Consider a country that produces two goods wheat

( W) and

cotton (

C) with two factors of

production: land (T) and labor (L). The technology for wheat

and cotton are as follows. Each unit

of wheat requires 10 units of labor and 1 unit of land. E

ach unit of cotton requires 30 units of

labor and 1 unit of land.

Denote the wage by

w

and the rent of land by

r.

a.

(8 points) Suppose a country has 500 units of labor and 20 units of land. Determine the

allocation of labor and land between the two goods algebraically and then show it

diagrammatically

. How much of wheat and cotton are produced in the economy?

b.

(6 points) Now suppose that the labor supply increases to 540 units. De

termine the

allocation of labor and land between the two goods algebraically and then show them

diagrammatically. Verify the Rybczynski's theorem.

c.

(4 points) Now Suppose

Malaysia has 500 units

of labor and 20 units of land, while

Indonesia

has 80 units of land and 8000 units of labor. Which country has a

comparative advantage in cotton? Which country has a comparative advantage in

wheat?

What is going to be the pattern of trade between these two countries?

d.

(6 points) Denote the price of cotton by P

C

and the price of wheat by P

W

. S

uppose the

autarky prices in the two countries are as follows.

Malaysia: P

C

=100, P

w

=40.

Indonesia

: P

C

= 80, P

w

= 60. Calculate the autarky levels of wage and rent in both

countries.