More on the invisible hand
Present value
Today: Wrap-up of the invisible
hand; present value of payments
made in the future
What is the invisible hand?
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Let self-interested actions determine
resource allocation
Prices help determine how much is
allocated for production of each good or
service
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Rationing function
Allocative function
Rationing function of price
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Efficiency cannot be obtained unless
goods and services are distributed to
those that value these goods and
services the most
In general, prices can obtain this goal
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We will examine exceptions in some of the
later chapters
Allocative function of price
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As prices of goods change, some
markets become overcrowded, while
others get to be underserved
Without any government controls or
barriers to entry/exit, resources will be
redirected in the long run such that
economic profits get driven to zero
Regulated markets
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Sometimes, markets are regulated with
public interest in mind
However, the invisible hand sometimes
leads to results that were not intended
Note that this type of regulation may
lead to barriers to entry
A regulated market of the
past: Airlines
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Most of you have lived a life without
regulation of major commercial airlines
in the U.S.
However, in the early to mid 1970s,
fares were set such that airlines could
make economic profits if the airplane
was full
Regulation of airlines
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Airlines were required to use some economic
profits of popular routes to pay for routes
that had negative economic profits
Problem: The invisible hand
See p. 233-234 for more on piano bars and
elaborate meals
Conclusion: Be careful what you regulate
Possible solution: Grant a
monopoly
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This sometimes happens, but it has its own
potential set of problems
Example: Regulated utilities
Regulation may state that economic profits
need to be set to zero
What if “profits are too high?”
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Solution: Extravagant office buildings
Another example: BC Ferries in British
Columbia
More on monopolies in Chapter 10
Before we move on…
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…we need to define and understand
present and future value
Money can be invested relatively safely
in many ways
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Government debt
Savings accounts and CDs in banks
Bonds of some corporations
Present and future value
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Suppose that the rate of return of safe
investments is 5%
If I invest $100 today, it will be worth
$105 in a year
Working backwards, I am willing to pay
up to $100 for a payment of $105 a
year from now
Working backwards
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We can calculate how much a future payment
is by discounting it by interest rate r
We calculate the present value of a future
payment as follows
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Payment of M is received T years from now
PV represents present value:
M
PV 
T
(1  r )
Example
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What is the present value of a $1,210
payment to be received two years from
now if the interest rate is 10%?
Plug in M = $12,100, r = 0.1, and T = 2
PV = $10,000
Present value of a permanent
annual payment
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What happens if we receive a constant
payment every year forever?
We can add up all of the discounted
payments, or we can use a simple
formula to calculate the PV of these
payments
Present value of a permanent
annual payment
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Present value of an
annual payment of
M every year
forever, when the
interest rate is r :
M
PV 
r
Question 18 from the practice
problems
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If you won a contest that pays you
$100,000 per year forever, how much is
its present value if the interest rate is
always at 10 percent?
Solution: M is $100,000 and r is 10%,
or 0.1  PV is M / r, or
$100,000 / 0.1 = $1,000,000
Finally, more on equilibrium
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Remember that equilibrium is not an
instantaneous process
Sometimes, trial and error is needed to find
what equilibrium is
By the time this is figured out, a new
equilibrium may emerge
The bigger the costs of finding equilibrium,
the less optimal the market generally is
Finally, more on equilibrium
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Some people have a good ability to
quickly determine what such an
equilibrium is
These people can earn money from this
skill
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Example: Recognizing the value of a stock
before other people
Example: Winning a contest
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Which is worth more: Winning $50,000
a year forever or $1,000,000 today?
Assume that the interest rate is 4%
The $50,000 forever has a present
value of $50,000 / 0.04, or $1,250,000
Take the $50,000 forever
Example: A stock
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Suppose that you own a stock that will
pay you $1 a year forever with no risk
Assume that the annual interest rate is
5% in this example
Value is $1 / 0.05, or $20, for the stock
Example: Winning a contest
that pays you only 30 years
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Back to winning a contest, except now
the two options are
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$50,000 a year for 30 years
$1,000,000 today
Which one is worth more?
Example: Winning a contest
that pays you only 30 years
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This is a perfect example of having to think
like an economist to solve this problem
quickly
You could discount each of the 30 payments
appropriately to determine how much the
present value of those payments is
However, there is another way of solving this
Example: Winning a contest
that pays you only 30 years
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To solve this, we must recognize that this
problem is equivalent to the previous contest
problem, except that we must take away
payments made 30 years or more in the
future
To calculate this, we must calculate how
much this contest is worth today and how
much this contest is worth 30 years from now
Example: Winning a contest
that pays you only 30 years
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If you won the contest that paid
forever, it would be worth $1,250,000
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We already did this calculation
How much is this contest worth 30
years from now?
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We need to discount $1,250,000 by thirty
years
$1,250,000 / (1.04)30 = $385398
Example: Winning a contest
that pays you only 30 years
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The present value of 30 yearly
payments is $1,250,000 – $385,398, or
$864,602
So, if the $50,000-per-year prize is only
over 30 years, you should take the
$1,000,000 prize today
Summary
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Today, we have finished our study of
the invisible hand
We also examined discounting, and
ways of summing constant yearly
payments made forever