23. Mr. Smith has a utility function CiC2, where Ci is his consumption in period
ID: 2439551 • Letter: 2
Question
23. Mr. Smith has a utility function CiC2, where Ci is his consumption in period 1 and C2 is his consumption in period 2. The sticker price of all goods in all periods is one. He has no income in period 2. If he had an income of $40,000 in period 1 and the interest rate increases from 10% to 12%, a. his consumption in both periods would increase. his savings would increase by 2% and his consumption in period 2 would also increase. chis consumption in both periods would decrease. d his savings would not change but his consumption in period 2 would increase by 400. his consumption in period 1 would decrease by 12%. e.Explanation / Answer
Ans. B) his savings will increase by 2% and consumption in period 2 will also increase.
U(C1,C2) = C1 C2
Interest rate = 10%
Income in period 1(m1) = 40,000
Income in period 2(m2) = 0
So, MRS = MU C1 / MU C2 = C2 / C1
MRS = C2/ C1 = 1 + r
C2 = (1 + r) C1
C2 =( 1 + 0.1) C1
C2 = 1.1C1 (substitute this in following budget line equation )
Budget line equation is :
( 1 + r) C1 + C2 = (1 + r) m1 + m2
1.1C1 + 1.1C1 = 1.1 * 40,000 + 0
2.2C1 = 44,000
C1 = 44,000/ 2.2
C1 = 20,000
Consumption in period 2 (C2) = 1.1C1 = 1.1 *20,000
C2 = 22,000
When interest rate increase from 10% to 12% ,then follow same steps till where C2 = (1+r) C1
C2 = (1+0.12)C1
C2 = 1.12C1
Substitute it in following budget line equation
(1+r)C1 + C2 = (1+r) m1 + m2
1.12C1 + 1.12C1 = 1.12 * 40,000 + 0
2.24 C1 = 44,800
C1 = 44,800/2.24
C1 = 20,000
C2 = 1.12*C1
C2 = 1.12 * 20,000
C2 = 22,400
Thus ,it can be seen that with increase in interest rate there is no increase in consumption in period 1 but increase in period 2 consumption from 22,000 to 22,400 i.e consumption in period 2 increased by 400. Moreover with increase in interest rate there is increase in savings by 2% as he is saving more for consumption in period 2.
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