Consider Diane's optimal labor and leisure decision. She earns a wage of $10 an hour and is able to work 180 hours a month. In order to work, she must pay $3 in childcare costs for every hour worked. Diane has a utility function over consumption spending and leisure equal to (, ) = 10 1/2 + Where is dollars of consumption and is hours of leisure.

Now suppose that Diane's income is subject to a flat tax of 10% and that child care expenses are not tax deductible.

A. Update Diane's budget constraint to reflect the 10% tax on income.

B. Determine Diane's optimal choice of leisure, consumption and labor under the tax.

C. How does Diane's supply of labor change in response to the tax? What does this imply about the relative strengths of the income and substitution effects for Diane?

D. How much tax does the government collect from Diane?