. Consider the specific-factors model (2 goods, 3 factors, where labor is the flexible factor) for a given country with the following Cobb-Douglas production technologies:
QC = ZCK0.5L 0.5 C (clothing, produced with capital and labor)
QF = ZF T 0.5L 0.5 F (food, produced with land and labor)
where ZC and ZF are the productivities in both sectors and L = LC + LF is the aggregate endowment of labor. K and T are the aggregate endowments of capital and land in the economy.
(a) Derive the equation of the relative supply curve for this economy (QC/QF as a function of the relative price PC/PF ). What can you say about the shape of the relative supply curve?
(b) Assume that this country opens up to trade at fixed world prices P T C = 1 and P T F = 1 (the country is small relative to its trading partners). Further assume that all consumers in this country have Leontief preferences over food and clothing— one unit of food is consumed with every unit of clothing. How will the country’s pattern of trade (which good will be exported or imported) depend on the parameters of the model (K, L, T, ZC, ZF )? How does the size of the labor force L affect the pattern of trade?
(c) (Bonus question) How will an increase in productivity in the clothing sector (an increase in ZC) affect the welfare of all 3 factor owners? Contrast your response with the welfare change induced by an increase in the aggregate capital endowment K.