Problem 4 Fisher model:. Two people, John and Jane follow the two-period Fisher

Question

Problem 4 Fisher model:. Two people, John and Jane follow the two-period Fisher model of consumption. John earns $150 both in the first and in the second period. While Jane earns $0 in the first and period and $320 in the second period. Both of them can borrow or lend at the interest rate r.

1. You observe both John and Jane consuming $150 in the first period and $150 in the second period. What is the interest rate r?

2. Suppose the interest rate increases. What will happen to John’s consumption in the first period? Is John better off or worse off than before the interest rate rise?

3. What will happen to Jane’s consumption in the first period when the interest rate increases? Is Jane better off or worse off than before the interest rate increase?

Explanation / Answer

Answer 1:- In order to solve the interest rate,   

C1+ C2/(1+r) = Y1+Y2/(1+r)

150+150/(1+r) = 0+320/(1+r)

170/(1+r) =150

1+r = 170/150

R=0.2605=26.05%

Jane borrowed $150 for consumption in the first period and in the second period used her $320 income to pay $189.075 on the loan (principal plus interest) and $150 for consumption

Answer 2:- Because of the substitution effect, the rise in interest rates leads Johnto consume less today and more tomorrow. The substitution effect costs him more to consume today than tomorrow, because of the higher opportunity cost in terms of forgone interest. However, John’s consumption in the first period can either rise of fall when we consider not only the substitution effect but also the income effect. The increase in the interest rate makes John better off (as reflected by the movement to a higher indifference curve) due to the income effect.

Answer 3:- Jane consumes less today, while her consumption tomorrow can either rise or fall. She faces both a substitution effect and income effect. Because consumption today is more expensive, she substitutes out of it. Also, since all her income is in the second period, the higher interest rate raises her cost of borrowing and, thus, lowers her income so she is worst off.

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