Question

1 Suppose that a consumer has a utility function u(x1, x2) = x2xı. He originally faces prices (1, 2) and has income 100. Then the price of good 1 increases to 2. What are the compensating and equivalent variations? O A 100V4 - 100; 100 - 502 B 100/4 - 100; 100 - 5072 100V4 - 100; 100 - 502 OD 100V4 - 100; 100 – 50/2

Answer 1

ANSWER ; A

Utility function; U (2, 3) = 1,442 P=1 M=100 P,'=2 P2=2 The MRS will be :- U= n5a2 MRS=512 222 At optimal level; 212= P = 1 P2 2 7 x, = 4x2 The budget constraint: 7, +212 = 100 4x2+2x2 = 100 [2 = 16.671 x = 4(16.67) 1x = 66.68 .. Utility will be: U = 66.68 | 16.67 U=272.25 Now, puice of good I changes : P,' = 2 The MRS will be : 222 ?, At optimal level; 222 = 2 2 O => 1 = 2x2

( Though the prices changed, the utility for both the goods will remain same: 272.25=1,552 Putting 272.25=2*2542 272.25 3/7 2 3/2 - 136.125 72= = 26.46 & x,=5292 Given the new P = 2, the budget constraint will be: M = 22, + 2x2 = 2152192)+2 /26.46) m'= 158.74 ..CV=M-M = 158.74-100 CV = 58.74 which can be written as: (v = 10034 -100

Now, for Evi Optimal condition with new price : 1,= 222 Putting this in old budget constraint, 100= 22,4 242 1,+22=50 2X2 + x2=50 3x₂=50 Y = 16.67 1,= 33.34 So, utility will be: U= 33.34 16-67 U=136.12 the optimal condition with old price : *,=402 136.12=0,512 136.12 = UX₂12 34.03=12 x2 = 10.50 x = 42 Putting this in new Budget constraint: M= x + 222 = 42 +21 M'=63 This can also be waitten as: = 100-63 LEV=100-50312 Ev=31 i Ev=M-M'