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PROFESSOR: Our topics part of
the course by revisiting

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another important topic that--

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00:00:33,430 --> 00:00:36,750
one of the most important topics
in economics which is

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where does capital come from.

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00:00:39,460 --> 00:00:41,950
This is a topic that is
essential in economics.

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00:00:41,950 --> 00:00:45,120
It's also really central, the
basis, for what is in finance.

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So a lot of what we'll
do today is really--

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00:00:47,860 --> 00:00:49,100
if you want to learn more about
it you take more in

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00:00:49,100 --> 00:00:51,960
economics but also more
courses in Course 15.

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00:00:51,960 --> 00:00:56,900
So, basically, we spent a lot of
time this semester talking

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00:00:56,900 --> 00:00:58,350
about one input to
the production

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00:00:58,350 --> 00:01:00,780
function which is labor.

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00:01:00,780 --> 00:01:04,560
We talked about labor supply,
labor demand, monopsony

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00:01:04,560 --> 00:01:06,680
models, et cetera.

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00:01:06,680 --> 00:01:09,280
We haven't talked much about
the other input into the

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00:01:09,280 --> 00:01:11,410
production function
which is capital.

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00:01:11,410 --> 00:01:13,820
Now, partly, that's because
that's a more awkward concept.

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00:01:13,820 --> 00:01:15,640
It's clear what labor is.

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00:01:15,640 --> 00:01:18,900
Labor is the workers working
in the production process.

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00:01:18,900 --> 00:01:20,820
Capital's a little bit harder
because capital's sort of

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00:01:20,820 --> 00:01:26,600
everything else-- the machine,
the land, the buildings, other

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00:01:26,600 --> 00:01:28,480
physical inputs.

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00:01:28,480 --> 00:01:29,870
And we know where labor
comes from.

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00:01:29,870 --> 00:01:31,780
Labor comes from our working.

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00:01:31,780 --> 00:01:34,190
But it's less clear where
capital comes from in some

33
00:01:34,190 --> 00:01:36,330
aggregate concept.

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00:01:36,330 --> 00:01:40,900
So, basically, the key thing is
that all forms of capital

35
00:01:40,900 --> 00:01:42,880
have a common feature.

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00:01:42,880 --> 00:01:45,430
All forms of capital have a
common feature which is what

37
00:01:45,430 --> 00:01:48,760
capital represents is a
diversion of current

38
00:01:48,760 --> 00:01:53,870
consumption towards future
production and consumption.

39
00:01:53,870 --> 00:01:57,560
So capital's about diverting
current consumption towards

40
00:01:57,560 --> 00:02:00,370
future production
and consumption.

41
00:02:00,370 --> 00:02:03,580
So the original concept of
capital came from farming

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00:02:03,580 --> 00:02:05,820
where the notion was that
farmers every year would take

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00:02:05,820 --> 00:02:09,300
some of their grain, and, rather
than eating it, they'd

44
00:02:09,300 --> 00:02:13,190
put it aside to become seed to
plant for the next year.

45
00:02:13,190 --> 00:02:14,530
That was their capital.

46
00:02:14,530 --> 00:02:16,620
And so they diverted their
consumption this year which

47
00:02:16,620 --> 00:02:21,900
was eating the grain they grew
to produce future consumption

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00:02:21,900 --> 00:02:23,730
through planting those
seeds and creating

49
00:02:23,730 --> 00:02:26,070
consumption for next year.

50
00:02:26,070 --> 00:02:30,390
So, basically, in a modern
economy the idea is the same.

51
00:02:30,390 --> 00:02:33,040
And so when we think about
capital, what I want you to

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00:02:33,040 --> 00:02:38,710
think about is I want you to
think about, basically, the

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00:02:38,710 --> 00:02:40,530
capital as money.

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00:02:40,530 --> 00:02:43,160
Think of the capital in the
production function as the

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00:02:43,160 --> 00:02:46,470
money that we invest in all
these other things that aren't

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00:02:46,470 --> 00:02:48,650
labor-- that we invest in
machines, and we invest in

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00:02:48,650 --> 00:02:51,020
buildings, and we
invest in land.

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00:02:51,020 --> 00:02:54,120
So we want to think about
capital not as physical

59
00:02:54,120 --> 00:02:56,360
capital but as financial
capital.

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That's the way to be thinking
about that one aggregate

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letter k is this financial
capital.

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00:03:01,160 --> 00:03:04,720
It's the money that's invested
in producing goods, in

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building machines, and
building buildings,

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and stuff like that.

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OK?

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Now, basically, where do
firms get that money?

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So you're a firm.

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You want to build a building
or new machine or

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something like that.

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Where do firms get that money?

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They get that money in
capital markets.

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Capital markets are basically
pools of money that firms draw

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00:03:27,585 --> 00:03:31,300
on to invest and
create capital.

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So a capital market--

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00:03:32,900 --> 00:03:35,410
literally think of it as a pool
of money that's out there

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that firms can tap into if they
want to build a building

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or build a machine
or buy some land.

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They tap into capital markets
to make those investments.

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So while capital physically
represents lots of different

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things, financially it
represents one thing which is

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the pool of money that firms tap
into to invest, to divert

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current consumption to
future consumption.

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00:04:02,930 --> 00:04:03,560
OK?

84
00:04:03,560 --> 00:04:05,690
It's the pool of money firms
tap into to invest. That's

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00:04:05,690 --> 00:04:07,060
what we mean by capital.

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00:04:07,060 --> 00:04:10,170
By capital market we represent
that pool of money.

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00:04:10,170 --> 00:04:13,370
So think of capital as financial
capital, and think

88
00:04:13,370 --> 00:04:16,740
of where you get financial
capital in a capital market as

89
00:04:16,740 --> 00:04:20,079
being that pool of money that
firms tap into to make

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00:04:20,079 --> 00:04:23,730
investments to divert
towards the future.

91
00:04:23,730 --> 00:04:27,420
Now, where does that supply
of money come from?

92
00:04:27,420 --> 00:04:28,800
Where does that supply
of money come from?

93
00:04:28,800 --> 00:04:31,380
Well it comes from households'
decisions on how

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00:04:31,380 --> 00:04:34,070
much to save. OK?

95
00:04:34,070 --> 00:04:37,340
So the pool of money in capital
markets, the pool of

96
00:04:37,340 --> 00:04:41,520
money that firms draw on to
build capital, comes from

97
00:04:41,520 --> 00:04:45,410
households' decisions
on how much to save.

98
00:04:45,410 --> 00:04:48,545
So now we see the tie to labor,
the other input in the

99
00:04:48,545 --> 00:04:49,690
production function.

100
00:04:49,690 --> 00:04:53,940
Just as households' decisions on
how hard to work determines

101
00:04:53,940 --> 00:04:56,750
the labor input into the
production function,

102
00:04:56,750 --> 00:05:00,170
households' decisions on how
much to save determines the

103
00:05:00,170 --> 00:05:04,045
capital input into the
production function.

104
00:05:04,045 --> 00:05:07,150
So just as my decision how much
to work determines how

105
00:05:07,150 --> 00:05:10,450
much labor is available to
firms, my decision on how much

106
00:05:10,450 --> 00:05:13,370
to save that's what fills
up this pool.

107
00:05:13,370 --> 00:05:13,860
OK?

108
00:05:13,860 --> 00:05:17,970
So this pool of financial
capital is filled up by

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00:05:17,970 --> 00:05:21,550
household savings and then drawn
down by firms' demand

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00:05:21,550 --> 00:05:23,410
for investment.

111
00:05:23,410 --> 00:05:24,970
And that's the way a capital
market works.

112
00:05:28,050 --> 00:05:30,060
So, basically, if we think
about capital market

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00:05:30,060 --> 00:05:31,300
equilibrium--

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00:05:31,300 --> 00:05:35,750
if you go to Figure 21-1--

115
00:05:35,750 --> 00:05:37,600
we have equilibrium in
capital markets.

116
00:05:37,600 --> 00:05:40,000
Now this is just like we talked
about-- this is the

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00:05:40,000 --> 00:05:40,860
other factor markets.

118
00:05:40,860 --> 00:05:44,320
Just like we talked about labor
markets and determining

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00:05:44,320 --> 00:05:46,430
what determines the wage rate
and the optimum amount of

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00:05:46,430 --> 00:05:48,530
labor hired, it's same
with capital markets.

121
00:05:48,530 --> 00:05:50,950
You have some demand
for capital.

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00:05:50,950 --> 00:05:53,550
That comes from firms' demand
for investment.

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00:05:53,550 --> 00:05:54,740
Firms want new machines.

124
00:05:54,740 --> 00:05:56,530
They want new buildings.

125
00:05:56,530 --> 00:06:00,430
That's downward sloping because,
initially, there's

126
00:06:00,430 --> 00:06:02,750
very high demand for capital.

127
00:06:02,750 --> 00:06:07,220
But there's a marginal
diminishing product.

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00:06:07,220 --> 00:06:09,460
The more capital I have the
less valuable it is on the

129
00:06:09,460 --> 00:06:12,060
margin, the less you are
willing to pay for it.

130
00:06:12,060 --> 00:06:15,215
So there's a downward sloping
demand curve for capital and

131
00:06:15,215 --> 00:06:17,810
an upward sloping
supply curve.

132
00:06:17,810 --> 00:06:22,120
And the price, in this market,
is the interest rate.

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00:06:22,120 --> 00:06:23,460
What is the interest rate?

134
00:06:23,460 --> 00:06:26,720
The interest rate is the rate
you have to pay households to

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00:06:26,720 --> 00:06:29,050
get them to lend you money.

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So the interest rate, i, is
the rate you have to pay

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00:06:31,950 --> 00:06:35,590
households to get them
to lend you money.

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00:06:35,590 --> 00:06:43,060
So if that interest rate is
very high, firms will not

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00:06:43,060 --> 00:06:45,610
demand much investment because
they'll have to pay a lot of

140
00:06:45,610 --> 00:06:47,910
money to get the financial
capital to finance that

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00:06:47,910 --> 00:06:49,510
investment.

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00:06:49,510 --> 00:06:52,000
But households will be delighted
to supply lots of

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00:06:52,000 --> 00:06:53,830
savings because they're
getting paid a

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00:06:53,830 --> 00:06:55,080
high price for it.

145
00:06:57,470 --> 00:07:01,980
So, basically, the interest
rate serves as the

146
00:07:01,980 --> 00:07:03,290
equilibrating price
in this market.

147
00:07:03,290 --> 00:07:06,020
Just as the wage serves as the
equilibrating price in the

148
00:07:06,020 --> 00:07:09,270
labor market, the interest
rate serves as the

149
00:07:09,270 --> 00:07:11,650
equilibrating price in
the capital market.

150
00:07:11,650 --> 00:07:16,060
As the interest rate rises,
folks want to save more,

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00:07:16,060 --> 00:07:18,730
filling more money into
that pool of capital.

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00:07:18,730 --> 00:07:21,870
And firms want to borrow less,
taking less money out of that

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00:07:21,870 --> 00:07:23,260
pool of capital.

