5. [24 marks] Robert's pre-tax income is $90,000. According to the income tax system, the first $30,000 of income is taxed at 10%, income between $30,000 and $60,000 is taxed at 20%, and income above $60,000 is taxed at 40%. a. [4 marks ] Draw a diagram accurately showing the average and marginal tax rates for incomes between 0 and $120,000. b. [4 marks] Calculate what taxes Robert legally owes. c. [4 marks] Assuming that Robert can hide some of his income, find and draw his marginal benefit of hiding income, with 'unreported income' (U) on the horizontal axis. d. [6 marks] There is a p=10% chance that the government will find out the amount of income Robert does not report. If he is caught, Robert faces a fine formula for unreported income, F=25(U/1000)2 (Which means the marginal fine is MF=0.00005U). Using the fact that the MC=pMF, find Robert's choice of unreported income and show this on a diagram. How much he will owe the government if he is caught? e. [6 marks] Now suppose Robert 'feels bad' when he does not report some of his income. Specifically, MC=pMF+h, where h is the honesty-cost per dollar of U. If h=0.15, how much will U be now? How high must h be for U=0 ? Explain. 5. [24 marks] Robert's pre-tax income is $90,000. According to the income tax system, the first $30,000 of income is taxed at 10%, income between $30,000 and $60,000 is taxed at 20%, and income above $60,000 is taxed at 40%. a. [4 marks ] Draw a diagram accurately showing the average and marginal tax rates for incomes between 0 and $120,000. b. [4 marks] Calculate what taxes Robert legally owes. c. [4 marks] Assuming that Robert can hide some of his income, find and draw his marginal benefit of hiding income, with 'unreported income' (U) on the horizontal axis. d. [6 marks] There is a p=10% chance that the government will find out the amount of income Robert does not report. If he is caught, Robert faces a fine formula for unreported income, F=25(U/1000)2 (Which means the marginal fine is MF=0.00005U). Using the fact that the MC=pMF, find Robert's choice of unreported income and show this on a diagram. How much he will owe the government if he is caught? e. [6 marks] Now suppose Robert 'feels bad' when he does not report some of his income. Specifically, MC=pMF+h, where h is the honesty-cost per dollar of U. If h=0.15, how much will U be now? How high must h be for U=0 ? Explain