Mr.O.B.Kandle has a utility function c₁c₂, where c₁ is his consumption in period 1 and c₂ 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

Quizplus · Accepted Answer

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 c₁ + (1 + r)c₂ = 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 c₁ + 1.1c₂ = $50,000. If r increases to 0.15, then his budget constraint becomes c₁ + 1.15c₂ = $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, saving₁ = c₁ - ($50,000 - c₁)/(1.10) or saving₁ = 0.818c₁ + $22,727. Similarly, saving₁ when r = 0.15 is equal to c₁ - ($50,000 - c₁)/(1.15) or saving₁ = 0.783c₁ + $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.

MrOBKandle Has a Utility Function C1c2, Where C1 Is His

MrOBKandle Has a Utility Function C₁c₂, Where C₁ Is His