Economics 103
Lecture # 13
Choice Over Time
And the Interest Rate:
The Microfoundations of Macroeconomics.
Interest Rates
For some reason we think these are magical or mystical.
Probably because we spend so
much time plotting and reporting
them.
However, an interest rate is just a price.
Like all prices, it is determined in a market through supply and
demand.
To understand interest rates takes only a minor adjustment to
our basic model.
What do you think that adjustment is?
We need to worry
about choice over time.
We constantly make choices across time
When you consume today,
you can’t consume that wealth
tomorrow.
When you borrow today, you
can’t consume that wealth
tomorrow.
Saving today is shifting wealth from
today to tomorrow.
We make choices over time because many goods are stocks.
Stocks are goods that yield service through time.
Any capital good is a form
of capital stock that provides
services through time.
To decide to buy one, rather
than rent, you need to consider
choices over time.
Eg. Renting an apartment vs. owning a home, is a choice that involves
intertemporal decision making.
How do we deal with this?
We just assume the goods are Consumption Today and
Consumption Tomorrow.
This is instead of assuming the goods are apples vs. oranges.
Now it is just apples today vs. apples tomorrow.
Just like there is a demand for apples, there is a demand for
apples today.
The demand for consumption today is:
“r” is the real interest rate
1+r is the amount of goods you
must pay back next period for
using them this period.
If you give up 1 unit of
consumption today, you get
back (1+r) next period.
So an interest rate is just the price of early consumption.
The interest rate is not the “price of money.”
The nominal interest rate is the “price of using money”.
But why is the demand curve positive?
Our sixth principle is called the Rate of Time Preference.
Principle #6
Other things equal, people always prefer a good today
rather than in the future.
Just using this idea, why do people want to generally smooth
consumption out over their life?
Why was it so valuable to shift consumption?
Suppose you will face one year of feasting, and one year of famine.
In the feast year your
TV is the area under the
demand, up to the Feast
level.
In the famine year your
TV is the area under the
demand curve up to the
Famine level.
Would you be better off having two years of “average” consumption?
The net gain having two average years, rather than
having a feast and then a famine year.
If there is a demand for consumption today, there must be a
supply.
We don’t “time warp” goods from the future to eat today, so
where do they come from?
They come from savers! Savers allow others to borrow.
Why is the supply
upward sloping?
Savers could invest their money in opportunities that grow over
time.
Like a fir tree that grows.
The more they save, the less they
invest in trees.
The less in trees, the higher the
marginal product of trees.
Therefore, the higher the opportunity
cost of saving. The supply is upward
sloping.
Putting it all together, we get the equilibrium price and quantity.
Note that in equilibrium
the interest rate is equal
to the value of the growth
of the “tree”.
Applications
Suppose a number of you think that tomorrow will bring:
What will happen to the interest rate?
Note: someone
must be
disagreeing with
you.
What if trees start to grow faster (or China or the third world starts
growing faster)?
Could this have been
what was happening in
the early 90s?
Question to ponder:
Suppose you were
Capital Theory
The economics of interest rates is a pretty basic application of our
model. However, understanding interest rates helps us understand how
CAPITAL gets priced.
A
A
Is.
If a capital asset yields service over time, how do we determine its
price?
Consider the rate of return of an asset that lasts one period.
What must this rate of return equal in equilibrium?
It must equal the rate of interest r*.
Why?
If in equilibrium we have: r* = (F – P)
P
Pr* = F - P
Pr* +P = F
P(1+r*) = F
In general:
IF the annuity lasts forever, and IF the interest rate is constant,
then this complicated formula simplifies to:
P=F
r*
Your book provides tables that calculate these values.
So there is a very simple relationship between the price of a
capital asset and the stream of income/services it provides.
The secret to this relationship is the rate of interest.
The difference between Income and Wealth.
Wealth = the PV of Income.
= M1 + M2
+ M3 …. MN
(1+r*) (1+r*)2 (1+r*)3
(1+r*)N
You could have a low income for some years, but still have a
high level of wealth. You could have a one time high income,
and not be very wealthy!
