A person chooses between leisure and consumption. All of their consumption comes from current...

Question

A person chooses between leisure and consumption. All of their consumption comes from current income. The utility derived from any combination of leisure and consumption is given by: u=YL-88Y

where u is utility, L is hours of leisure per week and Y is the number of dollars of income all of which will be spent on consumption. The person can work as many hours as they wish during the week at a constant wage of $4 per hour. There is no other source of income.

i. Identify the equation for this person's budget constraint.

ii. Draw this person's budget constraint (I will be able to do this with a confirmation on my answer for part i.)

iii. Draw on the same graph the indifference curves associated with u=6000, u=6400 and u=6800 (do I just plug in random points in the utility function above to find these indifference curves?)

iv. Find the utility maximizing combination of income and leisure. How many hours will this person work?

v. Imagine the wage rate increases to $8 per hour. Will this person work more hours?

David · Accepted Answer

A person chooses between leisure and consumption. All of their consumption comes from 
current income. The utility derived from any combination of leisure and consumption is given 
by: u=YL-88Y 
where u is utility, L is hours of leisure per week and Y is the number of dollars of income all of 
which will be spent on consumption. The person can work as many hours as they wish during the 
week at a constant wage of $4 per hour. There is no other source of income. 
i. Identify the equation for this person's budget constraint. 
Answer: 
Suppose total labor hours in a week are 120 (=24*5) 
A person’s consumption cannot be greater than his income in a given week. Therefore,

A person chooses between leisure and consumption. All of their consumption comes from current income. The utility derived from any combination of leisure and consumption is given by: u=YL-88Y where u...

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