Question

1. Suppose that Nation 1 can import good X from Nation 2 at a price P₁=1.20 or from Nation 3 at a price P₂=1.50. If the domestic demand and supply curves are given by the following equations:

Demand: P=80-2Q            Supply: P=5+3Q

1. Under free trade, how many units of good X are consumed? How many units of good X are produced domestically? How many units of good X are imported? From which Nation?
2. If a 30% import tariff is imposed, how many units of good X are consumed? How many units of good X are produced domestically? How many units of good X are imported? From which Nation?

Now, suppose that Nation 1 agrees about a custom union with Nation 3 only (that is, trade is free between Nation 1 and Nation 3, while a 30% import tariff is still in place between Nation 1 and Nation 2).

3. How many units of good X are consumed? How many units of good X are produced domestically? How many units of good X are imported? From which Nation?
4. What is the welfare change due to the custom union?

Answer 1

1/a).

Consider the given problem here the demand and the supply of the Nation1 are “P=80-2*Q” and “P=5+3*Q”. Now, nation1 can import the good from nation2 at a price $1.2 and from nation3 at a price $1.5. Under the free trade nation1 will import from nation2 at price $1.2.

At the price $1.2 the corresponding quantity demanded is “Q=40-P/2=40-1.2/2 = 39.4”. So, the total quantity demanded is “Qd=39.4”. Here the minimum price that a domestic producer wants to take is “5”. The price of import from nation2 is less than $5, => the domestic production is zero and “Qd=39.4 units” of good will be imported from nation2.

b).

If 30% tariff is imposed then the price of importable from nation2 will be “1.2*1.3 = $1.56” and the same from nation3 will be “1.5*1.3 = $1.95”. Here after the imposition of tariff the import price of nation2 is less than nation3, => nation1 will import from nation2 at the price 1.56.

So, if “P=1.56” the corresponding quantity demanded is “Qd = 40 – P/2 = 40 – 1.56/2 = 39.22”. So, after the imposition of tariff “39.22 units of X” will be imported from country 2.

2/a).

If nation1 and nation3 form a custom union then the trade between nation1 and nation3 will be completely free, but the trade restriction will be used for nation2.

After the custom union, if 30% tariff is imposed then the price of importable from nation2 will be “1.2*1.3 = $1.56” and the same from nation3 will be “1.5”. Here after the formation of custom union the import price of nation3 is less than nation2, => nation1 will import from nation3 at the price 1.5.

So, if “P=1.5” the corresponding quantity demanded is “Qd = 40 – P/2 = 40 – 1.5/2 = 39.25”. So, after the formation of custom union “39.25 units of X” will be imported from country 3.

b).

Before the formation of custom union “39.22 units of X” were imported from nation2 at price “P=1.56” and domestic producer were produce nothing. So, the total surplus is given by.

=> TS = CS+PS = 0.5*(80-1.56)*39.22 + 0 = 1,538.21, => TS = $1,538.21.

After the formation of custom union “39.25 units of X” were imported from nation3 at price “P=1.5” and domestic producer were produce nothing. So, the total surplus is given by.

=> TS = CS+PS = 0.5*(80-1.5)*39.25 + 0 = 1,540.56, => TS = $1,540.56 > $1,538.21.

So, the welfare change due to custom union is given by, => dW = 1540.56 – 1538.21 = 2.35 > 0.