A country's farming sector has many small firms with very similar production and cost configurations (let us assume that they are identical). Each firm has a production function of qF, where q is the amount of food produced per year (in tons), K is physical capital (tractors, seeds, fertilizer, etc.) expressed in dollars, and L is the number of laborers.
a) What is the equation for the marginal product of labor? Is there diminishing marginal product of labor? How do you know?
b) Assume that a given firm begins with $10,000 in physical capital K. The price of labor (wages) is $40,000. The price of one ton of food is $2,000. How many laborers should the firm hire?
c) The firm calculates that in 2020 it wants to produce 3,200 tons of food. How much capital and how much labor should it use?
d) An analyst argues that the agricultural sector of the economy is not functioning properly because firms are producing more than the minimum efficient scale. She estimates the firm's short-run average cost curve to be: AC = 9,000 - 4q + 0.001q^2. What is the least-cost level of production?