Suppose workers have the utility function U(C,L) = C - (L^2)/2, where C is consumption and L is hours worked. The worker is choosing how many hours to work in a year. The wage rate is w=10 per hour. There is no non-labor income. a. Solve for the amount of labor that maximizes utility.

b. Now suppose there are two people in the country, Bernie and Hillary. Hillary's wage is wh=20, while Bernie's is wb=10. The government implements a tax and transfer scheme. Income is taxed at a flat 20% rate. The proceeds are used to fund an equal lump-sum transfer to Bernie and Hillary. For both Bernie and Hillary, find hours worked and taxable income.

c. What is the tax revenue of the government? What is the income of Hillary and Bernie after taxes and transfers? How was labor supply impacted?