Taxes in international trade

Question

Q1. Taxes in International Trade

Cigarettes are a relatively small market, with few substitutes and complements, and therefore can be analyzed in separation from income effects. A country is in autarky, and the home demand is satisfied with home supply. Let the demand for cigarettes be

D(p) = 20 − 2p,

and the supply of cigarettes be

S(p) = 2p + 4.

a) Solve for autarky price, quantities, and consumer and producer surpluses.

The country has an opportunity to start trading with another much larger country that has a large cigarette supplier, which can provideany amount of cigarettes for p* = 2

b) Solve for demand, supply, import, consumer and producer surpluses.

c) How big is the bribe that home producers are eager to pay to not participate in free trade with that larger country?

d) How big is the bribe that home producers are eager to pay to guarantee themselves a 50% tax on cigarette imports after opening the borders? What is the consumer’s surplus in this case?

The country instead starts trading with another country of a similar size that has a cigarette supplier, which has an excess supply of cigarettes at S*(p) = 4p - 8

e) Solve for demand, supply, import, consumer and producer surpluses.

f) How big is the bribe that home producers are eager to pay to not participate in free trade with that smaller country?

g) How big is the bribe that home producers are eager to pay to guarantee themselves a 50% tax on cigarette imports after opening the borders? What is the consumer’s surplus in this case?

Q2. Heckscher-Ohlin Model

Let there be two goods, F and G. Both are produced with capital and labour:

Q_F(K,L) = K^0.6L^0.4, Q_G(K,L) = K^0.4L^0.6

The country owns K ¯ = 100 units of capital and L ¯ = 100 units of labour.

a) Let w be the price of labour and r be the price of capital.

– How much capital do you need to produce 1 unit of each good? How much labour?

– Which good is labour-intensive?

– Solve for the marginal cost function for both goods.

b) What does the free market entry assumption implies about prices of both goods?

c) Find the connection between the relative final good prices and relative factor prices.

d) Solve for the relative supply function.

– Under the prices of w and r, how much capital and labour you need to produce F ¯ units of F and G ¯ units of G?

– How much labour and capital you have in total?

– What does this together imply about F ¯ and G ¯ that your producers will produce when they face w and r? What about F ¯/G ¯ ?

– What is the connection between w/r and relative prices?

e) For the utility function u(F, G) = (Fρ + αGρ)^1/ρ, solve for the relative demand function.

f) If the amount of capital K ¯ increases, what happens with the relative supply function? What will happen with the relative prices?

g) If there are two countries with same level of L ¯, but different levels of K ¯, will they trade? Who will export F?

h) What would change if you had three countries?

i) What would change if you had three goods?