Solve each of the following q's:

Consider a 2 person/2 good exchange economy with consumer Ann (A) having a utility function defined as uA (x4, y4) := ryd and endowments (wx , wa) := (30,90) and consumer Bob (B) having a utility function defined as ub(xB, yB) := (xB)4(y) and endowments (wp, wp ) := (90, 30). (a) [14/32 ~ 4.38 marks] Assume p, = 1. Find the competitive equilibrium price pi and quantities (x4*, y4*), (aB*,y*). Show your work. (b) [8/32 ~ 2.5 marks] Find all allocations (x4, y4), (x, y) that are Pareto Efficient. Show your work. (c) [6/32 ~ 1.88 marks] Carefully draw the Edgeworth Box with Ann's origin in the lower-left and Bob's origin in the upper-right. Label the endowment point and the equilibrium derived in (a), in particular draw the budget line and mark the equilibrium quantities on Ann's axes and on Bob's axes. Draw two indifference curves for each trader, one through the endowment and one through the equilibrium quantities. (d) [4/32 ~ 1.25 marks] Does there exist an allocation that is a Pareto im- provement over the competitive equilibrium allocation? Explain your