1. Consider a static labour supply model for an individual. Assume that the person works a positive number of hours. Assume that the utility function is of the following form: U=x0.5 +8(T-h)(0.5) where x is consumption and his hours of work, and 8 is a parameter of the utility function. The person is paid a wage of w for each hour worked. The person has no other source of income other than employment earnings.
1. Consider a static labour supply model for an individual. Assume that the person works a positive number of hours. Assume that the utility function is of the following form: U=x0.5 +8(T-h)(0.5) where x is consumption and his hours of work, and 8 is a parameter of the utility function. The person is paid a wage of w for each hour worked. The person has no other source of income other than employment earnings.
Chapter9: Production Functions
Section: Chapter Questions
Problem 9.3P
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![1. Consider a static labour supply model for an individual. Assume that the person
works a positive number of hours. Assume that the utility function is of the following
form: U=x0.5 +8(T-h)(0.5) where x is consumption and his hours of work, and 8 is a
parameter of the utility function. The person is paid a wage of w for each hour
worked. The person has no other source of income other than employment earnings.
Assume that the price of x equals 1.
a) Specify the utility maximization problem, write down the Lagrange function, and
solve for the first order conditions.
b) Solve for the MRS condition between consumption and hours of work.
c) Assume that 8=2 if the person has a child living at home, and 8=1 otherwise.
Explain (and either show mathematically or graphically) how this will affect the
optimal number of hours of work of the person.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F1652026a-6ba6-42d7-9e35-ad3e7516e1ec%2Fd214fb5f-7ad7-4672-b9fb-4a53095827c5%2Fkb7890s_processed.png&w=3840&q=75)
Transcribed Image Text:1. Consider a static labour supply model for an individual. Assume that the person
works a positive number of hours. Assume that the utility function is of the following
form: U=x0.5 +8(T-h)(0.5) where x is consumption and his hours of work, and 8 is a
parameter of the utility function. The person is paid a wage of w for each hour
worked. The person has no other source of income other than employment earnings.
Assume that the price of x equals 1.
a) Specify the utility maximization problem, write down the Lagrange function, and
solve for the first order conditions.
b) Solve for the MRS condition between consumption and hours of work.
c) Assume that 8=2 if the person has a child living at home, and 8=1 otherwise.
Explain (and either show mathematically or graphically) how this will affect the
optimal number of hours of work of the person.
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