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00:07:23,260 --> 00:07:26,900
And when that supply and demand
is equilibrated, at

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00:07:26,900 --> 00:07:31,400
point e, is going to be where
the firm's drawing on the pool

156
00:07:31,400 --> 00:07:34,660
at exactly the rate people are
putting money into the pool.

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00:07:34,660 --> 00:07:37,320
And that's going to be
the equilibrium.

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00:07:37,320 --> 00:07:39,910
OK, so we want to focus on--

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00:07:39,910 --> 00:07:42,440
for today's lecture and
next lecture as well--

160
00:07:42,440 --> 00:07:46,180
is what determines the money
that goes into that pool.

161
00:07:46,180 --> 00:07:47,610
We know what determines the rate
at which firms want to

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00:07:47,610 --> 00:07:49,920
draw out of that pool.

163
00:07:49,920 --> 00:07:51,750
That's basically going to be
determined by the production

164
00:07:51,750 --> 00:07:53,900
function and all the stuff
we learned in lectures on

165
00:07:53,900 --> 00:07:55,430
production theory.

166
00:07:55,430 --> 00:07:58,310
You can get your optimal
demand for capital.

167
00:07:58,310 --> 00:08:01,060
It's going to be determined
by isocosts and isoquants.

168
00:08:01,060 --> 00:08:03,310
And you get some k star.

169
00:08:03,310 --> 00:08:06,730
But what's going to determine
what goes into that pool?

170
00:08:06,730 --> 00:08:09,620
That's going to be households'
decisions to save. And

171
00:08:09,620 --> 00:08:13,415
households' decisions to save,
we say, are determined by a

172
00:08:13,415 --> 00:08:15,950
process we call intertemporal
choice.

173
00:08:22,850 --> 00:08:27,110
Added some extra letters there--
intertemporal choice.

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00:08:27,110 --> 00:08:29,110
Intertemporal choice--

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00:08:29,110 --> 00:08:32,960
which is basically, instead
of thinking about someone

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00:08:32,960 --> 00:08:36,690
choosing between apples and
bananas, we think of them

177
00:08:36,690 --> 00:08:38,890
choosing between consumption
today

178
00:08:38,890 --> 00:08:41,150
and consumption tomorrow.

179
00:08:41,150 --> 00:08:45,040
So think of different periods
like different goods.

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00:08:45,040 --> 00:08:47,920
And I'm choosing between
consumption today and

181
00:08:47,920 --> 00:08:49,680
consumption tomorrow.

182
00:08:49,680 --> 00:08:51,720
That's my intertemporal
choice--

183
00:08:51,720 --> 00:08:56,800
the rate at which I choose to
trade off consumption in

184
00:08:56,800 --> 00:08:59,240
different periods.

185
00:08:59,240 --> 00:09:01,710
So for example, I'll illustrate
how this works.

186
00:09:01,710 --> 00:09:05,760
Let's say that I'm deciding
whether to just tell MIT,

187
00:09:05,760 --> 00:09:08,410
"Look, I don't want
to work next year.

188
00:09:08,410 --> 00:09:09,600
I want to stay home and
take care of my kids.

189
00:09:09,600 --> 00:09:10,730
You're not going to pay me.

190
00:09:10,730 --> 00:09:15,150
I'm taking an unpaid leave for
a year." Something professors

191
00:09:15,150 --> 00:09:17,590
can do with enough advance
warning to their

192
00:09:17,590 --> 00:09:18,750
chairman and such.

193
00:09:18,750 --> 00:09:20,300
So I'm going to take an unpaid
leave next year.

194
00:09:20,300 --> 00:09:21,550
I'm thinking about doing that.

195
00:09:24,660 --> 00:09:26,650
And now I have to
say, OK, fine.

196
00:09:26,650 --> 00:09:28,800
Next year I'm going to take this
unpaid leave so I have to

197
00:09:28,800 --> 00:09:30,850
decide how to allocate my--
and then I'm going to come

198
00:09:30,850 --> 00:09:32,840
back and life will be
the same thereafter.

199
00:09:32,840 --> 00:09:34,720
So it's just about next year I'm
going to take this unpaid

200
00:09:34,720 --> 00:09:38,880
leave. I have to decide how to
allocate my consumption across

201
00:09:38,880 --> 00:09:41,530
this year while I'm working and
next year while I'm taking

202
00:09:41,530 --> 00:09:43,360
an unpaid leave.

203
00:09:43,360 --> 00:09:47,930
And let's say my salary
is $80,000 a year.

204
00:09:47,930 --> 00:09:52,520
So one thing I could do is I can
consume all $80,000 this

205
00:09:52,520 --> 00:09:56,870
year and consume nothing
next year.

206
00:09:56,870 --> 00:10:01,340
That would not be a very
satisfactory outcome as I die.

207
00:10:01,340 --> 00:10:05,550
That's obviously not going to
be a satisfactory outcome.

208
00:10:05,550 --> 00:10:07,640
But what's the alternative?

209
00:10:07,640 --> 00:10:10,260
MIT's paying me this year,
and they're not

210
00:10:10,260 --> 00:10:11,480
paying me next year.

211
00:10:11,480 --> 00:10:12,750
What's the alternative?

212
00:10:12,750 --> 00:10:17,380
Well, the alternative is I can
save. And by saving, what we

213
00:10:17,380 --> 00:10:22,870
mean is I can loan some of the
money that I make out to firms

214
00:10:22,870 --> 00:10:26,140
to invest in their physical
capital in return for which

215
00:10:26,140 --> 00:10:31,320
they'll give me interest. And
next year I can live on the

216
00:10:31,320 --> 00:10:35,460
interest I've earned from
making that loan.

217
00:10:35,460 --> 00:10:40,800
Now, I don't literally go to
Genzyme and Microsoft and

218
00:10:40,800 --> 00:10:42,480
Apple and say I want to
loan you money and

219
00:10:42,480 --> 00:10:43,720
negotiate with them.

220
00:10:43,720 --> 00:10:45,350
That obviously would
be impossible.

221
00:10:45,350 --> 00:10:49,720
What I do is I implicitly loan
to firms through drawing on

222
00:10:49,720 --> 00:10:53,870
various aspects of the
capital market.

223
00:10:53,870 --> 00:10:57,510
So does anyone know, how can I
implicitly loan to a firm?

224
00:10:57,510 --> 00:10:58,190
Let's say I want to--

225
00:10:58,190 --> 00:10:58,460
Yeah?

226
00:10:58,460 --> 00:10:59,560
AUDIENCE: Banks.

227
00:10:59,560 --> 00:10:59,960
PROFESSOR: Banks.

228
00:10:59,960 --> 00:11:00,940
So explain what you mean.

229
00:11:00,940 --> 00:11:03,640
AUDIENCE: You deposit
money in a savings

230
00:11:03,640 --> 00:11:04,820
account for the bank.

231
00:11:04,820 --> 00:11:08,170
The bank pays you some interest
rate so that it can

232
00:11:08,170 --> 00:11:12,054
use your money to loan to bigger
companies that want to

233
00:11:12,054 --> 00:11:13,010
take money out of the bank.

234
00:11:13,010 --> 00:11:16,910
And they, in return, get money
from the other companies by

235
00:11:16,910 --> 00:11:18,417
the companies paying
some interest on

236
00:11:18,417 --> 00:11:20,080
what they took out.

237
00:11:20,080 --> 00:11:20,620
PROFESSOR: Exactly.

238
00:11:20,620 --> 00:11:23,260
We call banks financial
intermediaries.

239
00:11:23,260 --> 00:11:26,140
What that means is they
basically are the folks who

240
00:11:26,140 --> 00:11:29,060
can get a hold of firms
and make those loans.

241
00:11:29,060 --> 00:11:32,640
So, in other words, I don't
loan directly to Genzyme.

242
00:11:32,640 --> 00:11:34,920
I loan to the bank--

243
00:11:34,920 --> 00:11:36,850
Citizens Bank, my bank,
and Citizens

244
00:11:36,850 --> 00:11:38,650
Bank loans to Genzyme.

245
00:11:38,650 --> 00:11:43,240
Citizens Bank pays me an
interest rate on my savings--

246
00:11:43,240 --> 00:11:45,615
now close to zero, we'll come
to that-- but basically pays

247
00:11:45,615 --> 00:11:48,110
me some interest rate.

248
00:11:48,110 --> 00:11:52,500
Genzyme pays them an interest
rate to borrow money, higher

249
00:11:52,500 --> 00:11:54,240
than what they're paying
me, and the

250
00:11:54,240 --> 00:11:57,210
difference is bank profit.

251
00:11:57,210 --> 00:12:01,970
So, basically, one way I can
loan money is I can put in the

252
00:12:01,970 --> 00:12:04,080
bank and get paid interest. we
don't think about putting in

253
00:12:04,080 --> 00:12:06,010
the bank as a loan, but that's
basically what you're doing.

254
00:12:06,010 --> 00:12:08,640
You're loaning it to the bank.

255
00:12:08,640 --> 00:12:09,600
And they're paying you interest

256
00:12:09,600 --> 00:12:11,490
rate, i for that loan.

257
00:12:11,490 --> 00:12:12,850
What else can you do?

258
00:12:12,850 --> 00:12:13,580
How else can you--

259
00:12:13,580 --> 00:12:13,915
Yeah?

260
00:12:13,915 --> 00:12:15,730
AUDIENCE: You can
purchase stocks.

261
00:12:15,730 --> 00:12:17,200
PROFESSOR: You could
purchase stocks.

262
00:12:17,200 --> 00:12:18,970
So, in other words, what I could
do is I could directly

263
00:12:18,970 --> 00:12:23,990
go to a public company, and I
could take some of my $80,000

264
00:12:23,990 --> 00:12:25,730
and buy stock in that company.

265
00:12:25,730 --> 00:12:28,690
There I'm essentially directly
loaning to them.

266
00:12:28,690 --> 00:12:29,590
I'm directly giving
them money.

267
00:12:29,590 --> 00:12:33,620
Now, it's not a loan that's paid
back like a bank loan.

268
00:12:33,620 --> 00:12:36,280
It's loan that's paid back
hopefully with my stock

269
00:12:36,280 --> 00:12:38,775
becoming more valuable
or with a dividend.

270
00:12:41,430 --> 00:12:42,770
So how can I loan?

271
00:12:42,770 --> 00:12:43,940
One is I can invest--

272
00:12:43,940 --> 00:12:46,480
I could put it in the bank.

273
00:12:46,480 --> 00:12:48,100
The other is I can buy stock.

274
00:12:48,100 --> 00:12:52,610
I can put it in the bank, and
the bank pays me interest. I

275
00:12:52,610 --> 00:12:56,150
could buy stock, and that stock
pays off in two ways.

276
00:12:56,150 --> 00:13:00,500
One is many companies pay what
we call a dividend, what is

277
00:13:00,500 --> 00:13:03,570
called the dividend, which is
a quarterly payment that

278
00:13:03,570 --> 00:13:07,570
companies make to their
shareholders.

