Please help me solve this question: You sell a prescription drug (pills) in two
ID: 1091869 • Letter: P
Question
Please help me solve this question:
You sell a prescription drug (pills) in two countries-Country A and Country B. It costs S2 to produce and sell a pill in each country Demand for your pills in Country A is: QA 20 PA Demand for your pills in Country Bis: QB 316 2PB a Calculate the profit-maximizing quantity of pills and total profits if you use 3rd degree price discrimination. b) Calculate the profit-maximizing quantity of pills and total profits if price discrimination is banned by govemment and you are a law-abiding firm).Explanation / Answer
Revenue = Price * quantity sold
Revenue in Country A = PA(20-PA) = 20PA-PA^2
Revenue in country B = PB(16-2PB) = 16PB -2PB^2
a) In 3rd degree price descrimination, the firm would try to maximize revenue in each country treating their pricing separate.
Maximize revenue in country A: Differentiate with respect to PA and equate to 0:
20-2PA = 0
PA = $10
Double differentiation = -2 <0 i.e its a maxima
Quantity in country A= 20-10 =10 pills
revenue = 10*10 = $100
profit = revenue - cost = 100 - 2*10 = $80
Maximize revenue in country B: Differentiate with respect to PB and equate to 0:
16-4PB = 0
PB = $4
Double differentiation = -4 <0 i.e its a maxima
Quantity in country B= 16-8 =8 pills
revenue = 8*4 = $32
profit = revenue - cost = 32 - 2*8 = $16
Total quantity demanded = 10+8 = 18 pills
Total profit = $80+$16 = $96
b) if Price descrimination is banned, then PA = PB and we need to maximize total revenue in country A and B
Total revenue = 20PA - PA^2 + 16PA -2PA^2 = 36PA - 3PA^2
Maximize revenue: Differentiate with respect to PA and equate to 0:
36 - 6PA = 0
PA = 6
Double differentiation = -6<0 i.e its a maxima
Quantity demanded in country A = 20-6 = 14
revenue = 14*6 = $84
Profit = 84 - 14*2 = $56
Quantity demanded in country B = 16-2*6 = 4
revenue = 4*6 = $24
Profit = 24 - 4*2 = $16
Total quantity demanded = 14+4 = 18pills
Total profit = 56+16 = $72