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4. Consider an economy with two consumers, A and 8. They consume two goods, X1 and X1. Both consumers have identical utility functions over the two goods given by the Cobb glas function xi? 3'23 UA(x1,x2) = UB(x1,x2) =X1xZ, MRSA = xA, MRSB =xB. 1 1 Their initial endowments of the two goods are w'\" = (4,0) and w3 = (0,4); i.e., A has 4 units of good 1 and none of good 2. while B has 4 units of good 2 but none of good 1. Thus. there is a total of 4 units of each good in this economy. This means that if A receives (xix?) in an allocation, feasibility requires that B's allocation (xf, x23) must be such that xf=4xf, x=4x'. 'age 2 of 5 a) Suppose (xfc', x5\") represents an allocation of the two goods to consumer A that is efcient. write down the equation that (xf.x') must satisfy. Let :31 represent the price of good 1 and p: be the price of good 2. b) At p1 = $2.13: = $1. what is each consumer's income? Denote by M"1 and M\". c) Write down the equation of the budget-line for each consumer. d) What is consumer A's demand for each good? Denote by (xf'.x\")? e) What is consumer A's excess demand for each good? f) What is consumer B's demand for each good? Denote by (x131 xf")? Q) What is consumer B's excess demand for each good? h) What is the aggregate excess demand for each good at the given prices? i) Are p1 = $2,192 = $1 equilibrium prices? What must happen to price for aggregate excess demand of all goods to be zero. j) What is the Walrasian equilibrium price for good 1. p5? Assume that p5 = $1. k) Does the Walrasian equilibrium allocation satisfy the equation for efciency obtained in part a)