+1 862 207 3288 1) Thoreau has preferences for consumption goods (C) and time spent
on leisure (L). The utility function is u(C, L) = CL. The household
also has a home production technology summarized by a production
function. The production function
√ produces consumption goods with
labor (l) according to f (l) = 100 l. Time spent on leisure and labor
adds up to 24, L + l = 24.
a) How much time will Thoreau spend in leisure? How many units
of consumption good will he produce?
b) Using the production function from part a), what is the marginal
product of labor at the amount of labor in part a)?
c) Now suppose that
√ there is a competitive firm with the production
function f (l) = 100 l. The wage (w) is equal to the marginal product
of labor from part b) and the price of output is 1. What is the profit
maximizing demand for labor and amount of output? What is the
profit?
d) Let π be the profit from part c. Prices are also the same as in
part c). Now suppose that Thoreau has decided to rejoin civilization.
√
He now owns a firm with the production function f (l) = 100 l and
receives its profits. He can also provides some of his time to labor
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STEVEN STONG
markets. His budget constraint is C + wL = 24w + π. How much
leisure time and consumption goods will he provide.
e) Now consider an economy that consist of 10 consumers that are
identical to Thoreau who each own one firm like Thoreau’s firm. Prices
are the same as in part c). Show that both the labor market and the
consumption good market clear at these prices. That is the sum of
demand for leisure time from the consumers and demand for labor time
from the firms equals the total hours which is 240. And the supply and
demand for consumption goods are equal.
