Answer to Question #96092 in Microeconomics for Alex

Question

There is a monopoly producer of smartphones facing the following demand Q 400 2P  (where Q is # of smartphones). Its cost is given by C 100Q  . (a) What are the equilibrium quantity and price of smartphones sold by the monopolist? (b) If the government imposes an ad valorem tax of 20% on smartphones, what happens to the equilibrium quantity and price? What is the tax revenue collected? What is the tax incidence of this tax? (HINT: assume that the tax reduces MR not increases MC).

Answer 1

Q = 400 - 2P, so P = 200 - 0.5Q.

(a) The equilibrium quantity and price of smartphones sold by the monopolist are:

MR = MC,

MR = TR'(Q) = 200 - Q,

MC = C'(Q) = 100,

200 - Q = 100,

Q = 100 units,

P = 200 - 0.5Q = 150.

(b) If the government imposes an ad valorem tax of 20% on smartphones, then the equilibrium quantity will decrease and the equilibrium price will increase according to decrease in supply.

MR = (200 - Q)/1.2 = MC,

(200 - Q)/1.2 = 100,

200 - Q = 120,

Q = 80,

P = 200 - 0.5*80 = 160.

The tax revenue collected is TR = P*Q*t = 160*80*0.2 = 2560.

The tax will decrease consumption and create the deadweight loss.