Question

Suppose the Swiss monopolist’s costs equal

Costs = ¼ Q2.

A) How high is the monopolist’s marginal cost for a given quantity?

B) The monopolist will increase its quantity until the world price equals the marginal cost. Use this condition to find the monopolist’s supplied quantity depending on the price.

Assume that Switzerland’s demand is

D = 20 - P.

and show that Switzerland’s import demand will be

M = 20 - 3 · P

C) Suppose that the world price is equal to P W = 4. How much will Swiss consumers want to buy (D1)? How much of this demand is met by the Swiss firm (S1) and how much is imported (M1)?

D) Now suppose Switzerland imposes a tariff t = 2. How does that change demand (D2), supply (S2) and imports (M2)?

E) How big is the deadweight loss?

F) Now suppose that instead of the tariff, Switzerland imposes an import quota equal to M = 2. Assume that demand is the same as in part (B) and find the Swiss monopolist’s quantity. Show that the monopolist now charges P = 10.8.

Answer 1

Suppose the Swiss monopolist’s costs equal

Costs = ¼ Q²

A) monopolist’s marginal cost = dC/dQ

= 2Q/4

=Q/2

B) The monopolist will increase its quantity until the world price equals the marginal cost

i.e. Pw = Q/2

condition of monopolist’s supplied quantity depending on the price: Q = 2Pw

Assume that Switzerland’s demand is

D = 20 - P

Switzerland’s import demand will be = D - Q

= 20 - P - 2P

M = 20 - 3 P

C) P w= 4

Swiss consumers want to buy (D1) = 20 - P

= 20 - 4

= 16

demand met by the Swiss firm (S1) = 2Pw

= 2*4 = 8

quantity imported (M1) = 20 - 3P

= 20 - (3*4)

= 20- 12

=8

D) Now suppose Switzerland imposes a tariff t = 2.

change demand (D2) = 20 - (P+2)

D2 = 18 - P

supply (S2) = 2P

and imports (M2) = D2 - S2

= 18 - 3P

Note: max. 4 parts at a time