A country produces two goods: Food ( F) and cloth ( C) . Given the information below, please answers questions a to e:
Food production function: = 2^0.5
Cloth production function: c = c^0.5
Total labor = + c = = 10
a. Find the marginal product of labor (MPL) for both products? Show that the MPL is diminishing.
b. Draw the production possibilities frontier (PPF). Find the formula of the PPF slope.
c. If the price of cloth unit Pc=$2 and the price of the food unit Pf=$4. Furthermore, assume that Lc=1 and Lf=9. Compare the wage in both industries ( Wf Vs Wc)? Given the above information, Which industry should worker choose? 2
d. Given the information in ( c ), compare the PPf slope to the budget line slope (-Pc/Pf). Show this in a graph.
e. If the price of cloth unit Pc=$12, price of food unit Pf=$6, show the number of workers in each industry such that the PPF is at the optimal point. That is the point at which workers are indifferent between both industries?