The nation of Ectenia has 80 competitive apple orchards, which sell apples at the world price of $2 per apple. The following equations describe the production function and the marginal product of labor in each orchard:
$Q = 80L - L^2$
$MPL = 80 - 2L$
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.
Now, suppose the price of apples is back at $2 per apple, but a hurricane destroys half the orchards so only 40 orchards remain. Recall that each orchard's labor demand as a function of the daily wage is $L = 40 - 0.25W$.
What is the market's labor demand?
$L = 1,600 - 20W$
$L = 1,600 - 10W$
$L = 40 - 0.25W$
$L = 80 - 20W$
Ectenia continues to have 1,200 workers who supply their labor inelastically.
The equilibrium wage is now $\$$ per worker per day. Each orchard hires workers and makes a profit of $\$$ per day. (Note: Assume that wages are the firm's only costs.)
Total income in the country (defined as workers' income plus orchards' profit) was equal to $156,000 before the crop destruction.
True or False: Total income of Ectenia rose as a result of the crop destruction.
True
False
