Let us denote John's daily hours of work by H, and his hours of leisure by N = 24 - H. Suppose that John's only source of income is wages for hours worked. He derives utility from leisure, N, and from the consumption of a composite good, Y. The price of Y is 1. John's utility function is U(Y, N) = In(Y) + In(N). (a) Suppose the wage rate is $30 per hour. Write down John's constraint with Y and N as the choice variables. (b) Continue to assume that the wage rate is $30. How many hours will he choose to work? How many units of Y will he consume? (c) Suppose the wage rate decreases to $10 per hour. How many hours will he choose to work? How many units of Y will he consume? (d) Continue to assume that the wage rate is $10, but now assume that John also receives non-labour income T. What should T be so that John would consumes half as many units of Y as in part (b)?
Let us denote John's daily hours of work by H, and his hours of leisure by N = 24 - H. Suppose that John's only source of income is wages for hours worked. He derives utility from leisure, N, and from the consumption of a composite good, Y. The price of Y is 1. John's utility function is U(Y, N) = In(Y) + In(N). (a) Suppose the wage rate is $30 per hour. Write down John's constraint with Y and N as the choice variables. (b) Continue to assume that the wage rate is $30. How many hours will he choose to work? How many units of Y will he consume? (c) Suppose the wage rate decreases to $10 per hour. How many hours will he choose to work? How many units of Y will he consume? (d) Continue to assume that the wage rate is $10, but now assume that John also receives non-labour income T. What should T be so that John would consumes half as many units of Y as in part (b)?
Chapter6: Demand Relationships Among Goods
Section: Chapter Questions
Problem 6.9P
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just a b and c please thank you!
![Let us denote John's daily hours of work by H, and his hours of leisure by N = 24 – H. Suppose that John's
only source of income is wages for hours worked. He derives utility from leisure, N, and from the
consumption of a composite good, Y. The price of Y is 1. John's utility function is
U(Y, N) = In(Y) + In(N).
(a) Suppose the wage rate is $30 per hour. Write down John's constraint with Y and N as the choice
variables.
(b) Continue to assume that the wage rate is $30. How many hours will he choose to work? How many
units of Y will he consume?
(c) Suppose the wage rate decreases to $10 per hour. How many hours will he choose to work? How
many units of Y will he consume?
(d) Continue to assume that the wage rate is $10, but now assume that John also receives non-labour
income T. What should T be so that John would consumes half as many units of Y as in part (b)?](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F36c16d30-8080-41a6-9b28-34917665af49%2F10da053b-9633-486e-b7c6-345f5a0a28f9%2Frcprby_processed.png&w=3840&q=75)
Transcribed Image Text:Let us denote John's daily hours of work by H, and his hours of leisure by N = 24 – H. Suppose that John's
only source of income is wages for hours worked. He derives utility from leisure, N, and from the
consumption of a composite good, Y. The price of Y is 1. John's utility function is
U(Y, N) = In(Y) + In(N).
(a) Suppose the wage rate is $30 per hour. Write down John's constraint with Y and N as the choice
variables.
(b) Continue to assume that the wage rate is $30. How many hours will he choose to work? How many
units of Y will he consume?
(c) Suppose the wage rate decreases to $10 per hour. How many hours will he choose to work? How
many units of Y will he consume?
(d) Continue to assume that the wage rate is $10, but now assume that John also receives non-labour
income T. What should T be so that John would consumes half as many units of Y as in part (b)?
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