279
00:13:07,570 --> 00:13:09,790
So if I invest in a company
that pays a dividend, then

280
00:13:09,790 --> 00:13:12,200
I'll be getting a quarterly
check from that company that's

281
00:13:12,200 --> 00:13:14,020
a portion of my investment.

282
00:13:14,020 --> 00:13:18,450
The other is what we call a
capital gain which is the

283
00:13:18,450 --> 00:13:20,790
stock could go up in value.

284
00:13:20,790 --> 00:13:23,600
So next year, if the stock goes
up, if the stock market

285
00:13:23,600 --> 00:13:25,420
moves steadily-- it doesn't,
it jumps up and down, we'll

286
00:13:25,420 --> 00:13:26,270
come to that--

287
00:13:26,270 --> 00:13:28,480
but if it went steadily up I
could just sell some of that

288
00:13:28,480 --> 00:13:30,050
stock next year and
have extra money.

289
00:13:32,590 --> 00:13:35,070
So that's the other thing I
could do with my $80,000.

290
00:13:35,070 --> 00:13:37,670
I could loan to a company
by buying their stock.

291
00:13:37,670 --> 00:13:38,890
How else can I loan
to a company?

292
00:13:38,890 --> 00:13:39,645
Yeah?

293
00:13:39,645 --> 00:13:42,615
AUDIENCE: I don't know exactly
what the difference is, but

294
00:13:42,615 --> 00:13:44,595
couldn't you also invest
your money in a

295
00:13:44,595 --> 00:13:45,100
mutual fund or something?

296
00:13:45,100 --> 00:13:47,100
PROFESSOR: A mutual fund--
that's a good point.

297
00:13:47,100 --> 00:13:49,120
That would be loaning--

298
00:13:49,120 --> 00:13:53,640
a mutual fund is essentially
loaning money to an aggregate

299
00:13:53,640 --> 00:13:56,190
collection of companies.

300
00:13:56,190 --> 00:13:58,500
So there are very different
ways I can do stock.

301
00:13:58,500 --> 00:14:01,190
I can do a mutual fund, I can
buy individual stocks.

302
00:14:01,190 --> 00:14:02,560
There's lots of different
ways, but those are all

303
00:14:02,560 --> 00:14:03,830
different ways to buy stock.

304
00:14:03,830 --> 00:14:04,150
Yeah?

305
00:14:04,150 --> 00:14:04,470
AUDIENCE: You could buy bonds.

306
00:14:04,470 --> 00:14:05,640
PROFESSOR: You could
buy bonds.

307
00:14:05,640 --> 00:14:08,070
You could buy company bonds
which is I literally loan

308
00:14:08,070 --> 00:14:09,200
directly to the company.

309
00:14:09,200 --> 00:14:10,090
Stocks aren't really a loan.

310
00:14:10,090 --> 00:14:11,530
I'm literally buying an
ownership share in the

311
00:14:11,530 --> 00:14:12,900
company, and they're
paying me back.

312
00:14:12,900 --> 00:14:14,722
I could buy corporate bonds.

313
00:14:19,220 --> 00:14:22,630
I could buy corporate bonds, and
the way those work is it's

314
00:14:22,630 --> 00:14:25,310
literally cutting out
the middleman.

315
00:14:25,310 --> 00:14:28,310
I don't loan to Citizens Bank,
and they loan to the company.

316
00:14:28,310 --> 00:14:30,950
I just loan to the company,
and they pay me back.

317
00:14:30,950 --> 00:14:32,050
That's a corporate bond.

318
00:14:32,050 --> 00:14:34,610
I can also buy, by the
way, I can also buy

319
00:14:34,610 --> 00:14:37,360
a government bond.

320
00:14:37,360 --> 00:14:39,360
You may know the government's
running more than a trillion

321
00:14:39,360 --> 00:14:40,620
dollar deficit right now.

322
00:14:40,620 --> 00:14:42,230
Somebody's got to
finance that.

323
00:14:42,230 --> 00:14:44,050
So you can loan to the
government and get paid back

324
00:14:44,050 --> 00:14:45,500
by the government.

325
00:14:45,500 --> 00:14:46,880
OK, let's put the government
aside for a minute.

326
00:14:46,880 --> 00:14:48,940
Let's focus where we just--

327
00:14:48,940 --> 00:14:49,710
we haven't really
had a government

328
00:14:49,710 --> 00:14:50,490
sector in our models.

329
00:14:50,490 --> 00:14:52,550
We're where it's just you
and the companies.

330
00:14:52,550 --> 00:14:54,220
So let's leave the government
channel aside.

331
00:14:54,220 --> 00:14:56,640
But the other thing I can do
with my money is I can loan it

332
00:14:56,640 --> 00:14:58,760
through bonds.

333
00:14:58,760 --> 00:15:00,780
The point is that $80,000--

334
00:15:00,780 --> 00:15:01,800
yeah, I'm sorry.

335
00:15:01,800 --> 00:15:04,167
AUDIENCE: With stocks, if I
were to buy a stock from a

336
00:15:04,167 --> 00:15:06,937
company, wouldn't it be
primarily and usually through

337
00:15:06,937 --> 00:15:09,000
the secondary market?

338
00:15:09,000 --> 00:15:10,880
I wouldn't be giving any
money to the company.

339
00:15:10,880 --> 00:15:14,480
I'd just be giving money to
the previous stockholder.

340
00:15:14,480 --> 00:15:15,320
PROFESSOR: That's true.

341
00:15:15,320 --> 00:15:17,560
It basically depends on whether
the marginal stock

342
00:15:17,560 --> 00:15:20,120
comes from a new issuance as
stock by the company or

343
00:15:20,120 --> 00:15:21,730
through stock that's already
floating around

344
00:15:21,730 --> 00:15:23,010
the secondary market.

345
00:15:23,010 --> 00:15:23,880
That's a good point.

346
00:15:23,880 --> 00:15:26,540
So in some sense the--

347
00:15:26,540 --> 00:15:27,650
likewise with bonds.

348
00:15:27,650 --> 00:15:29,370
A lot of bonds are traded
in a secondary market.

349
00:15:29,370 --> 00:15:31,270
So I'm thinking about a simple
model where basically new

350
00:15:31,270 --> 00:15:33,270
stock gets issued by the
company, I buy it.

351
00:15:33,270 --> 00:15:34,470
More technically you're right.

352
00:15:34,470 --> 00:15:38,010
It's just trading among people,
but that sort of makes

353
00:15:38,010 --> 00:15:38,670
things complicated.

354
00:15:38,670 --> 00:15:41,630
Let's put that aside for now.

355
00:15:41,630 --> 00:15:44,480
So, basically, the point
is is my $80,000--

356
00:15:44,480 --> 00:15:47,720
there's lots of things
I can do with it.

357
00:15:47,720 --> 00:15:50,520
All of them yield
me some rate--

358
00:15:50,520 --> 00:15:54,240
the key point is all of them
have the feature that I'm

359
00:15:54,240 --> 00:15:58,890
diverting today's consumption
for tomorrow's consumption.

360
00:15:58,890 --> 00:16:00,980
I'm taking some of my money
and, rather than eating it

361
00:16:00,980 --> 00:16:05,020
this year when I'm working,
I'm loaning it out in some

362
00:16:05,020 --> 00:16:08,550
way, shape, or form and getting
payback in next year

363
00:16:08,550 --> 00:16:09,800
when I'm not working.

364
00:16:12,150 --> 00:16:14,090
And we can summarize.

365
00:16:14,090 --> 00:16:16,610
Now this is a very complicated
set of mechanisms, not to

366
00:16:16,610 --> 00:16:18,190
mention the secondary
market issues.

367
00:16:18,190 --> 00:16:23,060
And this is basically a
semester of 15.401.

368
00:16:23,060 --> 00:16:25,280
This is basically a semester
of finance theory.

369
00:16:25,280 --> 00:16:27,260
But basically what we're going
to do is compress this all

370
00:16:27,260 --> 00:16:31,250
down and say that I get some
interest rate on my money.

371
00:16:31,250 --> 00:16:35,270
However I do it, let's just say
that somehow I divert my

372
00:16:35,270 --> 00:16:37,790
money through one of these
mechanisms, and it yields some

373
00:16:37,790 --> 00:16:40,450
effective interest rate, i.

374
00:16:40,450 --> 00:16:42,530
And you can know behind that
there's lots of ways I can get

375
00:16:42,530 --> 00:16:45,140
that interest. But for now just
simplify it down and say

376
00:16:45,140 --> 00:16:48,540
the main thing is I'm diverting
my consumption now,

377
00:16:48,540 --> 00:16:51,800
and it's yielding some interest
earnings on that

378
00:16:51,800 --> 00:16:54,230
diverted consumption, i.

379
00:16:54,230 --> 00:16:59,340
So what that means is that for
every dollar I divert, I get 1

380
00:16:59,340 --> 00:17:02,350
plus i dollars the next year.

381
00:17:02,350 --> 00:17:05,109
So for every dollar of
consumption I divert, in one

382
00:17:05,109 --> 00:17:08,030
of these forms, I get 1 plus
i dollars next year.

383
00:17:11,920 --> 00:17:14,319
So, basically, I could
literally--

384
00:17:14,319 --> 00:17:17,040
if I wanted to-- let's say the
interest rate was 10%, just

385
00:17:17,040 --> 00:17:18,589
for example.

386
00:17:18,589 --> 00:17:21,990
Now what that means is instead
of consuming $80,000 this year

387
00:17:21,990 --> 00:17:24,740
and nothing next year, I could
consume nothing this year and

388
00:17:24,740 --> 00:17:28,550
$88,000 next year.

389
00:17:28,550 --> 00:17:31,570
Obviously, that's not very
satisfactory either.

390
00:17:31,570 --> 00:17:33,520
So how do we think about that?

391
00:17:33,520 --> 00:17:37,510
We think about that in
Figure 21-2 shows--

392
00:17:37,510 --> 00:17:39,060
now this is a complicated
diagram we gotta

393
00:17:39,060 --> 00:17:40,540
use to figure 21-2--

394
00:17:40,540 --> 00:17:44,280
this shows the intertemporal
choice model, intertemporal

395
00:17:44,280 --> 00:17:46,520
substitution we also call it.

396
00:17:46,520 --> 00:17:49,430
So the deal is that now instead
of the x-axis being

397
00:17:49,430 --> 00:17:51,630
pizza and the y-axis being
movies or all the other wacky

398
00:17:51,630 --> 00:17:54,930
things we've done, now the
x-axis is first period

399
00:17:54,930 --> 00:17:55,940
consumption.

400
00:17:55,940 --> 00:17:57,610
The y-axis is second
period consumption.

401
00:17:57,610 --> 00:17:58,620
You might say what's a period?

402
00:17:58,620 --> 00:18:00,550
Well a period's whatever I want
it to be-- a day, a year,

403
00:18:00,550 --> 00:18:02,050
10 years, whatever.

404
00:18:02,050 --> 00:18:02,890
Sometimes I'll say a year.

405
00:18:02,890 --> 00:18:03,930
Sometimes I'll say a period,
but the point

406
00:18:03,930 --> 00:18:04,880
is it doesn't matter.

