Texts: Production functions: QM(K, LM) = K^(1/3)L^(2/3) for manufacturing, and QA(T, LA) = T^(1/3)L^(2/3) for agriculture.
1) Determine the relative supply of the economy (Hint: Set M = QM(K, LM) and A = QA(T, LA); relative prices must be a function of M/A).
2) Consumers have Cobb-Douglas preferences with utility U(M, A) = M^(1/2)A^(1/2). Show relative demand is given by PM/PA = A/M.
3) Using the relative demand and relative supply calculated previously, find the equilibrium relative price and relative quantity. (Hint: both must be a function of the exogenous variables in the model, such as factor endowment).