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
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?