Gabe and Gita both obey the two period Fisher model of consumption. Gabe earns $

Question

Gabe and Gita both obey the two period Fisher model of consumption. Gabe earns $100 in the first period and $100 in the second period. Gita earns nothing in the first period and $210 in the second period. Both of them can borrow or lend at interest rate r.

a. You observe both Gabe and Gita consuming $100 in the first period and $100 in the second. What is the interest rate r?

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

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

Explanation / Answer

a. Since we observed both Gabe and Gita consuming $100 in the first period and $100 in the second, it means that Gita took a loan of 100 in period 1, which said in period 2 as 110 as her total earning is 210 and 100 she consumed in 2nd period

So, 100(1+r) = 110

r = 110/100 - 1

r = 10%

b. Gabe’s consumption will decrease in the first period. Gabe is better off than before the interest rate rise as due to increase in r , now she can consume more in second period by decreasing a small ammount in first period.

C. Gita’s consumption will decrease in the first period when the interest rate increases.

  Gita is worse off than before the interest rate increase as now she has to pay higher interest rate to consume in the first period , so she is worse off.

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