Question

Assume that a monopolist faces a demand curve given by:

                        Q = 100 – P

Also assume that marginal costs are such that MC = 2Q.

Calculate and graph the following:

Find the profit maximizing price and output in this market under autarky.

Now assume that the world price under free trade is $20 per unit. If the monopolist is a single price monopolist then find the profit maximizing output for this firm. Also find the amount imported under free trade.

Now assume that the country (small country) imposes a tariff of $20 on this product. Find the equilibrium price and quantity supplied by the monopolist. Also find the amount imported under the tariff. (assume single price monopoly).

Find the equilibrium price, quantity supplied, quantity demanded and the amount imported under an equivalent quota (assume single price monopoly).

Find and compare the efficiency loss under the quota to efficiency loss under the tariff.

Answer 1

Monopolist faces a demand curve given by Q = 100 – P or the inverse demand is P = 100 – Q. Marginal revenue is MR = 100 – 2Q.

a) Use MR = MC

100 – 2Q = 2Q

Q = 100/4 = 25 units

Price = 100 – 25 = $75 per unit

b) Monopoly supply function is MC = 2Q or P = 2Q.

At a price of $20, the monopolist produces 20/2 = 10 units. Quantity demanded at P = 20, is 100 -20 = 80 units. Hence imports are 80 – 10 = 70 units.

c) Now assume that the country (small country) imposes a tariff of $20 on this product. Price under tariff is $20 + $20 = $40. Hence quantity demanded is 100 – 40 = 60 units. Supply by monopolist is 40 = 2Q or Q = 40/2 = 20 units. Imports are 60 – 20 = 40 units.

When there is a quota on imports which is equal to 40 units, then the monopolist will supply 10 units at P = 20 and 10 units at = 40 so that domestic price is now $40, Quantity demanded is 60 units, imports are 40 units and monopolist supplies 20 units.