1. In his influential work on the impact of taxes on labor supply, Jerry Hausman assumed desired (or optimal) annual hours followed this formula:

   H* =a(1-q)w+by.

   (Note: I am not going to make you derive this formulait comes from a somewhat complicated mathematical formula for the utility function, so just trust me that this is correct.) Assume a two-bracket tax on annual earned income: the first $15,000 of earnings are taxed at a 10% marginal rate, with earnings above $15,000 taxed at a 30% marginal rate. Unearned income is not taxed. Assume $1,000 of unearned income and a gross wage of $20/hour.

   1. Draw the annual budget constraint for an individual with these tax and economic parameters. Carefully label all points and slopes.

   2. Calculate and report the virtual income for each budget-set segment.

   3. Calculate the utility-maximizing hours of labor supplied and indicate where on the budget constraint you drew in part #a the person locates for each of the following individuals:

      1. An individual with a = 50 and b = -0.50 .

      2. An individual with a = 50 and b = -1.

      3. An individual with a = 100 and b = -0.10 .

      4. An individual with a = 50 and b = -0.10 .

   4. In an effort to cut taxes paid for lower-income individuals, the government decides to increase the size of the bottom tax bracket from $15,000 to $25,000. Draw the new annual budget constraint. Carefully label all points and slopes.

   5. For each of the individuals in part #c, describe theoretically the impact of the tax change in part #d on their labor supply.

   6. For each of the individuals in part #c, calculate how increase in the bracket in part #d changed their actual labor supply and indicate where on the budget constraint you drew in part #d the person now locates.