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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?
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In addition to price-weighted and value-weighted indexes, an equally weighted index is one in which the index value is computed from the average rate of return of the stocks comprising the index.
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When a firm has risky debt, its equity can be viewed as an option on the total value of the firm with an exercise price equal to the face value of the debt.
Select a random sample of size 50 from the given 1000 cases. You will use this sample data to complete tasks 2 to 6. Explain how you obtained your sample in the appendix and provide a list of your customer data.
A bond was issued 2 years ago. It's original maturity was 20 years. The coupon rate is 4% and the current YTM is 6%. Compute its intrinsic value.
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