[Joseph_E._Stiglitz,_Carl_E._Walsh]_Economics(Bookos.org) (1)

Joan chooses among the points on this budget constraint according to her personal
preferences. Consider, for example, point D, where Joan is consuming very
little during her working life. Since she is spending very little in the present, any
additional consumption now will have a high marginal value. She will be relatively
eager to substitute present consumption for future consumption. At the other
extreme, if she is consuming a great deal in the present, say at point F, additional
consumption today will have a relatively low marginal value, while future consumption
will have a high marginal value. Hence, she will be relatively eager to save more
for the future. She chooses a point in between, E, where consumption in the two
periods is not too different. She has smoothed her consumption. That is, consumption
in each of the two different periods is about the same. This kind of saving,
intended to smooth consumption over a worker’s lifetime and to provide for retirement,
is called life-cycle saving. In Figure 9.1, the difference between the first-period
income, w, and what she consumes in the first period is her saving.
The Time Value of Money Because you can earn interest on your savings,
the cost of a dollar of current consumption is more than simply $1.00 of future consumption.
As we learned in Chapter 2, calculating costs correctly is one of the basic
steps in making rational decisions. But what if we are comparing costs that occur at
different times, such as the cost of current versus future consumption? Or to take
a more specific example, suppose one store advertises a car stereo system for $400
and another advertises it for $425 with no payment for a full year. How can we compare
these two? If you have the $400 to spend today, is it cheaper to pay $400 right
now for the stereo or to pay $425 in one year?
To think about this comparison, consider what you could do with your $400 if you
opted to buy from the store that lets you delay your payment. You might put the
money in a bank. When you deposit money in a bank, you have lent it your money.
In return, the bank pays you interest. If the interest rate is 5 percent per year, you
will receive $420 in a year—the $20 is the interest payment, while the $400 is the
repayment of the principal, the original amount you lent to the bank.
The interest rate is a price, and like other prices, it describes a trade-off. If the
interest rate is 5 percent, by giving up $1.00 worth of consumption today, a saver
can have $1.05 worth of consumption next year. Thus, the rate of interest tells us how
much future consumption we can get by giving up $1.00 worth of current consumption.
It tells us the relative price of purchases in the present and in the future.
Because interest rates are normally positive, $1.00 today becomes more than a
dollar in the future. Thus a dollar today is worth more than a dollar in the future.
Economists call this phenomenon the time value of money. The concept of present
discounted value tells us precisely how to measure the time value of money.
The present discounted value of $100 a year from now is what you would pay today
for $100 in a year. Suppose the interest rate is 5 percent. If you put $95.24 in the
bank today, then at the end of a year you will receive $4.76 in interest, which together
with the original principal will total $100. Thus, $95.24 is the present discounted
value of $100 one year from now, if the interest rate is 5 percent.
There is a simple formula for calculating the present discounted value of any
amount to be received a year from now: just divide the amount by 1 plus the annual
rate of interest (often denoted by r).
SUPPLY IN THE CAPITAL MARKET ∂ 193