In an economy, There are 600 consumers of Type A, with utility function UA(x1. x2) = x1x2 Each Type A consumer has income m A. There are 300 consumers of Type B, with utility function 1 3 U381, x2) = Zlogm) + Zlogbcz) Each Type B consumer has income m B. The prices of the two goods are pl, 112 > 0. ** Part a. (5 marks) Find the market demand curve, denoted by X1(p1, m A, m B). ** Part D. (5 marks) Does the distribution of income does/does not affect the market demand in this economy? If not, show a counterexample. Hint: to show that only the distribution of income matters, fix m A + m B = constant and see if X1 only depends on this constant