Question

A firm can sell pills in two countries; the pills cost fifty cents each to produce and sell.  Demand in country A is Q = 10 – P.  Demand in country B is Q = 10 – 2P.  The firm must sell an integer amount of pills. Determine the following: (a) Total quantity sold and total profits of the firm if it employs third degree price discrimination.  (b) Total quantity sold and total profits of the firm if it does NOT employ price discrimination.  (You must show or explain your calculations to get any credit for your answers.)

Answer 1

Demand in country A is Q = 10 – P or P = 10 – Q. This gives TR = 10Q – Q^2 and MR = 10 – 2Q.

Demand in country B is Q = 10 – 2P or P = 5 – 0.5Q. This gives TR = 5Q – 0.5Q^2 and MR = 5 – Q

When separate prices are charged, optimum rule is MR1 = MC and MR2 = MC

10 – 2Q = 0.50 and 5 – Q = 0.50

Q in country A = 9.5/2 = 5 pills (only integer values are taken). Price = 10 – 5 = $5.

In country B again use MR = MC

5 – Q = 0.5, Q = 4.50 = 5 pills (only integer values are taken). Price = 5 – 0.5*5 = $2.5.

Profits = TR – TC = (5*5 + 5*2.5) – (10*0.5) = 32.50

b) Single demand is Q = 20 - 3P or 3P = 20 - Q. This gives P = 20/3 - Q/3 and MR = 20/3 - 2Q/3

Use MR = MC

20/3 - 2Q/3 = 0.5

20/3 = 5Q/6

Q = 8 pills.

Price = 20/3 - 8/3 = $4.

Profit = (4*8) - (0.5*8) = $28.