407
00:18:04,880 --> 00:18:07,150
It's about the trade-off.

408
00:18:07,150 --> 00:18:10,400
So in my example, c1 is
consumption this year.

409
00:18:10,400 --> 00:18:13,620
c2's consumption next year.

410
00:18:13,620 --> 00:18:18,290
And my trade-off is I can
consume $80,000 this year, or,

411
00:18:18,290 --> 00:18:25,810
given the interest rate, I can
consume $88,000 next year.

412
00:18:25,810 --> 00:18:28,150
Now the trade-off-- that's
a typo, by the way.

413
00:18:28,150 --> 00:18:30,350
That should be minus 1.1.

414
00:18:30,350 --> 00:18:30,530
OK?

415
00:18:30,530 --> 00:18:33,230
This is a 10% interest rate.

416
00:18:33,230 --> 00:18:38,900
The key point is the trade-off
is that, basically, I can

417
00:18:38,900 --> 00:18:42,230
trade off for every dollar I
don't consume this year, I

418
00:18:42,230 --> 00:18:43,820
consume 1 plus i--

419
00:18:43,820 --> 00:18:46,830
1 plus r there, should
be 1 plus i dollars--

420
00:18:46,830 --> 00:18:49,460
next year.

421
00:18:49,460 --> 00:18:53,940
We use r and i interchangeably
for the interest rate, so 1

422
00:18:53,940 --> 00:18:58,710
plus i, 1 plus r dollars
next year.

423
00:18:58,710 --> 00:19:02,420
So, basically, what does the
interest rate represent?

424
00:19:02,420 --> 00:19:03,370
This is important.

425
00:19:03,370 --> 00:19:08,160
The wage rate I defined as
the price of leisure.

426
00:19:08,160 --> 00:19:09,260
Remember what the
wage rate was?

427
00:19:09,260 --> 00:19:17,420
It was the price of leisure,
that basically by working I

428
00:19:17,420 --> 00:19:21,360
forgoed the ability to--

429
00:19:21,360 --> 00:19:23,510
I'm sorry, by taking leisure
I forgoed the ability to

430
00:19:23,510 --> 00:19:25,270
earn a wage, w.

431
00:19:25,270 --> 00:19:27,645
So, literally, that was a price
of sitting around on the

432
00:19:27,645 --> 00:19:29,740
couch was the wage, w,
I could've earned.

433
00:19:29,740 --> 00:19:33,000
Likewise, the interest rate is
the price of first period

434
00:19:33,000 --> 00:19:34,440
consumption.

435
00:19:34,440 --> 00:19:37,900
By consuming today, I'm forgoing
the fact that I

436
00:19:37,900 --> 00:19:40,440
could've earned the interest on
that money had I consumed

437
00:19:40,440 --> 00:19:43,060
it tomorrow or next year.

438
00:19:43,060 --> 00:19:45,200
So the interest rate is the
price of first period

439
00:19:45,200 --> 00:19:50,570
consumption, just as the wage
is the price of leisure.

440
00:19:50,570 --> 00:19:51,050
Yeah?

441
00:19:51,050 --> 00:19:53,445
AUDIENCE: You said before
that r and i are used

442
00:19:53,445 --> 00:19:59,672
interchangeably for interest.
Does that play into the cost

443
00:19:59,672 --> 00:20:01,826
function at all?

444
00:20:01,826 --> 00:20:05,358
Is the cost for capital going
to be the interest rate?

445
00:20:05,358 --> 00:20:07,080
PROFESSOR: I'm going
to come to that.

446
00:20:07,080 --> 00:20:12,300
That's exactly what I'll talk
about next lecture.

447
00:20:12,300 --> 00:20:14,890
So, basically, this is the key
thing, but the key thing to

448
00:20:14,890 --> 00:20:16,580
understand intertemporal
choice-- and the other

449
00:20:16,580 --> 00:20:18,540
important point to understand on
why it's a bit harder than

450
00:20:18,540 --> 00:20:20,070
labor is there's an extra--

451
00:20:20,070 --> 00:20:20,950
well it's not harder.

452
00:20:20,950 --> 00:20:21,500
It's the same thing.

453
00:20:21,500 --> 00:20:23,940
Remember, we said we don't model
bads in this course.

454
00:20:23,940 --> 00:20:25,330
We model goods.

455
00:20:25,330 --> 00:20:27,000
So we're modeling your choice
of how hard to work.

456
00:20:27,000 --> 00:20:29,280
We model the trade-off between
consumption and leisure.

457
00:20:29,280 --> 00:20:32,560
And then we said define labor
as the total amount of hours

458
00:20:32,560 --> 00:20:33,750
available minus leisure.

459
00:20:33,750 --> 00:20:34,690
Same thing here.

460
00:20:34,690 --> 00:20:36,510
We don't model savings.

461
00:20:36,510 --> 00:20:38,450
That's a bad.

462
00:20:38,450 --> 00:20:39,310
Now you might not think
[? some of these ?]

463
00:20:39,310 --> 00:20:41,410
things are good, but
savings really by

464
00:20:41,410 --> 00:20:43,360
itself is not a good.

465
00:20:43,360 --> 00:20:44,700
Unless you're Scrooge McDuck--

466
00:20:44,700 --> 00:20:47,340
does anyone know who
Scrooge McDuck is?

467
00:20:47,340 --> 00:20:48,690
Wow, that hurts.

468
00:20:48,690 --> 00:20:50,546
OK, he was this old cartoon
character when I was a kid who

469
00:20:50,546 --> 00:20:51,710
used to, like, fill a
swimming pool with

470
00:20:51,710 --> 00:20:53,490
money and swim in it.

471
00:20:53,490 --> 00:20:55,940
Basically, unless you're like
that, the savings itself does

472
00:20:55,940 --> 00:20:56,770
not give you utility.

473
00:20:56,770 --> 00:20:59,140
We don't have savings entering
utility functions.

474
00:20:59,140 --> 00:21:01,460
We have consumption entering
utility functions.

475
00:21:01,460 --> 00:21:02,810
Savings is a bad.

476
00:21:02,810 --> 00:21:05,350
Savings is the mean by which
you translate consumption

477
00:21:05,350 --> 00:21:07,570
period one into consumption
period two.

478
00:21:07,570 --> 00:21:09,800
But from the effect of today
you wish you didn't have to

479
00:21:09,800 --> 00:21:10,910
save. You just do it because
you want to make

480
00:21:10,910 --> 00:21:12,660
sure you eat tomorrow.

481
00:21:12,660 --> 00:21:14,560
So we model the good.

482
00:21:14,560 --> 00:21:18,040
The good is consumption in
period one, and savings is the

483
00:21:18,040 --> 00:21:20,900
difference between income and
consumption in period one.

484
00:21:20,900 --> 00:21:22,600
So we don't model savings.

485
00:21:22,600 --> 00:21:25,550
We define savings
as y minus c1.

486
00:21:25,550 --> 00:21:31,570
We model c1, and define
savings as y minus c1.

487
00:21:31,570 --> 00:21:34,040
You can see that there
in the diagram.

488
00:21:34,040 --> 00:21:37,310
Now what happens when the
interest rate changes?

489
00:21:37,310 --> 00:21:42,580
Let's go to Figure 21-3.

490
00:21:42,580 --> 00:21:44,550
What happens when the interest
rate changes?

491
00:21:44,550 --> 00:21:45,670
Actually, go to 21-4.

492
00:21:45,670 --> 00:21:45,960
OK?

493
00:21:45,960 --> 00:21:46,680
Skip 21-3.

494
00:21:46,680 --> 00:21:48,990
Got to 21-4.

495
00:21:48,990 --> 00:21:51,190
What happens when the interest
rate changes?

496
00:21:51,190 --> 00:21:54,850
So, initially, we're at a point
like a and then the

497
00:21:54,850 --> 00:22:00,760
interest rate goes
up from r to r2.

498
00:22:00,760 --> 00:22:03,960
The interest rate goes up.

499
00:22:03,960 --> 00:22:05,260
Now what does that do?

500
00:22:05,260 --> 00:22:08,290
Well, graphically, it steepens
the budget constraint.

501
00:22:08,290 --> 00:22:13,120
What that means is it's raised
the opportunity cost of first

502
00:22:13,120 --> 00:22:15,470
period consumption.

503
00:22:15,470 --> 00:22:17,550
First period consumption is now
effectively more expensive

504
00:22:17,550 --> 00:22:22,040
because I'm forgoing a better
savings rate by eating today.

505
00:22:22,040 --> 00:22:25,190
The more of my $80,000 I consume
today, the less I get

506
00:22:25,190 --> 00:22:26,370
to save for tomorrow.

507
00:22:26,370 --> 00:22:28,390
And that's now a better deal to
save for tomorrow because

508
00:22:28,390 --> 00:22:29,720
I'm getting a higher interest
rate on that.

509
00:22:33,660 --> 00:22:34,730
So what does that do?

510
00:22:34,730 --> 00:22:36,380
Well that has two effects.

511
00:22:36,380 --> 00:22:38,640
Just like a change in the wage
rate has two effects-- a

512
00:22:38,640 --> 00:22:41,920
substitution effect and
an income effect.

513
00:22:41,920 --> 00:22:46,650
The substitution effect, which
we can unambiguously sign, is

514
00:22:46,650 --> 00:22:50,760
the fact that now first period
consumption's gotten more

515
00:22:50,760 --> 00:22:53,600
expensive, so we
do less of it.

516
00:22:53,600 --> 00:22:55,570
Substitution effects are always
price goes up, you do

517
00:22:55,570 --> 00:22:56,860
less of the activity.

518
00:22:56,860 --> 00:22:59,530
The substitution effect is first
period consumption's

519
00:22:59,530 --> 00:23:01,180
gotten more expensive, there'll
be less of it.

520
00:23:01,180 --> 00:23:03,510
Now here, once again, don't
slip into thinking about

521
00:23:03,510 --> 00:23:04,200
savings yet.

522
00:23:04,200 --> 00:23:05,720
You'll really get yourself
in trouble, and

523
00:23:05,720 --> 00:23:07,170
it's a natural tendency.

524
00:23:07,170 --> 00:23:10,000
Model consumption that makes
savings a residual.

525
00:23:10,000 --> 00:23:11,880
So the activity we're modeling
here is first period

526
00:23:11,880 --> 00:23:12,630
consumption.

527
00:23:12,630 --> 00:23:14,810
The price of first period
consumption's gone up, so you

528
00:23:14,810 --> 00:23:15,800
do less of it.

529
00:23:15,800 --> 00:23:18,860
That's the substitution
effect.

530
00:23:18,860 --> 00:23:22,670
The income effect is
you're now richer.

531
00:23:22,670 --> 00:23:23,620
And you might say what do
you mean I'm richer?

532
00:23:23,620 --> 00:23:26,860
I still have the same
$80,000 in income.

533
00:23:26,860 --> 00:23:31,250
But any given dollar of savings
yields more income in

534
00:23:31,250 --> 00:23:32,920
the second period.

535
00:23:32,920 --> 00:23:35,860
So, overall, you're richer.

