Take the median voter model, in which the net income of an individual (after tax and redistribution) is (1 - t)y_i + f, where y_i is the income of individual i, t is the tax rate, and f is a lumpsum transfer financed by taxation. Assume that the distortionary cost of taxation is b¹/2 t²y,

where y is average income. The government budget constraint is thus (t-b¹/₂t²)y = f. Assume average income is equal to 20 and median income is equal to 15. Calculate the equilibrium tax rate under democracy as a function of b. What is the equilibrium tax rate if b = 1, b 1.5, b = 2, b.5? Explain your results. How does the equilibrium tax rate vary as b increases? Why?