Consider a general model of Ricardian trade with 2 countries (Home and Foreign) and 2 goods (Clothing and Food): unit labor costs are aLC and aLF in Home anda ∗ LC and a ∗ LF in Foreign. Home and Foreign are endowed, respectively, with L and L ∗ units of labor. Workers in both countries have the same preferences represented by a Cobb-Douglas utility function:
U(DC, DF ) = (DC) α · (DF ) 1−α
where 1 > α > 01. Further, assume that Home has a comparative advantage in clothing: aLC/aLF < a∗ LC/a∗ LF .
1. Let Pt = PC/PF be the equilibrium relative price of clothing under free trade. What will be the range of possible prices for P T that will lead to complete specialization in both countries?
2. Find P t as a function of the parameters of the model (aLF , aLC, a∗ LF , a∗ LC, L, L∗ , α).
3. How will an increase in Home’s labor force (L) or an increase in Home’s productivity (a proportional decrease in aLC and aLF ) affect Pt ? Contrast the effects on Pt of a 1% increase in L with a 1% increase in productivity (aLC and aLF both decrease by 1%).
4. Write the relative wage w/w∗ as a function of the parameters of the model (substitute out the expression for Pt using your answer to 2).
5. How will the increase in Home’s labor force or its productivity affect the relative wage w/w*