536
00:23:35,860 --> 00:23:38,500
If you take the perspective of
saying I have two periods in

537
00:23:38,500 --> 00:23:40,910
this model-- first and
second period.

538
00:23:40,910 --> 00:23:42,920
Any given level of savings
makes me richer

539
00:23:42,920 --> 00:23:43,490
in the second period.

540
00:23:43,490 --> 00:23:45,470
That means I'm richer.

541
00:23:45,470 --> 00:23:49,220
If I'm richer, I consume more of
everything including first

542
00:23:49,220 --> 00:23:50,680
period consumption.

543
00:23:50,680 --> 00:23:52,140
So first period consumption
goes up

544
00:23:52,140 --> 00:23:53,370
from the income effect.

545
00:23:53,370 --> 00:23:54,450
I find this confusing.

546
00:23:54,450 --> 00:23:56,440
I don't know if you guys do, but
once again-- run through

547
00:23:56,440 --> 00:23:57,520
this again.

548
00:23:57,520 --> 00:24:00,840
I'm richer because for any given
amount of savings I now

549
00:24:00,840 --> 00:24:03,770
have a total larger sum of
money over both periods.

550
00:24:03,770 --> 00:24:06,770
When I'm richer I consume
more of everything.

551
00:24:06,770 --> 00:24:09,060
One of the things that I consume
more of is first

552
00:24:09,060 --> 00:24:10,070
period consumption.

553
00:24:10,070 --> 00:24:11,620
So, actually, first period
consumption goes

554
00:24:11,620 --> 00:24:12,870
up, and I save less.

555
00:24:12,870 --> 00:24:15,160
It's sort of bizarre.

556
00:24:15,160 --> 00:24:16,500
Because I'm getting
more return to my

557
00:24:16,500 --> 00:24:19,480
savings I save less.

558
00:24:19,480 --> 00:24:21,090
Here is the way I like
to think of the

559
00:24:21,090 --> 00:24:24,080
intuition to make it easier.

560
00:24:24,080 --> 00:24:26,920
The way I like to think of the
intuition is imagine that you

561
00:24:26,920 --> 00:24:29,510
have a goal for saving--
something I call a target

562
00:24:29,510 --> 00:24:30,620
savings level.

563
00:24:30,620 --> 00:24:33,280
Imagine you said, look.

564
00:24:33,280 --> 00:24:37,840
Imagine you said that I really
want to make sure that I have

565
00:24:37,840 --> 00:24:41,950
certain level of savings
to live on next year.

566
00:24:41,950 --> 00:24:45,450
Well if the interest rate goes
up, I can save less to get to

567
00:24:45,450 --> 00:24:47,030
that target.

568
00:24:47,030 --> 00:24:47,350
Right?

569
00:24:47,350 --> 00:24:50,930
If I have a target, c2, and the
interest rate is higher I

570
00:24:50,930 --> 00:24:54,490
can consume more c1 and still
hit my target of c2.

571
00:24:54,490 --> 00:24:56,150
So that's the income effect.

572
00:24:56,150 --> 00:24:58,920
I can effectively consume more
c1 because I'm made richer

573
00:24:58,920 --> 00:25:01,890
because any given level of
savings allows me to consume

574
00:25:01,890 --> 00:25:03,270
more the next period.

575
00:25:03,270 --> 00:25:05,450
Now the target's an extreme
case, but I find it a useful

576
00:25:05,450 --> 00:25:08,240
intuition for thinking about
what's going on.

577
00:25:08,240 --> 00:25:11,190
And that's the income effect.

578
00:25:11,190 --> 00:25:14,240
Now, obviously, as with
anything, this is ambiguous.

579
00:25:14,240 --> 00:25:17,810
If you go to Figure 21-3 now
here's a case where the income

580
00:25:17,810 --> 00:25:20,070
effect dominates.

581
00:25:20,070 --> 00:25:21,360
Well, actually, go
back to 21-4.

582
00:25:21,360 --> 00:25:22,710
Let's finish this example.

583
00:25:22,710 --> 00:25:25,280
So here with the substitution
effect dominating, when the

584
00:25:25,280 --> 00:25:28,570
interest rate goes up I consume
less in period one

585
00:25:28,570 --> 00:25:30,000
which means I save more.

586
00:25:30,000 --> 00:25:31,220
And that was prior intuition.

587
00:25:31,220 --> 00:25:32,890
A higher interest rate
means you save more.

588
00:25:32,890 --> 00:25:35,270
But we'll work through the
mechanics of how we get there.

589
00:25:35,270 --> 00:25:37,260
And the reason the mechanics
is important is because of

590
00:25:37,260 --> 00:25:39,620
Figure 21-3.

591
00:25:39,620 --> 00:25:45,950
Which as in 21-3, the interest
rate goes up, but I save less.

592
00:25:45,950 --> 00:25:50,110
The interest rate goes up, but
I consume more in period one

593
00:25:50,110 --> 00:25:53,620
and therefore save less.

594
00:25:53,620 --> 00:25:56,270
And that's consistent with
this target notion.

595
00:25:56,270 --> 00:25:57,520
That basically I'm so--

596
00:25:57,520 --> 00:26:00,830
All I care about-- let's say
in the limit if all I care

597
00:26:00,830 --> 00:26:02,650
about in the limit is exactly
what I consume the second

598
00:26:02,650 --> 00:26:06,590
period, then, basically, my
period one's consumption will

599
00:26:06,590 --> 00:26:09,470
definitely go up from a raise in
the interest rate because,

600
00:26:09,470 --> 00:26:11,480
basically, I'm saying, look, all
I care about is what I get

601
00:26:11,480 --> 00:26:11,950
in the second period.

602
00:26:11,950 --> 00:26:14,390
Now I can save less and
get to that target.

603
00:26:14,390 --> 00:26:16,410
So my consumption first
period goes up.

604
00:26:16,410 --> 00:26:19,580
The income effect dominates.

605
00:26:19,580 --> 00:26:21,800
So the bottom line is, just
like with labor supply, we

606
00:26:21,800 --> 00:26:23,350
can't tell.

607
00:26:23,350 --> 00:26:26,900
Unlike with goods where it's
rare to see a Giffen good,

608
00:26:26,900 --> 00:26:29,530
here we honestly don't know
whether a raise in the

609
00:26:29,530 --> 00:26:31,870
interest rates will raise
savings or lower savings.

610
00:26:31,870 --> 00:26:33,630
It all depends on the
strength of the

611
00:26:33,630 --> 00:26:34,880
substitution and income effects.

612
00:26:38,040 --> 00:26:40,120
Let me actually say one of the
most disturbing things in

613
00:26:40,120 --> 00:26:44,480
empirical economics is we
actually do have no idea.

614
00:26:44,480 --> 00:26:46,830
Literally, there's no convincing
study out there

615
00:26:46,830 --> 00:26:48,900
which even tells us which way
the effect of interest rates

616
00:26:48,900 --> 00:26:49,890
goes on savings.

617
00:26:49,890 --> 00:26:52,380
We think probably the
substitution effect dominates,

618
00:26:52,380 --> 00:26:54,490
but it's been very
hard to find a

619
00:26:54,490 --> 00:26:56,090
convincing estimate of that.

620
00:26:56,090 --> 00:26:57,000
So it's a little bit disturbing

621
00:26:57,000 --> 00:26:58,370
for empirical economics.

622
00:26:58,370 --> 00:27:00,970
We'll typically assume it
dominates, but don't

623
00:27:00,970 --> 00:27:03,660
necessarily assume that
in the real world.

624
00:27:03,660 --> 00:27:05,700
OK, questions about that--

625
00:27:05,700 --> 00:27:07,380
intertemporal choice
framework?

626
00:27:07,380 --> 00:27:12,120
OK, now, with that in mind,
let's now talk about how

627
00:27:12,120 --> 00:27:13,400
capital markets work.

628
00:27:17,660 --> 00:27:19,600
How do capital markets work?

629
00:27:19,600 --> 00:27:22,050
And the key concept for thinking
about capital markets

630
00:27:22,050 --> 00:27:24,560
is the concept of
present value.

631
00:27:30,180 --> 00:27:32,480
And the concept of the present
value is simple.

632
00:27:32,480 --> 00:27:38,360
It's that $1 tomorrow is worth
less than $1 today.

633
00:27:38,360 --> 00:27:42,660
$1 tomorrow is worth
less than $1 today.

634
00:27:42,660 --> 00:27:43,880
And why is that?

635
00:27:43,880 --> 00:27:46,660
It's because if I had the
dollar today, I could've

636
00:27:46,660 --> 00:27:49,670
invested it in something
productive and had 1 plus i

637
00:27:49,670 --> 00:27:52,190
dollars tomorrow.

638
00:27:52,190 --> 00:27:54,230
So if you give me a dollar today
I could have 1 plus i

639
00:27:54,230 --> 00:27:55,010
dollars tomorrow.

640
00:27:55,010 --> 00:27:57,740
If you give it to me tomorrow,
I just have $1.

641
00:27:57,740 --> 00:28:00,610
So by definition, $1 today is
worth more because I have the

642
00:28:00,610 --> 00:28:02,920
opportunity to save it.

643
00:28:02,920 --> 00:28:04,150
Whereas a $1 tomorrow
I don't have the

644
00:28:04,150 --> 00:28:04,780
opportunity to save it.

645
00:28:04,780 --> 00:28:07,770
It's too late.

646
00:28:07,770 --> 00:28:12,510
So the key point is you can't
add up dollars that you

647
00:28:12,510 --> 00:28:16,160
receive in different periods.

648
00:28:16,160 --> 00:28:17,920
So, in other words,
if I said to you--

649
00:28:17,920 --> 00:28:20,430
if this intertemporal choice
graph was back pizzas and

650
00:28:20,430 --> 00:28:25,570
movies, and I said you have
nine pizza plus movies.

651
00:28:25,570 --> 00:28:26,490
You have a total of nine.

652
00:28:26,490 --> 00:28:28,280
You'd be like, what the
hell does that mean?

653
00:28:28,280 --> 00:28:31,960
It matters if it's nine pizzas
and zero movies or five movies

654
00:28:31,960 --> 00:28:32,580
and four pizzas?

655
00:28:32,580 --> 00:28:33,370
I don't know what that means.

656
00:28:33,370 --> 00:28:33,910
Those are different things.

657
00:28:33,910 --> 00:28:35,800
You can't add them up.

658
00:28:35,800 --> 00:28:37,530
You can't just say
I have nine.

659
00:28:37,530 --> 00:28:41,360
Well consumption over time--
it's the same thing.

660
00:28:41,360 --> 00:28:43,890
You can't just add up your
consumption tomorrow and

661
00:28:43,890 --> 00:28:46,840
consumption today or a dollar
tomorrow and a dollar today.

662
00:28:46,840 --> 00:28:50,200
They're different things.

663
00:28:50,200 --> 00:28:54,090
And so you have to account for
the fact that $1 tomorrow is

664
00:28:54,090 --> 00:28:57,360
worth less than $1 today in
trying to add them up.

