Answer to Question #157982 in Macroeconomics for Qurban Ali

Question

Road Runner Co is a Pakistani manufacturer making Bicycles. It exports to two markets,Bangladesh and Sri Lanka. Demand for Bicycles in thesetwo markets is given by the following Functions:

Bangladesh Q1 = 12 – P1

Sri Lanka Q2 = 8 – P2

Where Q1 and Q2 are respective quantities sold (in thousands) andP1 and P2 are the respective prices (in Pak. Rupees per unit) in the two markets. Total cost function is

C = 5 + 2 (Q1+ Q2)

a. Determine the company’s total profit function. Also,

(i) What are the profit maximizing levels of price and output for the two markets?

(ii) Calculate the marginal revenues in each market.

b. Now consider two cases:

(i) Company is effectively able to price discriminate in thetwo markets. What will be the total profits?

(ii) Suppose the company does not engage in price discrimination. By charging thesameprice in the two markets what are the profit maximizing levels of price,output, and the total profits?

c. Analyze, with graphs, the two alternative pricing strategies available to the company.

Answer 1

a. The company’s total profit function is:

$TP = TR1 + TR2 - C = (12 - Q1)×Q1 + (8 - Q2)×Q2 - 5 - 2(Q1+ Q2) = -Q1^2 - Q2^2 + 10Q1 + 6Q2 - 5.$

(i) The profit maximizing levels of price and output for the two markets are at the quantities for which MR = MC.

(ii) Calculate the marginal revenues in each market are:

MR1 = TR1'(Q1) = 12 - 2Q1,

MR2 = TR2'(Q2) = 8 - 2Q2.

(i) if company is effectively able to price discriminate in the two markets, then the total profits will increase.

(ii) By charging the same price in the two markets the profit-maximizing levels of price, output, and the total profits are:

Q = 20 - P,

MR = 20 - 2Q,

MC = 2,

20 - 2Q = 2,

Q = 9 units,

P = 20 - 9 = 11,

TP = 11×9 - 5 - 2×9 = 76.

c. The pricing strategy with different prices will be better to the company.