A farmer uses land and labor to grow soybeans. He has the following production function Q = 126.2 A0.6 L0.4 where Q is the amount of soybeans in bushels, A is land in acres and L is number of farm hands.
(a) If this farmer has 100 acres of land, how many farm workers must he employ in order to produce 10,000 bushels of soybeans? What is the marginal product of labor at this level of employment?
(b) Assume this farmer pays each farm worker $1,000 over the growing season and spends $2,000 for seed and fertilizer. If the price of soybeans is $14.75 a bushel, what is the farmer's profit?
(c) Is this farmer paying his workers the value of their marginal product?
(d) If this farmer doubles the amount of land and labor, how many bushels of soybeans he can produce?