More on the invisible handPresent value

Today: Wrap-up of the invisible hand; present value

of payments made in the future

Leaving the test before time expires

The following rule applies to leaving before the end of a test You are allowed to turn in your test

early if there are at least 10 minutes remaining. As a courtesy to your classmates, you will not be allowed to leave during the final 10 minutes of the test.

Previously…

…we saw that market forces will tend to lead to suppliers having zero economic profits

However, the transition to zero economic profit often takes time (as we saw in Las Vegas)

Today

More on the invisible hand Regulated markets Stocks and bonds More on equilibrium

Present value Future payments Permanent annual payments

Today:More on the invisible hand

Let self-interested actions determine resource allocation

Prices help determine how much is allocated for production of each good or service Rationing function Allocative function

Rationing function of price

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 We will examine exceptions in some

of the later chapters

Allocative function of price

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

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

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 Airlines were required to use some

economic profits of popular routes to pay for routes that had negative economic profits

Problem: The invisible hand Piano bars, extravagant meals, and more

frequent flights Conclusion: Be careful what you

regulate

Possible solution: Grant a monopoly

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?”

Solution: Extravagant office buildings

Part of British Columbia (heavily populated area circled)

Possible solution: Grant a monopoly

Another example: BC Ferries in British Columbia

More on monopolies in Chapter 8

Before we move on…

…we need to define and understand present and future value

Money can be invested relatively safely in many ways Government debt Savings accounts and CDs in banks Bonds of some corporations

Present and future value

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 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 Payment of M is received T years from now PV represents present value:

Tr

MPV

)1(

Example

What is the present value of a $12,100 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

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 Present value of an

annual payment of M every year forever, when the interest rate is r :

r

MPV

Question 18 from the practice problems

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 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

Some people have a good ability to quickly determine what such an equilibrium is

These people can earn money from this skill Example: Recognizing the value of a

stock before other people

Example: Winning a contest

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

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

Back to winning a contest, except now the two options are $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 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 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

If you won the contest that paid forever, it would be worth $1,250,000 We already did this calculation

How much is this contest worth 30 years from now? We need to discount $1,250,000 by thirty

years $1,250,000 / (1.04)30 = $385,398

Example: Winning a contest that pays you only 30 years

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

Today, we have finished our study of the invisible hand

We also examined discounting, and ways of summing constant yearly payments made forever