24 1. (24 total points) Suppose there are two consumers, A and B, and two goods, X and Y. Their initial endowments of Good X and Good Y are: A: X =4; Y = 14 B: X = 12; Y = 2 Consumer A's utility function is given by: UA(X,Y) = X*Y', And consumer B's utility function is given by UB(X,Y) = X*Y. Therefore, consumer A's marginal utilities for each good are given by: MUx = Y' MUY = 3XY? Hero.com Also, consumer B's marginal utilities for each good are given by: MUx = Y MUy = X a) (8 points) Suppose the price of good Y is equal to one. Calculate the price of good X that will lead to a competitive equilibrium. Py = 1 WA = 4 A = MA = 8 MA = PX . X + By . y = 4Px + 14 4 Px W/ = 14 3MA = 12 MB= 12 Px +2 DA = APy DA + DB = WA + WE WX = 12 RIS stu DB = MB = 8 2 Px 4 Px+ 14 12 R* + 2 4 Px 21x - = 4+12 Me = 4 sharon 2 Py 4 Px + 14 + 24 Rx + 4 = 16 x 4/x 28Rx + 18= 64Px 18 = 36 PX MA = 4 Px + 14= 2+14=16 PX = 2 Me = 6+2 = 8