Question

6.  Consider the monopoly firm of the previous problem with the cost function TC=4Q2. Assume that in addition to facing the aforementioned domestic demand curve P=300-2Q, the company can also sell any quantity of its product in a foreign market at a constant price of $240 (independent of quantity).

Determine (i) the company’s optimal sales (quantity of product sold) in domestic and foreign markets,

(ii) price at which the company will sell the product in domestic market.

(iii) Determine the company’s total profit. Compare it to that reported in your solution of problem 5(e) and comment on the comparison.

Answer 1

Answer : 6) i) Given,

Domestic demand : P = 300 - 2Q

TR (Total Revenue) = P*Q = (300 - 2Q) * Q

=> TR = 300Q - 2Q^2
MR (Marginal Revenue) = TR / Q

=> MR = 300 - 4Q

Given, TC = 4Q^2

MC (Marginal Cost) = TC / Q

=> MC = 8Q

Domestic market:

For monopoly firm at equilibrium, MR = MC.

=>  300 - 4Q = 8Q

=> 300 = 8Q + 4Q

=> 300 = 12Q

=> Q = 300 / 12

=> Q = 25

Therefore, in domestic market the firm's optimal output level is, Q = 25 units.

Foreign market :

Price (P) = $240 (Given)

From demand function we get,

P = 300 - 2Q

=> 240 = 300 - 2Q

=> 2Q = 300 - 240

=> 2Q = 60

=> Q = 60 / 2

=> Q = 30

Therefore, in foreign market the firm's optimal output level is, Q = 30 units.

ii) Price in domestic market:

P = 300 - (2 * 25) [As domestic market Q is 25]

=> P = $250

Therefore, in domestic market the firm's price is $250 for per unit.

iii) Domestic market :

TR = P*Q = 250 * 25 = $6,250

TC = 4 * (25)^2

=> TC = $2,500

Profit = TR - TC = 6,250 - 2,500

=> Profit = $3,750

Foreign market :

TR = P*Q = 240 * 30

=> TR = $7,200

TC = 4 * (30)^2

=> TC = $3,600

Profit = TR - TC = 7,200 - 3,600

=> Profit = $3,600

Total profit = Profit of domestic market + Profit of foreign market = 3,750 + 3,600

=> Total profit = $7,350

Therefore, firm's total profit is $7,350.