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4. (16 marks) Consider a municipality composed of identical households who earn income i and have utility given by u(x, y) = xy where x is composite private good expenditure and y is local public good expenditure. The local public good is provided by the municipality and financed by an income tax such that the municipality's revenue per household is given by: r (t ) = it (6 - t)its8 where t E [0,1] is the tax rate, 6 6 (0,1] is the tax rate at and beyond which the representative household is induced to flee the municipality and e > 0 is a parameter representing the distortionary effect of taxation. The municipality is benevolent in the sense that it seeks to maximize a representative household's utility a. Determine the values of t s 6 for which no revenue is raised. Derive the revenue- maximizing tax rate to and verify that to