Suppose marginal utility from consumption is given by 1.2e0.4/(c0.7) and marginal utility from leisure is given by 1.6c0.3/(e0.6) and that an individual can work up to 20 hours per day at a wage of $19 per hour. A. What must be true about the wage in order for a given worker to be a participant? Give the mathematical condition which expresses this. Now write the two mathematical conditions which a participant's optimal choice must satisfy (write them in terms of c and e rather than Y and e). B. Write the mathematical formula for this worker's marginal rate of substitution between leisure and labour. For this utility function, write the reservation wage as a function in terms of non-labour income YN and time available T. If Yn=$245 then WR= . In this case will the individual choose to work? (Enter "1" for yes, "-1" for no. Enter "0" if the individual is indifferent.) If YN=$723 then WR= . In this case will the individual choose to work? (Enter "1" for yes, "-1" for no. Enter "0" if the individual is indifferent.) C. Suppose YN=$5957. Write the formula for this individual's potential income constraint. This individual will choose to work hours. So they will have hours of leisure and spend $ on consumption. D. Suppose YN=$30. Write the formula for this individual's potential income constraint. This individual will choose to work on consumption. hours, So they will have hours of leisure and spend $
Suppose marginal utility from consumption is given by 1.2e0.4/(c0.7) and marginal utility from leisure is given by 1.6c0.3/(e0.6) and that an individual can work up to 20 hours per day at a wage of $19 per hour. A. What must be true about the wage in order for a given worker to be a participant? Give the mathematical condition which expresses this. Now write the two mathematical conditions which a participant's optimal choice must satisfy (write them in terms of c and e rather than Y and e). B. Write the mathematical formula for this worker's marginal rate of substitution between leisure and labour. For this utility function, write the reservation wage as a function in terms of non-labour income YN and time available T. If Yn=$245 then WR= . In this case will the individual choose to work? (Enter "1" for yes, "-1" for no. Enter "0" if the individual is indifferent.) If YN=$723 then WR= . In this case will the individual choose to work? (Enter "1" for yes, "-1" for no. Enter "0" if the individual is indifferent.) C. Suppose YN=$5957. Write the formula for this individual's potential income constraint. This individual will choose to work hours. So they will have hours of leisure and spend $ on consumption. D. Suppose YN=$30. Write the formula for this individual's potential income constraint. This individual will choose to work on consumption. hours, So they will have hours of leisure and spend $
Chapter16: Labor Markets
Section: Chapter Questions
Problem 16.10P
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Transcribed Image Text:Suppose marginal utility from consumption is given by 1.280.4/(c0.7) and marginal utility from leisure is given by 1.6c0.3/(e0.6) and that an individual can work up to 20
hours per day at a wage of $19 per hour.
A. What must be true about the wage in order for a given worker to be a participant? Give the mathematical condition which expresses this. Now write the two
mathematical conditions which a participant's optimal choice must satisfy (write them in terms of c and & rather than Y and e).
B. Write the mathematical formula for this worker's marginal rate of substitution between leisure and labour. For this utility function, write the reservation wage as
a function in terms of non-labour income YN and time available T. If YN=$245 then WR=
. In this case will the individual choose to work?
(Enter "1" for yes, "-1" for no. Enter "0" if the individual is indifferent.) If YN=$723 then WR=
In this case
will the individual choose to work?
(Enter "1" for yes, "-1" for no. Enter "0" if the individual is indifferent.)
C. Suppose YN=$5957. Write the formula for this individual's potential income constraint. This individual will choose to work
they will have
hours. So
hours of leisure and spend $
on consumption.
D. Suppose YN=$30. Write the formula for this individual's potential income constraint. This individual will choose to work
hours. So
they will have
hours of leisure and spend $
on consumption.
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