Who, generally, are the wealthiest people in the country?
Yet they have low incomes, so
we often call them “poor”.
Real poor people look like:
Statistics Canada calculates poverty based on income.
They use a “cut-off”: the fraction of income spent on “needs”.
That means:
.
The result: poor don’t get enough transfers, and welfare is extremely
costly.
If you’re not poor, then why should society subsidize your
education?
Why should we take money from
or
And give it to:
It doesn’t make any sense if you understand wealth and income.
Other Applications of Capital Theory
1. The Rule of 72.
The time it takes for an investment to double: 72/ r*.
2. You’ve won $1,000,000 in 20 installments of $50,000. How much
did you win?
If r* = 10%, then
$50,000 x 8.51 = $ 425,500.
If r* = 5%, then
$50,000 x 12.5 = $625,000
3. Dad forgot to pay me my allowance in 1974.
$10 x 17.45 = $174.50.
4. How much extra would you pay for “super insulation” if it
saves you $150 per year on heat, forever?
Suppose the interest rate was 2%
150/.02 = $7500.
What happens to the price of a pine board relative to a cedar board,
when r* increases?
Pp/ Pc will increase.
5. How is it that firms using old machinery can compete with firms
using the latest technology? Or how do stores with poor locations
stay in business with firms in great locations?
The price of the machine, or location adjusts until the
rate of return is equalized.
r* = F – P
P
if r* and F are fixed, then
P must adjust
6. Here are three majors:
Why would different majors have different rates of return?
- because some jobs are more enjoyable.
The “total” rates of return must be equal across the degrees.
Let Fu be the utility you get from a job.
Ff be the financial income you get from a job.
The rate of return in job A would be RA = (Fu + Ff) – P
P
Similarly for job B.
So, … RA = RB
Quite often, to make choices we need to compare two different
streams of income. If you keep present values in mind, this is
really quite easy.
Remember you must compare dollar values within the same
time period.
7. Lane wants to reduce his mortgage interest by renegotiating. The
bank will charge a $6000 fine to do so, but he will save $23,000
ten years from now. Is this a good deal?
6000 = 23,000
(1+r)10
.
8. The suppression of improvements.
We’ve all heard stories of
inventions that get suppressed.
-the car that gets 100 mpg.
- the light bulb that lasts
20 years.
Suppose one year of light is worth 50¢ and r*=10%
A two year light bulb would be worth 50¢ + 50¢/(1.1) = 95¢
Suppose it costs 35¢ to make a one year bulb, and 60¢ to make a
two year bulb.
Should the firm sell two years worth of light with 2 one year bulbs, or
one two year bulb?
Profit with 2 bulbs = 2 x 50¢ - 2x35¢ = 30¢
Profit with 1 bulb = 95¢ - 60¢ = 35¢
If the cost of the two year bulb is less than ½ the cost of the one
year bulb, the firm sells the long lasting bulb.
This is true, even though the firm sells fewer bulbs!
Later one, in the third section of the book, we’ll see conditions when
the firm might not sell the long lasting bulb, but the reason is never
because the firm sells less units.
9. Investments.
If a capital market is in equilibrium, what is the rate of return
of an asset?
r*.
So over time, an asset that yielded only financial returns, would have
to grow in value at what rate?
r*
So if the asset yielded services or utility, as well as a financial
return, how fast would its value grow?
- at a rate less than r*!
- eg. A bond should grow in value faster than a painting.
If you’re looking for financial investments, you shouldn’t invest in
assets that yield utility!
Like an engagement ring!
Try convincing your spouse to sell it when
diamond prices increase!
10. Selling stocks.
Suppose you have two stocks A and B. One falls in price and
the other increases. If you only care about rates of return,
which one should you sell?
-either, they both have the same rate of return.
11. Selling
Publishers argue that authors are hurt by
-no, the second hand price is capitalized into the initial price
of the book.