Question 2 Consider a society divided into two groups, the rich (r) and the poor (p) with respective utility functions up and up such that: ur(ty) = y(1 - t) - by up(t, y ) = ty where y is income generated (at a cost) by the rich and t is the tax rate. Most members of the society are poor. (a) Derive the income generated by the rich as a function of the tax rate. (b) What is the tax rate that would be set by the poor if y was constant? (c) Suppose that the tax rate is set by politicians competing for o ce in a democracy in which all citizens vote. Find the (Nash ) equilibrium { and 7