665
00:28:57,360 --> 00:29:02,445
And the way we do that is we
actually do it through the

666
00:29:02,445 --> 00:29:03,620
concept of present value.

667
00:29:03,620 --> 00:29:07,290
And the idea of present value
is to translate all future

668
00:29:07,290 --> 00:29:10,550
dollars into today's dollars.

669
00:29:10,550 --> 00:29:12,920
Translate all future dollars
into today's dollars

670
00:29:12,920 --> 00:29:17,550
recognizing the fact they're
less valuable in the future.

671
00:29:17,550 --> 00:29:21,540
So the concept of present value
is the concept of any

672
00:29:21,540 --> 00:29:26,500
future payment's value from
the perspective of today.

673
00:29:26,500 --> 00:29:28,400
And you should know that any
future payment will be worth

674
00:29:28,400 --> 00:29:30,050
less than a payment today.

675
00:29:30,050 --> 00:29:32,820
How much less-- that's what
present value tells you.

676
00:29:32,820 --> 00:29:38,050
How much is a future payment
worth in today's terms?

677
00:29:38,050 --> 00:29:43,010
So suppose that the interest
rate is 10%.

678
00:29:43,010 --> 00:29:47,220
Suppose the interest rate
is 10%, and you want to

679
00:29:47,220 --> 00:29:50,300
have $100 next year.

680
00:29:50,300 --> 00:29:53,170
So you know next year there's
something you want to buy, and

681
00:29:53,170 --> 00:29:56,750
you have to decide how much do
I have to save today to have

682
00:29:56,750 --> 00:30:02,970
$100 in period two.

683
00:30:02,970 --> 00:30:04,490
How much do I have to
save today to have

684
00:30:04,490 --> 00:30:07,000
$100 in period two?

685
00:30:07,000 --> 00:30:11,290
Well if you put in an amount,
PV, into the bank--

686
00:30:11,290 --> 00:30:15,970
you put PV into the bank, then
you know next year you're

687
00:30:15,970 --> 00:30:19,070
going to have-- if you put in
PV in period one, next year

688
00:30:19,070 --> 00:30:25,210
you're going to have
PV times 1 plus i.

689
00:30:25,210 --> 00:30:27,270
You're going to have your PV
plus all the interest you

690
00:30:27,270 --> 00:30:34,730
earned on it, or in our
example, PV times 1.1.

691
00:30:34,730 --> 00:30:38,870
So what that says is that,
basically, you have to put in

692
00:30:38,870 --> 00:30:43,500
100 over 1.1 into the
bank today, or

693
00:30:43,500 --> 00:30:48,300
90.9 dollars, $90.90.

694
00:30:48,300 --> 00:30:53,810
If you put $90.90 in the bank
today, you will have $100

695
00:30:53,810 --> 00:30:56,730
tomorrow or $100 next year--
whenever the periodicity of

696
00:30:56,730 --> 00:30:59,940
the interest rate.

697
00:30:59,940 --> 00:31:05,280
So, basically, more generally,
the present value of any

698
00:31:05,280 --> 00:31:12,570
stream of payments is equal to
that stream's future value--

699
00:31:12,570 --> 00:31:13,695
I'm going to write
it over here.

700
00:31:13,695 --> 00:31:15,570
It's bigger.

701
00:31:15,570 --> 00:31:17,750
The present value of any stream
of payments is that

702
00:31:17,750 --> 00:31:22,400
stream's future value over 1
plus the interest rate to the

703
00:31:22,400 --> 00:31:27,000
t, where t is the year in
which you get the money.

704
00:31:27,000 --> 00:31:33,800
So any future money you get in
year t is worth that amount

705
00:31:33,800 --> 00:31:37,806
you get over 1 plus the interest
rate to the t.

706
00:31:40,610 --> 00:31:43,590
So, basically, the point
is you have to weigt.

707
00:31:43,590 --> 00:31:46,300
Any money you're going to get,
you to weight by how far into

708
00:31:46,300 --> 00:31:49,540
the future it is, just like
if you're adding up these

709
00:31:49,540 --> 00:31:50,380
different goods.

710
00:31:50,380 --> 00:31:52,950
So, essentially, this is kind
of like saying let's add a

711
00:31:52,950 --> 00:31:57,770
converter machine which can
convert pizza into movies.

712
00:31:57,770 --> 00:32:00,425
Then I could say well I'll
just take pizza, put it

713
00:32:00,425 --> 00:32:01,760
through the converter machine,
and that'll tell me how many

714
00:32:01,760 --> 00:32:03,130
movies I have. That's
what a utility

715
00:32:03,130 --> 00:32:05,590
function basically does.

716
00:32:05,590 --> 00:32:07,160
This we're saying the
interest rate is

717
00:32:07,160 --> 00:32:09,100
the converter function.

718
00:32:09,100 --> 00:32:11,490
This present value formula is
the converter function by

719
00:32:11,490 --> 00:32:14,080
which we convert two goods
that are different

720
00:32:14,080 --> 00:32:15,350
into the same good.

721
00:32:15,350 --> 00:32:16,730
You convert them through
this formula.

722
00:32:19,890 --> 00:32:24,800
So, basically, suppose that you
say to me, "Look, loan me

723
00:32:24,800 --> 00:32:29,290
$30, and I'll pay you back $10
a year each of the next three

724
00:32:29,290 --> 00:32:33,450
years." Well I should
say, "Wait a second.

725
00:32:33,450 --> 00:32:36,500
What's the value of that to me?"
Well the present value of

726
00:32:36,500 --> 00:32:40,320
those repayments is I'm going
to have $10 in one year, so

727
00:32:40,320 --> 00:32:42,470
that's $10 over 1 plus i.

728
00:32:42,470 --> 00:32:45,360
Let's say the interest
rate's 10% again.

729
00:32:45,360 --> 00:32:46,145
Next year I got $10.

730
00:32:46,145 --> 00:32:48,510
That's worth 10 over 1 plus 1.

731
00:32:48,510 --> 00:32:50,260
The year after, you're going
to give me 10 more dollars,

732
00:32:50,260 --> 00:32:53,610
but that's worth 10 over 1 plus
1 squared because that's

733
00:32:53,610 --> 00:32:54,700
in two years.

734
00:32:54,700 --> 00:32:57,730
If I had that money today, I
could've invested it, earned

735
00:32:57,730 --> 00:33:00,600
10% and then 10% on that.

736
00:33:00,600 --> 00:33:02,770
And, likewise, the money you
give me in the third year is

737
00:33:02,770 --> 00:33:05,180
worth 10 over 1.1 cubed.

738
00:33:05,180 --> 00:33:08,260
If you'd given me that money
today, I could've invested it

739
00:33:08,260 --> 00:33:10,930
and and earned interest
three times on it.

740
00:33:10,930 --> 00:33:13,770
So the bottom line is
your repayments

741
00:33:13,770 --> 00:33:18,110
are only worth $24.87.

742
00:33:18,110 --> 00:33:22,030
So I've just given you $30 today
in return for a stream

743
00:33:22,030 --> 00:33:24,740
of payments that's only
worth $24.87 today.

744
00:33:24,740 --> 00:33:27,980
I've lost money from that loan
because I gave you the money

745
00:33:27,980 --> 00:33:29,460
today, and you're paying me back
in the future when the

746
00:33:29,460 --> 00:33:31,780
money's worth less.

747
00:33:31,780 --> 00:33:34,750
So, basically, the general
formula we have is that the

748
00:33:34,750 --> 00:33:41,830
present value of any stream of
future payments is that the

749
00:33:41,830 --> 00:33:45,040
amount of the future payment--
let's call it f for any fixed

750
00:33:45,040 --> 00:33:48,570
stream of future payments, $10
forever or $15 forever--

751
00:33:48,570 --> 00:33:56,550
fixed stream of that amount, f,
times 1 over 1 plus i, plus

752
00:33:56,550 --> 00:34:03,790
1 over 1 plus i squared, plus
da da da da, plus 1 over 1

753
00:34:03,790 --> 00:34:06,850
plus i to the t.

754
00:34:06,850 --> 00:34:09,949
So if you're going to pay me a
fixed amount, f, for t years,

755
00:34:09,949 --> 00:34:13,210
here what it's worth
to me today.

756
00:34:13,210 --> 00:34:15,770
You pay me a fixed amount, f,
for t years, it's worth this

757
00:34:15,770 --> 00:34:17,830
much to me today.

758
00:34:17,830 --> 00:34:19,680
I'm accounting for how far
off in the future it is.

759
00:34:22,670 --> 00:34:25,989
Now one important trick we're
going to do now for the rest

760
00:34:25,989 --> 00:34:28,710
of the semester is we're going
to take the trick of saying

761
00:34:28,710 --> 00:34:29,540
this is actually--

762
00:34:29,540 --> 00:34:31,210
well this is a messy formula.

763
00:34:31,210 --> 00:34:33,820
It's actually a rather easy
formula to write down if the

764
00:34:33,820 --> 00:34:36,810
future stream of payments is
infinite, if we have what we

765
00:34:36,810 --> 00:34:40,150
call a perpetuity.

766
00:34:40,150 --> 00:34:41,400
If we have what we call
a perpetuity.

767
00:34:45,630 --> 00:34:48,010
A perpetuity is a future stream
of payments that goes

768
00:34:48,010 --> 00:34:52,610
on forever or long enough that
we'd consider it forever.

769
00:34:52,610 --> 00:34:55,199
Fifty years is probably
good enough.

770
00:34:55,199 --> 00:34:58,990
If you have a perpetuity,
then this formula

771
00:34:58,990 --> 00:35:02,940
can be reduced to--

772
00:35:02,940 --> 00:35:06,140
the present value of any
perpetuity is the amount of

773
00:35:06,140 --> 00:35:09,720
that perpetuity over
the interest rate.

774
00:35:09,720 --> 00:35:12,150
It's just taking the infinite
sum of that product.

775
00:35:12,150 --> 00:35:13,480
They're just taking
the infinite sum.

776
00:35:13,480 --> 00:35:15,240
Those mathematically inclined
will know this already.

777
00:35:15,240 --> 00:35:17,920
But it's just taking the
infinite sum here, you can get

778
00:35:17,920 --> 00:35:19,390
this formula.

779
00:35:19,390 --> 00:35:22,980
So any perpetuity, if you're
getting a payment forever, the

780
00:35:22,980 --> 00:35:25,660
value of that payment today-- so
if I said I'll give you $10

781
00:35:25,660 --> 00:35:28,295
forever and the interest rate's
going to be 10% then

782
00:35:28,295 --> 00:35:31,150
you'd say that's worth
$100 to me.

783
00:35:31,150 --> 00:35:34,630
If I'm going to give you $10
forever at a 10% interest

784
00:35:34,630 --> 00:35:39,310
rate, then you'd say well that's
worth $9.90 the next

785
00:35:39,310 --> 00:35:41,320
year and $8 something the
next year, et cetera.

786
00:35:41,320 --> 00:35:46,640
And if I add all those up, I get
approximately the amount

787
00:35:46,640 --> 00:35:48,270
of the payment over
the interest rate.

