There are 8760 hours in a (non-) leap year. Assume that a typical upper middle income worker earns $80 per hour and has no other source of income. The worker can use his income to purchase a consumption good priced at $1 per unit. a) Illustrate the budget set of a typical upper middle income worker. Suppose that the government levies a Social Security tax on wage income. The tax is levied only on the first $100,000 of income. The marginal tax rate is 10% so the worker pays $.10 on every dollar earned up to 100,000. There are no taxes levied on income earned over $100,000. b) In your diagram illustrate the effect of the tax system on the worker's budget set. Given the wage rate and the tax system the typical worker chooses to work 40 hours per week for 50 weeks in the year for a total of 2000 hours per year. You may assume that leisure and consumption goods are not perfect complements. c) How much does the typical worker pay in taxes? How much does he earn after taxes? What is his MRS at his best bundle? The government proposes to change the tax code. The government will lower the marginal tax rate to 6.25% (.0625). Simultaneously the government will tax every dollar earned (including income earned above $100,000). In other words, the worker will pay $.0625 in taxes on every dollar earned. d) Show algebraically that the bundle chosen by the worker under the old tax scheme is still available under the new tax scheme. Illustrate the new budget line in your diagram in part (a). Will the new tax scheme encourage or discourage more work? Briefly explain your answer. Will the new tax scheme raise more money, less money or do you need more information to answer this question? Briefly explain your answer. Bonus: On HW 3 you calculated the Marshallian and Hicksian demand functions for the utility function U(x,y) = xy. Use these demand functions to verify that the Slutsky equation holds for own price derivative of the x good i.e. verify that dx" = ax" -x * dx"