In

Economics 3563: International Trade

Chapter 6: H-O Model

Homework 3 – SOLUTIONS

Problem 6-4

(a) Food is labor intensive, and cars are capital intensive. Home is relatively rich in labor, and

Foreign is relatively rich in capital.

Thus, according to the H-O theorem, Home exports food and Foreign exports cars.

(b) We can find out about production in each country using the full employment conditions. In

Home, these are 5 4 600 F C

Q Q    for labor and 3 4 400 F C

Q Q    for capital. The solution

to this system is 100 F

Q  and 25 C

Q  .

In Foreign the full employment conditions are 5 4 600 F C

Q Q    for labor and

3 4 500 F C

Q Q    for capital. The solution is 50 F

Q  and 87.5 C

Q  .

(c) To find the relative price in autarky in Home, we use the demand function and the relative

supply found in part ii), Q

F

QC =

100

25 = 4 . The price is 1.1 0.075 4 0.8F

C

P

P     .

(d) To find the price under free trade we need the world relative supply. The total amount of food

produced in the world is the sum of the production of both countries, 50 100 150 W

F Q    . The

world supply of cars is 87.5 25 112.5 W

C Q    . The relative world supply is

Q F W

Q C

W =

150

112.5 = 1.333 .

The intersection of the world relative supply and the world relative demand (given by the same

equation as each country's demand in autarky since they have the same preferences), is the new

equilibrium. The relative price is 1.1 0.075 1.333 1F

C

P

P     .

The aggregate gains from trade are shown on the graph below

The dashed line is the free-trade line. The solid line is the autarky line.

25

131.5 125 100

Cars

Food

Home

105

125