Suppose there are 100 units of good x and 50 units of good y in an exchange economy with 2 people.
Suppose consumer 1 has a utility function u1(x1,y1)= x1y1 and consumer 2 has a utility function of u2(x2,y2)= √x2y2
Answer with "yes" or "no." Is the allocation where each consumer receives half of good x and half of good y Pareto efficient?
Consider the given problem here there two individual agents having utility function “U1 = X1*Y1” and “U2 = X2^1/2*Y2”.
The MRS of two individual agents are given below.
=> MRS1 = MUx1/MUy1 = Y1/X1, => MRS1 = Y1/X1, for individual 1.
=> MRS2 = MUx2/MUy2 = [0.5*Y2*X2^-0.5]/X2^0.5 = [0.5*Y2]/X2 = Y2/2X2.
=> MRS2 = Y2/2X2.
If each consumer receives half of “good X” and “good Y” then “X1 = X2 = 50 units” and “Y1 = Y2 = 25 units”. At the pareto efficient allocation the MRS of both individual should be equal.
=> MRS1 = MRS2. Here given the information the vale MRS are given below.
=> MRS1 = Y1/X1 = 25/50 = ½.
=> MRS2 = Y2/2X2 = 25/2*50 = 25/100 = ¼. So, here MRS1 > MRS2, => the given allocation is not pareto efficient.
Suppose there are 100 units of good x and 50 units of good y in an...