The nation of Ectenia has 20 competitive appleorchards, all of which sell apples at the world priceof $2 per apple. The following equations describethe production function and the marginal product oflabor in each orchard:100100 2 ,2 5 25 2Q L LMPL Lwhere Q is the number of apples produced in a day,L is the number of workers, and MPL is the marginalproduct of labor.a. What is each orchard’s labor demand as a functionof the daily wage W? What is the market’s labordemand?b. Ectenia has 200 workers who supply their laborinelastically. Solve for the wage W. How manyworkers does each orchard hire? How much profitdoes each orchard owner make?c. Calculate what happens to the income of workersand orchard owners if the world price doubles to$4 per apple.d. Now suppose that the price is back at $2 perapple but a hurricane destroys half the orchards.Calculate how the hurricane affects the income ofeach worker and of each remaining orchard owner.What happens to the income of Ectenia as a whole?
The nation of Ectenia has 20 competitive apple
orchards, all of 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:
100
100 2 ,
2 5 2
5 2
Q L L
MPL L
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 doubles to
$4 per apple.
d. Now suppose that the price is back at $2 per
apple 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?
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