Consider an economy with a single (representative) agent with utility function u(x, lc) = x1/5 4/5 and an endowment of 0 units of x and 10 units of time, which the agent can use as leisure (lc) or labor (L) (i.e., L + L = 10). The agent owns a firm that produces good x using L as an input, with technology of production given by x(L) = 3√L. Let the price of x be p = 1 and let w denote the price of time (i.e., the price of leisure and the wage). Find the competitive price of time w and the competitive allocation.
Consider an economy with a single (representative) agent with utility function u(x, lc) = x1/5 4/5 and an endowment of 0 units of x and 10 units of time, which the agent can use as leisure (lc) or labor (L) (i.e., L + L = 10). The agent owns a firm that produces good x using L as an input, with technology of production given by x(L) = 3√L. Let the price of x be p = 1 and let w denote the price of time (i.e., the price of leisure and the wage). Find the competitive price of time w and the competitive allocation.
Chapter1: Making Economics Decisions
Section: Chapter Questions
Problem 1QTC
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5. Consider an economy with a single (representative) agent with utility function u(x, lc) =
x¹/514/5 and an endowment of 0 units of x and 10 units of time, which the agent can use
as leisure (c) or labor (L) (i.e., L + lc = 10). The agent owns a firm that produces good
x using L as an input, with technology of production given by x(L) = 3√L. Let the price
of x be p = 1 and let w denote the price of time (i.e., the price of leisure and the wage).
Find the competitive price of time w and the competitive allocation.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F43a8b0b7-999e-4467-bace-5fb5d34f08e1%2F2751ca4d-e1a1-41af-8314-dfd20b7e1f6e%2Ffdla8hq_processed.jpeg&w=3840&q=75)
Transcribed Image Text:=
5. Consider an economy with a single (representative) agent with utility function u(x, lc) =
x¹/514/5 and an endowment of 0 units of x and 10 units of time, which the agent can use
as leisure (c) or labor (L) (i.e., L + lc = 10). The agent owns a firm that produces good
x using L as an input, with technology of production given by x(L) = 3√L. Let the price
of x be p = 1 and let w denote the price of time (i.e., the price of leisure and the wage).
Find the competitive price of time w and the competitive allocation.
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