In a recent paper [3], Livingston analyzes the relationship between bond prices and market discount rates in a market with taxes, but which is otherwise frictionless. Two main cases are addressed. In the first, all investors are assumed to be in the same tax bracket and a relationship [17] is derived between the price of a bond, the rates of tax on income and capital gains, and the aftertax term structure. In a subsequent section, it is claimed that, when the assumption of a common tax bracket is removed, but maintaining the frictionless market assumption, the analysis is more or less unchanged:
”..there must still be a unique price of an annuity of maturity j and a unique price of a discount note of maturity j. There will be implicit tax rates in these annuities and discount notes for each maturity.… The bond pricing equation is the same except that TP and TG are replaced by TPj. and TGj., implicit marginal tax rates for each maturity” [3, p. 20].