Consider an economy that produces food and cloth. Food is produced using land and labor. Cloth is produced using capital and labor. In other words, land is a factor that is specific to the food sector, capital is specific to the cloth sector, and labor is mobile between the two sectors. This means that the wage paid to labor in both sectors is equalized.

Suppose the marginal product of labor in the food sector is given by MPLF = 100 – LF, where LF is the number of workers in the food sector, and the marginal product of labor in the cloth sector is given by MPLC = 80 – LC, where LC is the number of workers in the cloth sector.

Suppose that there are 100 workers in the economy.

(i) Initially, the world price of food and the world price of cloth are both $1 per unit. Find the equilibrium allocation of labor to each sector, the quantity of each good produced in this economy, and the wage.

(ii) Now, suppose the world price of cloth increases to $3 per unit, while the world price of food stays constant. Repeat the analysis of part (i).

(iii) Derive budget lines for workers, capital owners, and land owners, before and after the change. Who benefits from this change? Who is hurt? Is there any group for which you cannot tell?