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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 the hours of leisure per week and Yis 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 persons budget constraint with income as function of leisure. ii. Using graph paper or a computer, draw this persons budget constraint. iii. Draw on the same graph the indifferences curves associated with u 6000, u-6400 and -6800. iv. By trial and error (or other means) find the utility maximizing combination of income and leisure. How many hours will this person work? Explain. v. Imagine the wage rate increases to $8 per hour. Will this person work more hours? (Hint: repeat the earlier steps doubling both the wage and the three utility levels for the indifference curves.)
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