= 4. (30 points) In an economy with two agents and two goods, the utility functions are given by UA (21, 22) = x1 + 02 UB(21,22) = max(221, 22) (a) Compute the demand functions of these two agents, as a function of price p ER} - {0} and initial endowment WER. (b) Draw the offer curves of these two agents, given the initial endowments wA = (0,4), WB (6,2). (c) In an Edgeworth box, sketch the set of Pareto optimal allocations. (d) In an Edgeworth box, sketch the core. (e) Does the competitive equilibrium exist? If yes, find all competitive equilibria. If not, give a reason for this nonexistence. In addition, why can't we apply the existence theorem into this case? = 4. (30 points) In an economy with two agents and two goods, the utility functions are given by UA (21, 22) = x1 + 02 UB(21,22) = max(221, 22) (a) Compute the demand functions of these two agents, as a function of price p ER} - {0} and initial endowment WER. (b) Draw the offer curves of these two agents, given the initial endowments wA = (0,4), WB (6,2). (c) In an Edgeworth box, sketch the set of Pareto optimal allocations. (d) In an Edgeworth box, sketch the core. (e) Does the competitive equilibrium exist? If yes, find all competitive equilibria. If not, give a reason for this nonexistence. In addition, why can't we apply the existence theorem into this case