788
00:35:51,600 --> 00:35:58,490
So, basically, that is what
determines present value.

789
00:35:58,490 --> 00:36:02,530
Now we can flip this around and
we could say, OK, well, if

790
00:36:02,530 --> 00:36:05,560
that's present value what
determines future value?

791
00:36:05,560 --> 00:36:10,510
Well the future value of getting
a payment today--

792
00:36:10,510 --> 00:36:13,030
So that's the present value of
getting payments tomorrow.

793
00:36:13,030 --> 00:36:17,120
The only other thing is what's
the future value?

794
00:36:17,120 --> 00:36:21,610
What's the future value of
getting a stream of payments

795
00:36:21,610 --> 00:36:22,710
starting today?

796
00:36:22,710 --> 00:36:25,390
So let's say, starting today,
I'm going to get $10.

797
00:36:25,390 --> 00:36:27,060
I'm going to get it for a
certain number of years.

798
00:36:27,060 --> 00:36:29,220
What's that going to be worth
at the end of the day given

799
00:36:29,220 --> 00:36:31,070
that I can save it
along the way.

800
00:36:31,070 --> 00:36:37,910
So, in other words, if you
give me $10 today--

801
00:36:37,910 --> 00:36:42,920
if you give me $10 today, well
then in one year, next year, I

802
00:36:42,920 --> 00:36:48,150
have $11 because I got to save
it at the interest rate.

803
00:36:48,150 --> 00:36:52,670
So if you give me $10 today,
next year I'll have $11.

804
00:36:52,670 --> 00:36:57,870
Now let's say that I
then keep it in the

805
00:36:57,870 --> 00:36:59,460
bank for another year.

806
00:36:59,460 --> 00:37:07,490
Well the next year, it's worth
10 times 1 plus i squared, so

807
00:37:07,490 --> 00:37:13,250
10 times 1.1 squared, 10
times 1.1 squared, or

808
00:37:13,250 --> 00:37:20,660
$12.10 and so on.

809
00:37:20,660 --> 00:37:27,700
So, basically, the point is that
at the end of each year I

810
00:37:27,700 --> 00:37:31,280
earn the interest on my original
$10, plus I earn the

811
00:37:31,280 --> 00:37:34,680
interest on the interest I
earned the previous periods.

812
00:37:34,680 --> 00:37:38,750
So in the long run, at the end
of t years, which of the

813
00:37:38,750 --> 00:37:43,140
future value, is the amount
invested, f, times 1

814
00:37:43,140 --> 00:37:46,110
plus i to the t.

815
00:37:46,110 --> 00:37:47,600
That's your future value.

816
00:37:47,600 --> 00:37:49,970
So if you invest a given amount
of money today for t

817
00:37:49,970 --> 00:37:54,570
years, you end up
with that much.

818
00:37:54,570 --> 00:37:56,620
If you invest a given amount,
f, today you end

819
00:37:56,620 --> 00:37:57,170
up with that much--

820
00:37:57,170 --> 00:38:00,810
And the key point, the key
insight, is the miracle of

821
00:38:00,810 --> 00:38:03,140
compounding.

822
00:38:03,140 --> 00:38:06,130
The miracle of compounding is
the point that you earn

823
00:38:06,130 --> 00:38:13,580
interest on your interest. And
what this means is the earlier

824
00:38:13,580 --> 00:38:18,110
you save, the more you'll
have later on.

825
00:38:18,110 --> 00:38:22,420
So there's an example in the
book which is very important.

826
00:38:22,420 --> 00:38:23,980
So it's actually thinking
about--

827
00:38:23,980 --> 00:38:25,540
let's think for a minute
about retirement.

828
00:38:25,540 --> 00:38:26,720
You might say this
is sort of crazy.

829
00:38:26,720 --> 00:38:28,650
Maybe not crazy for an old guy
like me, but you're thinking

830
00:38:28,650 --> 00:38:30,010
I'm just starting
on my career.

831
00:38:30,010 --> 00:38:31,320
Why would I think about
retirement?

832
00:38:31,320 --> 00:38:33,340
Here's why you want
to think about it.

833
00:38:33,340 --> 00:38:38,070
Let's say, for example, that
you plan to work full time

834
00:38:38,070 --> 00:38:40,640
from age 22 to age 70.

835
00:38:40,640 --> 00:38:41,990
You've got a great idea.

836
00:38:41,990 --> 00:38:43,290
Screw grad school.

837
00:38:43,290 --> 00:38:44,900
You're going right to work.

838
00:38:44,900 --> 00:38:46,250
You've got a great idea,
and you know you want

839
00:38:46,250 --> 00:38:47,020
to retire at 70.

840
00:38:47,020 --> 00:38:53,640
So you plan to work full time
from age 22 to age 70.

841
00:38:53,640 --> 00:38:57,030
And let's say that you want to
save money for your retirement

842
00:38:57,030 --> 00:38:58,030
because you're going
to retire at 70.

843
00:38:58,030 --> 00:38:58,840
You're going to live forever.

844
00:38:58,840 --> 00:39:00,140
You're a healthy young person.

845
00:39:00,140 --> 00:39:02,000
You think you're going to
live forever at 70.

846
00:39:02,000 --> 00:39:03,840
So you want to have money
around when you retire.

847
00:39:03,840 --> 00:39:05,230
And let's say that the
interest rate you

848
00:39:05,230 --> 00:39:08,680
can save at is 7%.

849
00:39:08,680 --> 00:39:13,120
So you can save money for your
retirement at 7%, and that's

850
00:39:13,120 --> 00:39:13,600
your choice.

851
00:39:13,600 --> 00:39:16,830
Now let's consider two different
savings plans.

852
00:39:16,830 --> 00:39:21,640
Savings plan one is that I'm
going to save $3,000.

853
00:39:21,640 --> 00:39:24,960
You're going to save $3,000
right off the bat.

854
00:39:24,960 --> 00:39:27,390
And for the first 15 years
of your working life--

855
00:39:27,390 --> 00:39:29,550
so from 22 to 37--

856
00:39:29,550 --> 00:39:32,450
you're going to save $3,000.

857
00:39:32,450 --> 00:39:44,690
You're going to save $3,000 a
year savings for 15 years, and

858
00:39:44,690 --> 00:39:45,870
then nothing.

859
00:39:45,870 --> 00:39:47,890
And then once you're 37 and
you've got to start worrying

860
00:39:47,890 --> 00:39:49,770
about kids' college and
mortgage, you're not going to

861
00:39:49,770 --> 00:39:51,150
save anything.

862
00:39:51,150 --> 00:39:53,355
So from 22 to 37, when you're
living high on the hog, you've

863
00:39:53,355 --> 00:39:56,440
got no obligations, you're going
to save. Once you're 37,

864
00:39:56,440 --> 00:39:58,280
you've got a house, you've got
kids, you've got things that

865
00:39:58,280 --> 00:39:59,730
are expensive, you're not
going to save anymore.

866
00:39:59,730 --> 00:40:01,600
So then you go to zero.

867
00:40:01,600 --> 00:40:07,400
Zero savings from age
37 to age 70.

868
00:40:07,400 --> 00:40:09,590
That's a pretty bold plan.

869
00:40:09,590 --> 00:40:12,720
You're just going to save 15
years then zero savings.

870
00:40:12,720 --> 00:40:14,190
Well what do you get?

871
00:40:14,190 --> 00:40:19,360
Well after 15 years, if you use
our future value formula,

872
00:40:19,360 --> 00:40:22,410
if you save $3,000 every year,
you work out that you will

873
00:40:22,410 --> 00:40:27,670
have $75,387 in the bank.

874
00:40:27,670 --> 00:40:31,010
So it's more than 45-- is not
just 3,000 times 15 because

875
00:40:31,010 --> 00:40:33,300
you get the compounding.

876
00:40:33,300 --> 00:40:34,760
It's not just 3,000 times 15.

877
00:40:34,760 --> 00:40:36,820
You actually get more than
that because you got the

878
00:40:36,820 --> 00:40:38,980
compounding along the way.

879
00:40:38,980 --> 00:40:41,970
Then if you just let it sit
there in the bank-- you don't

880
00:40:41,970 --> 00:40:42,500
do anything.

881
00:40:42,500 --> 00:40:43,300
No more active savings.

882
00:40:43,300 --> 00:40:44,670
You let it sit there.

883
00:40:44,670 --> 00:40:50,460
Then by the time you retire,
you have that $75,387 times

884
00:40:50,460 --> 00:40:54,940
1.07 to the 33 because you
let that money sit

885
00:40:54,940 --> 00:40:57,960
there for 33 years.

886
00:40:57,960 --> 00:40:59,720
You let that money sit
there for 33 years.

887
00:40:59,720 --> 00:41:08,330
That works out to be $703,010.

888
00:41:08,330 --> 00:41:11,880
So by saving for 15 years-- all
you did was save $3,000

889
00:41:11,880 --> 00:41:15,500
for 15 years, a fraction
of your career.

890
00:41:15,500 --> 00:41:20,730
And you retire with $703,000.

891
00:41:20,730 --> 00:41:23,630
Now we'll contrast that with
an alternative plan.

892
00:41:23,630 --> 00:41:27,490
My alternative plan is I'm going
to save nothing for the

893
00:41:27,490 --> 00:41:31,460
first 15 years because I figure,
like, I'm young.

894
00:41:31,460 --> 00:41:32,020
I'm gonna party.

895
00:41:32,020 --> 00:41:32,900
I'm going to use
the money now.

896
00:41:32,900 --> 00:41:33,590
I'll save later.

897
00:41:33,590 --> 00:41:35,490
I'm nowhere near retirement.

898
00:41:35,490 --> 00:41:36,740
Then I get to 37.

899
00:41:36,740 --> 00:41:37,560
I say, wait a second, I'm

900
00:41:37,560 --> 00:41:38,690
starting to see more mortality.

901
00:41:38,690 --> 00:41:39,910
I better worry about
retirement.

902
00:41:39,910 --> 00:41:43,700
Then I start to save, and I save
for the next 33 years.

903
00:41:43,700 --> 00:41:51,270
So the new plan is zero per year
from age 22 to 37, and

904
00:41:51,270 --> 00:41:56,980
then $3,000 a year
from 37 to 70.

905
00:41:56,980 --> 00:41:58,580
So it's a lot more savings.

906
00:41:58,580 --> 00:42:02,400
You're saving for more than
twice as long, more

907
00:42:02,400 --> 00:42:05,180
than twice as long.

908
00:42:05,180 --> 00:42:06,650
What do you end up with?

909
00:42:06,650 --> 00:42:13,760
You end up with $356,800--

910
00:42:13,760 --> 00:42:19,050
half, just slightly more than
half, than what you end up

911
00:42:19,050 --> 00:42:21,630
with the first plan, even though
you save for twice as

912
00:42:21,630 --> 00:42:22,880
many years.

913
00:42:25,020 --> 00:42:29,220
This is like the parents'
lecture why you should save.

914
00:42:29,220 --> 00:42:33,620
The point is that saving early
lets you ride the wave of

915
00:42:33,620 --> 00:42:36,090
compounding for many,
many years.

