Answer to Question #179955 in Microeconomics for SMK

Question

A monopoly firm has demand function, q=50-2p and cost function, c=q2 .

a) Compute the equilibrium quantity and price for this firm. (5 MARKS)

b) Calculate the consumer surplus and producer surplus when this firm is at

the equilibrium position. (5 MARKS)

c) Let t is the government tax levied on/subsidy given to this monopoly firm.

i) What is the price paid by the consumer?

ii) Calculate the equilibrium quantity and price after the tax is introduced

iii) Compute the after-tax/subsidy consumer surplus and producer

surplus for this firm.

(15 MARKS)

d) If t in question (c) can give the same welfare as under perfect competition,

what is the price paid by the consumer? What is the value of t ? Is t a tax or

subsidy? What is the price received by the monopoly firm? (5 MARKS)

Answer 1

a) The equilibrium quantity and price for this firm are:

MR = MC,

p = 25 - 0.5q,

MR = TR'(q) = 25 - q,

MC = c'(q) = 2q,

25 - q = 2q,

q = 8.33 units,

p = 25 - 0.5×8.33 = 20.83.

b) The consumer surplus and producer surplus when this firm is at the equilibrium position are:

CS = 0.5×(25 - 20.83)×8.33 = 17.37,

PS = 0.5×20.83×8.33 = 86.76.

c) If t is the government tax levied on/subsidy given to this monopoly firm:

i) The price paid by the consumer will increase for tax and decrease for subsidy.

ii) The equilibrium quantity will decrease and price will increase after the tax is introduced.

iii) The after-tax/subsidy consumer surplus will decrease/increase and producer surplus for this firm will decrease/increase.

d) If t in question (c) can give the same welfare as under perfect competition,

then the price paid by the consumer will decrease. The value of t will be negative, because t is a subsidy. The price received by the monopoly firm will increase.