Zoe lives for two periods and has life-time utility V+0.8Vo2. Zoe\'s income are
ID: 1114149 • Letter: Z
Question
Zoe lives for two periods and has life-time utility V+0.8Vo2. Zoe's income are as follows: Y1 = 60,000 and 25,000. The real interest rate r = 7% 1. (3 points) How much will Zoe consume in each period? How much does she save? 2. (3 points) Now suppose that Zoe cares about her future more; the subjective discount factor increases to 0.9. The increase of the subjective discount factor could due to technology advances in medicine; Zoe could stay healthy and live longer. How much will Zoe consume in each period? How much does she save? Compared with part (1), what do you find?Explanation / Answer
a) From the incomes, the budget equation is c1 + c2/1.07 = 60000 + 25000/1.07
83364.50 = 1.07c1 + c2
Optimum choice has slope of the intertemporal indifference curve and budget line.
1.25(c2/c1)^0.5 = 1.07
c2 = 0.733c1
This result is now used in budget equation
83364.50 = 1.07c1 + 0.733c1
c1* = 46236.50, s1* = 60000-46236.5 = 13763.50
c2* = 33891.50 so there is no saving. It borows whatever is above c2* = 33891.50
b) When discounting is done at 9% we have
From the incomes, the budget equation is c1 + c2/1.09 = 60000 + 25000/1.9
82935.8 = 1.09c1 + c2
Optimum choice has slope of the intertemporal indifference curve and budget line.
1.25(c2/c1)^0.5 = 1.09
c2 = 0.76c1
This result is now used in budget equation
82935.8 = 1.07c1 + 0.76c1
c1* = 45320
c2* = 34443.30
We see that the consumption decreases and saving increases when discouting rate is increased.
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