10. Intertemporal Choice

# 10. Intertemporal Choice - Chapter 10 NAME Intertemporal...

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Chapter 10 NAME Intertemporal Choice Introduction. The theory of consumer saving uses techniques that you have already learned. In order to focus attention on consumption over time, we will usually consider examples where there is only one consumer good, but this good can be consumed in either of two time periods. We will be using two “tricks.” One trick is to treat consumption in period 1 and consumption in period 2 as two distinct commodities. If you make period-1 consumption the numeraire , then the “price” of period-2 con- sumption is the amount of period-1 consumption that you have to give up to get an extra unit of period-2 consumption. This price turns out to be 1 / (1 + r ), where r is the interest rate. The second trick is in the way you treat income in the two diFerent periods. Suppose that a consumer has an income of m 1 in period 1 and m 2 in period 2 and that there is no inﬂation. The total amount of period- 1 consumption that this consumer could buy, if he borrowed as much money as he could possibly repay in period 2, is m 1 + m 2 1+ r .A sy o u work the exercises and study the text, it should become clear that the consumer’s budget equation for choosing consumption in the two periods is always c 1 + c 2 1+ r = m 1 + m 2 r . This budget constraint looks just like the standard budget constraint that you studied in previous chapters, where the price of “good 1” is 1, the price of “good 2” is 1 / (1 + r ), and “income” is m 1 + m 2 (1+ r ) . Therefore if you are given a consumer’s utility function, the interest rate, and the consumer’s income in each period, you can ±nd his demand for consump- tion in periods 1 and 2 using the methods you already know. Having solved for consumption in each period, you can also ±nd saving, since the consumer’s saving is just the diFerence between his period-1 income and his period-1 consumption. Example: A consumer has the utility function U ( c 1 ,c 2 )= c 1 c 2 .The rei s no inﬂation, the interest rate is 10%, and the consumer has income 100 in period 1 and 121 in period 2. Then the consumer’s budget constraint c 1 + c 2 / 1 . 1 = 100 + 121 / 1 . 1 = 210 . The ratio of the price of good 1 to the price of good 2 is 1 + r =1 . 1. The consumer will choose a consumption bundle so that MU 1 /M U 2 . 1. But 1 = c 2 and 2 = c 1 ,sothe consumer must choose a bundle such that c 2 /c 1 . 1. Take this equation together with the budget equation to solve for c 1 and c 2 . The solution is c 1 = 105 and c 2 = 115 . 50. Since the consumer’s period-1 income is only 100, he must borrow 5 in order to consume 105 in period 1. To pay back principal and interest in period 2, he must pay 5.50 out of his period-2 income of 121. This leaves him with 115.50 to consume.

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132 INTERTEMPORAL CHOICE (Ch. 10) You will also be asked to determine the efects oF inﬂation on con- sumer behavior. The key to understanding the efects oF inﬂation is to see what happens to the budget constraint.
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10. Intertemporal Choice - Chapter 10 NAME Intertemporal...

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