Tony Taxpayer earns $2000 in income. Income is taxed at 20%. Tony can underreport his income to the IRS and pay taxes only on the amount he reports, but should he be audited, the IRS will impose a surcharge of 200% on his unpaid taxes; that is, Tony will have to pay 60% of any unreported income if he is audited. He realizes that the probability of being audited is .25. Tony’s von Neumann-Morgenstern utility index is
U = ln Y.
(a) On a graph showing income if he is audited on the horizontal axis and income if he is not audited on the vertical axis, show Tony’s bundle of contingent claims if he reports all income, his bundle of contingent claims if he reports no income, and his budget constraint. Find the equation of Tony’s budget constraint for contingent claims to income if he is audited and income if he is not audited. Over what range of contingent claims does this equation describe his options? What is the slope of the budget constraint? Give an economic interpretation of the value of the slope.
(b) Calculate Tony’s optimal bundle of contingent claims. How much income will he report to the IRS? How much will he not report?
(c) Suppose the IRS increases the penalty for underreporting income. How will this affect Tony’s budget line? How will he adjust his bundle of contingent claims and the amount of income he reports to the government?