916
00:42:36,090 --> 00:42:39,520
Savings late does not
let you do that.

917
00:42:39,520 --> 00:42:43,370
And as a result, you end
up with less money.

918
00:42:43,370 --> 00:42:45,530
I take my kids to the science
museum, and at the science

919
00:42:45,530 --> 00:42:46,960
museum they have these
little ramps.

920
00:42:46,960 --> 00:42:48,010
And you can drop a ball.

921
00:42:48,010 --> 00:42:51,770
And one is flat then steep, and
one is steep then flat.

922
00:42:51,770 --> 00:42:54,420
And the one that's steep then
flat always wins because

923
00:42:54,420 --> 00:42:58,450
there's compounding in
acceleration the same way.

924
00:42:58,450 --> 00:43:01,430
The point is building up early
and then riding that velocity

925
00:43:01,430 --> 00:43:05,610
going forward is a lot better
than starting late.

926
00:43:05,610 --> 00:43:08,070
Questions about that?

927
00:43:08,070 --> 00:43:10,640
So make sure when you get those
jobs, and they offer

928
00:43:10,640 --> 00:43:12,245
you-- we'll talk next time about
savings incentives-- and

929
00:43:12,245 --> 00:43:15,230
they offer you those good 401K
packages, that you take them,

930
00:43:15,230 --> 00:43:17,810
and don't say I'll worry
about that later.

931
00:43:17,810 --> 00:43:20,580
Now, one last thing.

932
00:43:20,580 --> 00:43:23,650
Last thing I want to cover is
that we've ignored, so far,

933
00:43:23,650 --> 00:43:25,920
the whole concept
of inflation.

934
00:43:25,920 --> 00:43:28,330
When I've talked about savings,
I've presumed that

935
00:43:28,330 --> 00:43:29,660
you've saved the money and
it's worth something.

936
00:43:29,660 --> 00:43:31,750
But who the hell knows
what $703,000 will

937
00:43:31,750 --> 00:43:36,180
be worth in 48 years?

938
00:43:36,180 --> 00:43:37,450
What's that even going
to be worth?

939
00:43:37,450 --> 00:43:38,750
How do we even think
about that?

940
00:43:38,750 --> 00:43:41,160
Well we have to account for the
fact that stuff's going to

941
00:43:41,160 --> 00:43:42,880
be more expensive.

942
00:43:42,880 --> 00:43:46,880
So we have to account for
inflation in doing this.

943
00:43:46,880 --> 00:43:49,710
And the way we do this is by
recognizing that what we've

944
00:43:49,710 --> 00:43:51,940
done so far is we've
talked about the

945
00:43:51,940 --> 00:43:54,950
nominal interest rate.

946
00:43:54,950 --> 00:43:56,635
By the nominal interest rate, I
meant the interest rate that

947
00:43:56,635 --> 00:43:59,620
you actually see posted
in the bank.

948
00:43:59,620 --> 00:44:04,620
But what matters, ultimately
for your well-being, is the

949
00:44:04,620 --> 00:44:09,400
real interest rate which is
what your money can do in

950
00:44:09,400 --> 00:44:13,010
terms of actually
buying goods.

951
00:44:13,010 --> 00:44:18,390
So I should not care about how
much money I have next year.

952
00:44:18,390 --> 00:44:22,390
I should care about how many
goods I can buy next year.

953
00:44:22,390 --> 00:44:23,940
The money's just paper.

954
00:44:23,940 --> 00:44:26,530
What matters is what
I can get with it.

955
00:44:26,530 --> 00:44:28,760
That's what matters.

956
00:44:28,760 --> 00:44:30,700
So let's say, for example,
I want to use

957
00:44:30,700 --> 00:44:32,190
all my money on Skittles.

958
00:44:32,190 --> 00:44:34,070
That's just what I want
to use my money on.

959
00:44:34,070 --> 00:44:38,960
So let's say I have $100,
and I want to spend

960
00:44:38,960 --> 00:44:41,230
that money on Skittles.

961
00:44:41,230 --> 00:44:43,530
And let's say Skittles
today are $1 a bag.

962
00:44:47,330 --> 00:44:52,500
And let's say the interest
rate, once again, is 10%.

963
00:44:52,500 --> 00:44:55,080
And let's say there's
no inflation.

964
00:44:55,080 --> 00:44:56,330
Inflation equals zero.

965
00:44:59,990 --> 00:45:03,930
So my choice is I can spend
$100 on Skittles

966
00:45:03,930 --> 00:45:06,020
today and get 100 bags.

967
00:45:06,020 --> 00:45:07,640
So I could have 100
bags today.

968
00:45:10,630 --> 00:45:15,050
Or I can save it, have
$110 tomorrow and

969
00:45:15,050 --> 00:45:20,700
get 110 bags of Skittles.

970
00:45:20,700 --> 00:45:21,440
That's my choice.

971
00:45:21,440 --> 00:45:22,690
That's my trade-off.

972
00:45:24,620 --> 00:45:27,650
Now let's say there's
inflation.

973
00:45:27,650 --> 00:45:33,450
Let's say that prices are rising
at 10% a year, as well.

974
00:45:33,450 --> 00:45:35,910
So the prices are rising
10% a year, as well.

975
00:45:35,910 --> 00:45:40,580
What that means is next year
Skittles cost $1.10 a bag.

976
00:45:40,580 --> 00:45:43,150
So now what's my trade-off?

977
00:45:43,150 --> 00:45:44,480
That means I could
have 100 bags

978
00:45:44,480 --> 00:45:47,940
today or 100 bags tomorrow.

979
00:45:47,940 --> 00:45:50,650
I don't get any more
Skittles tomorrow.

980
00:45:50,650 --> 00:45:53,820
I get 10 more dollars,
but who cares?

981
00:45:53,820 --> 00:45:56,230
Everything costs more.

982
00:45:56,230 --> 00:45:59,930
If everything cost 10% more and
I get a 10% interest rate,

983
00:45:59,930 --> 00:46:02,070
that interest rate is
effectively zero in terms of

984
00:46:02,070 --> 00:46:03,200
what I can buy.

985
00:46:03,200 --> 00:46:07,410
The real interest rate
is the nominal

986
00:46:07,410 --> 00:46:10,490
interest rate minus inflation.

987
00:46:13,070 --> 00:46:15,880
What I care about is
what I can buy.

988
00:46:15,880 --> 00:46:18,560
So I have to take out
of the interest rate

989
00:46:18,560 --> 00:46:21,700
what happens to prices.

990
00:46:21,700 --> 00:46:24,890
Because if prices go up,
it offsets what I'm

991
00:46:24,890 --> 00:46:26,240
earning in the bank.

992
00:46:26,240 --> 00:46:31,270
And so what I care about is I
care about what the bank posts

993
00:46:31,270 --> 00:46:32,790
minus what inflation will be.

994
00:46:32,790 --> 00:46:33,680
So it's even trickier, right?

995
00:46:33,680 --> 00:46:35,070
Because it's not about what
inflation was, it's what

996
00:46:35,070 --> 00:46:35,710
inflation will be.

997
00:46:35,710 --> 00:46:39,310
You'll have to guess what
inflation is going to be.

998
00:46:39,310 --> 00:46:41,840
And so what we care about is
this real interest rate.

999
00:46:41,840 --> 00:46:45,680
And that's why the interest rate
that banks pay, a primary

1000
00:46:45,680 --> 00:46:47,700
determinant of it
is inflation.

1001
00:46:47,700 --> 00:46:51,320
Right now, we are in the lowest
inflation period this

1002
00:46:51,320 --> 00:46:54,110
nation's seen since
World War II.

1003
00:46:54,110 --> 00:46:55,380
Core inflation--

1004
00:46:55,380 --> 00:46:56,920
we don't really get into
inflation in this course-- but

1005
00:46:56,920 --> 00:46:59,170
core inflation, which is
inflation minus some things

1006
00:46:59,170 --> 00:47:04,870
which fluctuate a lot, is
basically zero in the US.

1007
00:47:04,870 --> 00:47:06,790
So, basically, nominal interest
rates are the same as

1008
00:47:06,790 --> 00:47:08,770
real interest rates, and that's
why the interest rates

1009
00:47:08,770 --> 00:47:12,290
you see posted are so incredibly
low because there's

1010
00:47:12,290 --> 00:47:13,760
no inflation.

1011
00:47:13,760 --> 00:47:16,490
In the late 1970's, when
inflation was running at

1012
00:47:16,490 --> 00:47:21,170
10-15% a year, interest rates
were 15 to 20% a year.

1013
00:47:21,170 --> 00:47:23,110
Now it wasn't that you could
get so much more for your

1014
00:47:23,110 --> 00:47:24,500
savings in the 1970's.

1015
00:47:24,500 --> 00:47:27,010
It was just that stuff was going
to cost more next year,

1016
00:47:27,010 --> 00:47:29,820
so banks, if they wanted to
induce you to save, had to pay

1017
00:47:29,820 --> 00:47:31,550
you a higher interest rate.

1018
00:47:31,550 --> 00:47:33,120
So, essentially, banks are going
to have to pay you to

1019
00:47:33,120 --> 00:47:34,850
get you to put your money in.

1020
00:47:34,850 --> 00:47:40,230
If in 1978, when the inflation
rate was 15%--

1021
00:47:40,230 --> 00:47:43,500
if banks had offered a 3%
interest rate no one would've

1022
00:47:43,500 --> 00:47:49,880
put money in the banks because
you would end up losing

1023
00:47:49,880 --> 00:47:50,310
effectively.

1024
00:47:50,310 --> 00:47:52,760
Effectively, that's a negative
12% real interest rate.

1025
00:47:52,760 --> 00:47:56,020
So what matters is how much
the bank pays you in cash

1026
00:47:56,020 --> 00:47:58,830
minus how much more stuff is
going to cost. And that's

1027
00:47:58,830 --> 00:47:59,570
often what matters.

1028
00:47:59,570 --> 00:48:00,980
Now that's a distinction
we won't spent a lot of

1029
00:48:00,980 --> 00:48:02,880
time on later on.

1030
00:48:02,880 --> 00:48:03,860
I'll just say interest rate.

1031
00:48:03,860 --> 00:48:05,370
I won't say real
versus nominal.

1032
00:48:05,370 --> 00:48:07,840
But you've got to know in your
head that what matters is the

1033
00:48:07,840 --> 00:48:09,480
interest rate is the real
interest rate, what the bank

1034
00:48:09,480 --> 00:48:12,880
pays you, minus how much more
stuff's going to cost.

1035
00:48:12,880 --> 00:48:14,800
Questions about that?

1036
00:48:14,800 --> 00:48:15,910
Alright, we'll come
back next time.

1037
00:48:15,910 --> 00:48:16,740
There is class on Wednesday.

1038
00:48:16,740 --> 00:48:17,940
It does matter.

1039
00:48:17,940 --> 00:48:19,360
And on Wednesday we're going
to talk about the rest of

1040
00:48:19,360 --> 00:48:21,000
capital markets and people's
savings decisions.