Question

5. Demand function for the good supplied by the domestic monopolist is given by: P = 640-29 Marginal cost of the monopolist is: MCQ - 40 +22. The world price equals Pw = 120. a. Calculate and illustrate graphically supply, demand and imports under free trade. b. Calculate the lowest possible specific tariff that would eliminate imports completely. What would be the equilibrium price and output then? Illustrate it graphically. c. Calculate the equilibrium price and output when instead of the tariff the import quota equal to zero is used. Which instrument is more harmful to the domestic welfare? Why?

Answer 1

a).

Here the demand function faced by domestic monopolist is “P=640-2*q” and the MC function is “MC = 40+2*q”. So, the demand function can be written as “qd = 320 – P/2” and marginal cost is “qs = P/2 - 20”. So, the import demand function is given by, => M = qd-qs.

=> M = (320-P/2) - (P/2-20) = 320 - P/2 - P/2 + 20 = 340 – P, => M = 340 - P.

The export supply function is “P=120”. So, under the free trade the export is equal to import.

=> M = 340-P = 340 – 120 = 220. So, the free trade equilibrium price and the import are “P=120”, “M=220”.

b).

The import demand function is “M=340-P”, where for “P1 = 340” the corresponding import is zero, and the free trade price is “Pw=120”, => the required tariff is “t = P1-Pw = 340-120 = 220”, => t=220. Consider the following fig.

P1=340 Pw+t Pw=120 - > M, X M*=220

Here the downward sloping curve is the import demand function and the horizontal curve is the export supply and the intersection of import demand and the export supply determine the equilibrium.

c).

Here the free trade price is “Pw=120”, as the tariff of “t=220” is imposed the price increases to “Pc=340” and the import decreases to zero. So, for “t=220” the price and quantity are “Pc=340” and “Q=150” respectively. So, the consumer and the producer surplus are “A2PcEc” and “A1PcEc” respectively, => total surplus is “A1A2Ec”.

Pm=440 ---- Pc=340 Em Pw=120 > Q Qm=100 MR Qc=150

If an import quota equal to zero is imposed then the domestic producer will act as a monopolist and will charge “Pm” and reduce the production to “Qm”. So, now the total surplus decreases to “A2A1EmA3” < “A1A2Ec”. So, the import quota is harmful as it enables the monopolist to supply and charge more.