Mr.O.B.Kandle has a utility function c 1 c 2 , where c 1 is his consumption in period 1 and c 2 is his consumption in period 2.He has no income in period 2.If he had an income of $50,000 in period 1 and the interest rate increased from 10 to 15%,A) his savings would increase by 5% and his consumption in period 2 would also increase.B) his savings would not change but his consumption in period 2 would increase by 1,250.C) his consumption in both periods would increase.D) his consumption in both periods would decrease.E) his consumption in period 1 would decrease by 15% and his consumption in period 2 would also decrease.

Question

Mr.O.B.Kandle has a utility function c 1 c 2 , where c 1  is his consumption in period 1 and c 2  is his consumption in period 2.He has no income in period 2.If he had an income of $50,000 in period 1 and the interest rate increased from 10 to 15%,A) his savings would increase by 5% and his consumption in period 2 would also increase.B) his savings would not change but his consumption in period 2 would increase by 1,250.C) his consumption in both periods would increase.D) his consumption in both periods would decrease.E) his consumption in period 1 would decrease by 15% and his consumption in period 2 would also decrease.

Avery Damjanovic · Accepted Answer

Final Answer : B, Explanation :  According to the utility function, Mr. O.B. Kandle maximizes his utility by choosing his consumption in two periods subject to the budget constraint. His budget constraint can be written as c 1  + (1 + r)c 2  = Y, where Y is his income in period 1 and r is the interest rate.If Y = $50,000 and r = 0.10, then his budget constraint is c 1  + 1.1c 2  = $50,000.If r increases to 0.15, then his budget constraint becomes c 1  + 1.15c 2  = $50,000.Since he has no income in period 2, his savings in period 1 will be equal to his consumption in period 1 minus his budget constraint divided by (1 + r). That is, saving 1  = c 1  - ($50,000 - c 1 )/(1.10) or saving 1  = 0.818c 1  + $22,727.Similarly, saving 1  when r = 0.15 is equal to c 1  - ($50,000 - c 1 )/(1.15) or saving 1  = 0.783c 1  + $21,739.Since the interest rate has increased, the opportunity cost of consumption today has gone up. Therefore, Mr. O.B. Kandle will choose to consume more in period 1 and less in period 2. His savings in period 1 will remain the same, but his consumption in period 2 increases by ($21,739 - $22,727) or $988/(1.15) which is approximately $1,250. Therefore, choice B is the correct answer.

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