Question

Neverlandia is a small country with a single firm in Gadget industry. The demand for Gadget in Neverlandia is given by P=210-2Q. The firm's cost function is given by: C=0.5Q^2+10Q+100. (P is the price of Gadget and Q is the quantity）

Currently, the imports of Gadgets to Neverlandia are prohibited and, as a result, the Gadget producer in Neverlandia is a monopolist.

1. Calculate the profits of the monopolist.

2. The government is now contemplating liberalizing trade in Gadget, in which case the Gadget producer would lose its monopoly power and the price of Gadgets would fall to the $100(the world price). how much profits does this firm lose if the ban on imports are removed?

Answer 1

Total cost (C) = 0.5Q² + 10Q + 100

Marginal cost (MC) = dC/dQ = Q + 10

(1) With monopoly power, the firm will equate Marginal revenue (MR) with MC.

P = 210 - 2Q

Total revenue (TR) = P x Q = 210Q - 2Q²

MR = dTR/dQ = 210 - 4Q

Equating with MC,

210 - 4Q = Q + 10

5Q = 200

Q = 40

P = 210 - (2 x 40) = 210 - 80 = 130

TR = 130 x 40 = 5200

C = (0.5 x 40 x 40) + (10 x 40) + 100 = 800 + 400 + 100 = 1300

Profit = TR - C = 5200 - 1300 = 3900

(2) In competitive market, firm will equate Price with MC.

210 - 2Q = Q + 10

3Q = 200

Q = 66.67

P = MC = Q + 10 = 66.67 + 10 = 76.67

TR = 76.67 x 66.67 = 5111.59

TC = (0.5 x 66.67 x 66.67) + (10 x 66.67) + 100 = 2222.44 + 666.7 + 100 = 2989.14

Profit = 5111.59 - 2989.14 = 2122.45

Profit lost due to removal of ban = 2900 - 2122.45 = 1777.55