More on the invisible hand Present value

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More on the invisible handPresent value

• Today Wrap-up of the invisible hand present
  value of payments made in the future

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What is 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

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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

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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

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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

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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

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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
• See p. 233-234 for more on piano bars and
  elaborate meals
• Conclusion Be careful what you regulate

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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
• Another example BC Ferries in British Columbia
• More on monopolies in Chapter 10

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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

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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

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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

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Example

• 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

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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

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Present value of a permanent annual payment

• Present value of an annual payment of M every
  year forever, when the interest rate is r

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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

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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

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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

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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

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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

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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?

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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

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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

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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 385398

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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

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Summary

• Today, we have finished our study of the
  invisible hand
• We also examined discounting, and ways of summing
  constant yearly payments made forever