Consider individuals who have the following form for their utility function from leisure and consumption: U (c, 1) = A₁c¹10₂ where A, is an individual specific parameter. That is, each individual in the population is born with a different A₁. Let V be the non-labor income for the individual, let w and p be the hourly rate and the price of the consumption good respectively. Assume that an individual must sleep at least 7 hours a day, so the number of hours available for him/her is 24 - 7 = 17. Please complete the following questions: A. Derive the optimal number of leisure hours and the corresponding hours of labor supply. B. Discuss the impact that the non-labor income has on the labor supply of individuals. C. Suppose that there are two individuals, i and j, with the same 0₁, but with different 02, namely 8,2 and 02, with 0,2 0,2. How would the optimal behavior of the two individuals differ, if at all?

Microeconomic Theory
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Chapter16: Labor Markets
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Question 2-Labor Supply
(5,000 character limit on all answers combined)
Consider individuals who have the following form for their utility function from leisure and
consumption:
U (c, 1) = A₁c110₂,
where A, is an individual specific parameter. That is, each individual in the population is
born with a different A₁.
Let V be the non-labor income for the individual, let w and p be the hourly rate and the
price of the consumption good respectively. Assume that an individual must sleep at least 7
hours a day, so the number of hours available for him/her is 24 - 7 = 17.
Please complete the following questions:
A. Derive the optimal number of leisure hours and the corresponding hours of labor supply.
B. Discuss the impact that the non-labor income has on the labor supply of individuals.
C. Suppose that there are two individuals, i and j, with the same 0₁, but with different
02, namely 0,2 and 02, with 02 > 2. How would the optimal behavior of the two
individuals differ, if at all?
D. Suppose now that individuals with larger A, also have higher ability A₁. How would
your answer to question C change, if at all, if the two individuals ended up getting the
same level of schooling? Discuss.
2
E. Suppose that the individuals from C are also exposed to two levels of hourly rate, wi,
and w,, with w, > w,, How would your answer to C change, if at all. Explain.
Transcribed Image Text:Question 2-Labor Supply (5,000 character limit on all answers combined) Consider individuals who have the following form for their utility function from leisure and consumption: U (c, 1) = A₁c110₂, where A, is an individual specific parameter. That is, each individual in the population is born with a different A₁. Let V be the non-labor income for the individual, let w and p be the hourly rate and the price of the consumption good respectively. Assume that an individual must sleep at least 7 hours a day, so the number of hours available for him/her is 24 - 7 = 17. Please complete the following questions: A. Derive the optimal number of leisure hours and the corresponding hours of labor supply. B. Discuss the impact that the non-labor income has on the labor supply of individuals. C. Suppose that there are two individuals, i and j, with the same 0₁, but with different 02, namely 0,2 and 02, with 02 > 2. How would the optimal behavior of the two individuals differ, if at all? D. Suppose now that individuals with larger A, also have higher ability A₁. How would your answer to question C change, if at all, if the two individuals ended up getting the same level of schooling? Discuss. 2 E. Suppose that the individuals from C are also exposed to two levels of hourly rate, wi, and w,, with w, > w,, How would your answer to C change, if at all. Explain.
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