Suppose the only financial instruments available in Minneapolis are a taxable Federal Treasury Bill (T-Bill) and a municipal bond from the city of Minneapolis. The municipal bond is tax exempt. Assume both the municipal bond and the taxable bond are risk free, i.e. there is no chance of default for each.
A. The before-tax rate of return on the T-Bill is 3 percent, while the municipal bond returns 2.5 percent. Minnesota taxes all eligible interest income at a rate of 15% percent. What fraction of his wealth, w, will the investor invest in the municipal bond? Why?
B. Now, the before-tax rate of return on the T-Bill is 5 percent. The state taxes all eligible interest income at a rate of 10 percent. The municipal bond has a rate of return of r percent. What should the City of Minneapolis set r equal to so that investors are indifferent between investing in the taxable bond and investing in the municipal bond?
C. Now, the before-tax rate of return on the T-Bill is r percent, where 0 ≤ r ≤ 1. Tax on all eligible interest income is levied at a rate of t percent, 0 ≤ t ≤ 1. The municipal bond provides the investor a rate of return rm percent, 0 ≤ rm ≤ 1. Suppose investors are indifferent between investing in the T-Bills and investing in the municipal bond. Write an equation that describes the relationship between r, t, and rm.
D. Call G = (t, rm) a goverment policy. Given r, illustrate in a graph that has rm on the vertical axis and t in the horizontal axis the collection of all government policies that leave the investor indifferent between investing in the two types of bonds.