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ECON 3420 Notes 1 [Intertemporal Choice]

ECON 3420 Notes 1 [Intertemporal Choice] - ECON 3420A...

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1 ECON 3420A - Lecture 1 Intertemporal Choice In this chapter, we study how decisions of consumption and investment can be made in a world of two periods and when there is no uncertainty over future incomes. In such a setting, the analysis is actually very similar to what we have learned in utility maximization in basic micro. However, our analysis does produce new insights. In particular, we see how utility maximization turns out to be equivalent to present value maximization. This gives rise to an important decision rule in investment, i.e. choose the investment project that gives the highest present value of future incomes. Although this rule is derived under the assumption of certainty, we will see later on that the same rule essentially applies in a world of uncertainty as well. 1. Present Value Rule Suppose you have $100. You can either consume it now or put it in a bank, which pays you an interest rate of say, 10%. This means you can withdraw $110 one year from now. The money market provides you with a choice of instant consumption of $100 or $110 one year from now. In other words, $ 110 one year from now is worth only $110/(1+10%) today. Since a dollar at different future dates has different value, one needs to discount future cash flows appropriately so that cash flows at different dates can be added together. One method to do this is the present value method i.e. we “discount” each future cash flow to the present before we add them up. Consider a cashflow stream: -C 0 , C 1 , 0, C 3 . If we invest C 0 now (note the negative sign), then we get C 1 at the end of the first year, nothing the second year and C 3 the third year. The present value of this stream is: 3 3 2 1 0 ) 1 ( ) 1 ( 0 ) 1 ( r C r r C C PV where r is the interest rate. If we were given numbers for the stream and a suitable interest rate, we could calculate PV . The general rule of investment decision is: If PV turns out to be positive, then the investment project is profitable at the interest rate of r . Suppose the opportunity
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2 cost of investing in the project is some foregone interest that could have been earned by putting the money in a bank. Then using the bank interest rate as r , a positive PV means we get a higher return from investing C 0 in this project than from putting it in the bank for three years. Alternatively, if C 0 has to be borrowed, then using the borrowing interest rate as r , a positive PV means we will end up, after repaying loans, with a surplus in three years. In either case, the investment decision is positive. The simple rule of thumb is therefore,
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ECON 3420 Notes 1 [Intertemporal Choice] - ECON 3420A...

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