Home can produce machinery and flowers (in bundles of 1,000). The production functions of the two industries are
Qm = squareroot(K*Lm)
Qf = squareroot(T*Lf)
where K is capital, T is land, and L is labor. Consider goods prices PM = PF =1. Factor supply is Lm + Lf = 100 and T = K = 100.
Derive the marginal products of labor MPLm(K/Lm) and MPLf (T/Lf)
for the two industries.
Autarky wages. Graph the labor demand curves in the machinery and
flowers industries, and calculate the equilibrium wage rate in autarky.
Trade pattern. After opening up to free trade, Home faces a relative price of Pm/Pf = 2. How do the allocation of labor and wages change?
Production possibility frontier. Using the general labor demand relation-ships for the two industries, show that the production possibility frontier is
-MPLf/MPLm = -Pm/Pf in labor market equilibrium.
Gains from trade. Draw the production possibility frontier. How does the change in relative prices after trade affect production? Depict the gains from trade.