The nation of Ectenia has 20 competitive apple orchards, which sell apples at the world price of $2. The following equations describe the production function and the marginal product of labor in each orchard:
Q = 100L - L^2
MPL = 100 - 2L
where Q is the number of apples produced in a day, L is the number of workers, and MPL is the marginal product of labor.
a. What is each orchard's labor demand as a function of the daily wage W? What is the market's labor demand?
b. Ectenia has 200 workers who supply their labor inelastically. Solve for the wage W. How many workers does each orchard hire? How much profit does each orchard owner make?
c. Calculate what happens to the income of workers and orchard owners if the world price ofapples doubles to $4.
d. Now suppose the price of apples is back at $2, but a hurricane destroys half the orchards. Calculate how the hurricane affects the income of each worker and of each remaining orchard owner. What happens to the income of Ectenia as a whole?