PROFIT MAXIMIZATION MC=MR

24-Q/1250=2

Q=27500

P=24-27500/2500=13

Profits=R-C

= 24*27500-27500*27500/2500 - 50000-2*27500 = 252500

(b) In US

Q=50000-2000P

P=25-Q/2000

R = P*Q = 25Q-Q²/2000

MR=dR/dQ=25-Q/1000

C=50000+2Q

MC=dC/dQ = 2

FOR PROFIT MAXIMIZATION MC=MR

25-Q/1000=2

Q=23000

P=25-23000/2000=13.5

In England

Q=10000-500P

P=20-Q/500

R = P*Q = 20Q-Q²/500

MR=dR/dQ=20-Q/250

C=50000+2Q

MC=dC/dQ = 2

FOR PROFIT MAXIMIZATION MC=MR

20-Q/250=2

Q=4500

P=20-4500/500=11

Profits=R-C

= 11*4500+23000*13.5 - 50000-2*27500 = 255000