Suppose a person's utility for leisure (L) and consumption (Y) can be expressed as U = Y + L0.5. Show what happens to the person's labor supply curve when the income tax is cut from 70 percent to 30 percent. Denote hours worked as H and wage per hour as w
What will be an ideal response?
Let t = income tax rate. Since Y = net income, U = w(1 - t)H + (24 - H)0.5. Maximizing utility with respect to hours worked, H, yields H = 24 - (2(1 - t)w)-2. Any decrease in t would increase the number of hours worked. Note: This person is a workaholic. Even at a net wage of $1, this person only relaxes for 3/4 of an hour!
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