# How many hours does he choose to work per day?

s utility for money income (M) and leisure (L) is U(M L) = M^1/3*L. There are Show more Labor Economics Mikes utility for money income (M) and leisure (L) is U(M L) = M^1/3*L. There are 16 hours in a day that can be dedicated to work or leisure. Mike earns \$12 per hour. Assume Mike has no unearned income. Given Mikes utility function it can be shown that his marginal utility of leisure is MUL = M^1/3 and his marginal utility of money income is MUM = L/(3M^2/3) . 1. What is Mikes marginal rate of substitution between leisure and money income (MRSLC)? 2. Assuming Mike is at an interior optimal point what is his optimal amount of money income and leisure per day? How many hours does he choose to work per day? 3. We can be sure that Mike does indeed choose to be at an interior point (that is working a positive amount and taking a positive amount of leisure) by comparing his utility at the interior optimal point with his utility at each corner point. What is Mikes utility at the interior optimal point in Part #2? What is his utility if he works all 16 hours a day (so that L = 0)? What is his utility if he does not work at all (so that L = 16)? As a result are we sure that Mike will choose an interior point? 4. Now suppose that Mikes wage increases to \$18 per hour. Now what is his optimal amount of money income and leisure per day? How many hours does he choose to work per day? When Mikes wage changes from \$12 to \$18 does the income or substitution effect dominate? 5. Continue to suppose that Mikes wage is \$18 per hour. Suppose that the government starts a welfare policy that pays \$B per day to non-workers (and pays \$0 per day to workers). At what value of B will Mike opt out of the labor force in order to go on welfare? (Hint: Mike ranks any two possible combinations of M and L by comparing the utility levels associated with each alternative). 6. (tough) Suppose the government sets B = 50. Will Mike work at \$18 per hour? Now what is the lowest wage that will induce Mike to go back into the labor market? (Hint: this is the wage at which if Mike works he gets the same utility as when he is on welfare.) Show less

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\$12