Question: clark gains utility from consumption c and leisure l and...
Clark gains utility from consumption c and leisure l and his preferences for consumption and leisure can be expressed as U(c, l) = 2(√ c)(l). This utility function implies that Clark’s marginal utility of leisure is 2√ c and his marginal utility of consumption is l √ c . He has 16 hours per day to allocate between leisure (l) and work (h). His hourly wage is $12 after taxes. Clark also receives a daily check of $30 from the government no matter how much he works.
1. Graph Clark’s budget constraint with leisure on the x-axis and consumption on the y-axis.
2. What is Clark’s marginal rate of substitution (MRS) when l = 3 and he is on his budget line?
3. At what wage rate would Clark be indifferent between working his first hour and being unemployed (his “reservation wage”)?
4. Find Clark’s optimal amount of consumption and leisure (the values that maximizes his utility).