Assume that a country is endowed with equal amounts of capital (K) and land (T). The two goods in this economy are x-ray machines (X) and yucca (Y). Prices are P_x=P_y=$8 and the country's total labor force is L=L_x+ L_y. Labor is fully mobile between the two sectors. K is specific to the x-ray sector and T is specific to the yucca sector. Marginal products are given

MP_L^X= 2K/L_xand MP_L^Y₌T/L_y. MP_K^X=L_x/K and MP_T^Y=L_y/4T.

1. Draw a graph to illustrate the allocation of labor in equilibrium. Your graph should have two vertical axes, one representing price of labor in the yucca sector and the other representing price of labor in the x-ray machine sector.
2. How is labor distributed between the x-ray and yucca sectors in equilibrium?
3. Now assume, the prices of both x-rays and yucca suddenly decrease by 50%. What is the new labor distribution?
4. Has output of x-rays and yucca changed?