Suppose there are 2 countries, Home and Foreign, two factors of production, capital and labor and two products, food and cloth.
a) Suppose the production functions for cloth and food are:
\(Q_{F}=L_{F}^{0.8}K_{F}^{0.2}\)
\(Q_{c}=L_{c}^{0.2}K_{c}^{0.8}\)
Write down formulas for the unit-isoquants (HINT: set Qc and Qf: both equal to 1, and then express labor input as a function of capital input). On the axis below, draw the two unit-isoquants you have just derived. The graphs do not have to be exact, they should capture the important characteristics. Label them clearly.
b) Which good is capital-intensive? Which good is labor intensive?
c) Suppose Home has 100 units of labor and 200 units of capital, while Foreign has 300 units of labor and 150 units of capital. Under free trade, which country would export cloth? Which country would export food?
d) When the two countries start trading, what will happen to real wages in the Home country?
e) Suppose that Foreign has 3000 units of labor and 1500 units of capital (it is 10 times bigger than before). Will the pattern of trade change? Explain.
f) Numbers as in part e). Will the change in wages that followed trade liberalization in the Home country be bigger or smaller than in part d? Explain.