Economics for CED

1
Economics for CED

• Noémi GiszpencSpring 2004Lecture 5 Micro
  Markets and InformationInvestment and Insurance
• March 30, 2004

2
What is investment?

• Investment means to apply resources in ways that
  you hope will produce more resources later.
• Wealth creation
• Also necessary to shore up used-up
  resources--replacement maintenance
• Does not add to net investment

3
How do firms decide to invest?

• Based on calculation By the book--will
  expected returns exceed expected costs by an
  acceptable margin?
• A great deal of uncertainty exists about the
  future a lot of guesswork involved
• Based on confidence leap in the dark
• Expectations about what other investors are doing

4
A detour into accounting

• Basic accounting equationAssets Liabilities
  Equity
• Can be seen as a description of capitals Uses
  and Sources
• Different (combos of) uses bring different
  returns
• Different sources have different costs

5
Structure of a balance sheet
Assets Liabilites and Equity
Current Assets(cash, A/R, inventory) Current Liabilities(A/P, ST loans)
Non-current Assets(Land, plant, equipment) Non-current Liabilities(LT loans, mortgages)
Non-current Assets(Land, plant, equipment) Owners Equity Retained Earnings
Total Assets Total Liabilities Equity
6
Uses sources returns costs
Annual costs/returns per 100
Cost of capital funds
Investment 1
Investment 2
Investment 3
Investment 4
Investment projects
0
Quantity of funds
7
4 sources of capital

• Equity creating selling new shares
• Pays dividends dependent on performance
• Dilutes stock of existing shareholders
• Retained earnings internal funds
• Cheapest most common source
• Bonds promises to pay interest principal
• Buyers of bonds can trade these in markets
• Bank debt easier to obtain than bond-buyers
• Must pay market rate of interest, meet conditions

8
Calculating return (5 ways)

• Total return good for one-off, immediate
  definite return projects
• Compare percent difference between returns and
  costs with market interest rate
• Payback useful for comparing similar investments
  with similar lifetimes
• How long will it take for project to cover costs
  and start earning?
• What will assets be worth and what will they earn
  after the payback period?
• Ex Farm, office building, bus

9
Calculating return 5 ways (cont.)

• Accounting rate of return
• Good for productive investments with regular
  returns, analogous to interest rates
• Discounted present value of cash flow
• For investments with different patterns of
  earning over time
• The amount of money that would need to be
  invested now, at compound interest at current or
  expected interest rates, to generate the future
  asset or income.

10
Calculating return 5 ways (cont.)

• Internal rate of return
• The rate of compound interest that would yield
  the expected return to an investment
• Discounts returns in the future because tied-up
  capital could be used earning elsewhere
• Can be used to compare alternative investments
  compare expected returns w/market returns
  estimate present value of future returns

11
Example Bonds vs. Pine trees
Outlay Avg. Acctg rate of return Internal rate of return Payback Total return Present value
8 bonds 1 m. 8 8 Year 9 4.66 m. 1 m.
Pine trees 1 m. 8 4.9 Year 20 2.6 m. 0.56 m.
12
Effects of different tax regimes

• Net profit split between dividends to
  shareholders and retained earnings
• Retained earnings lead to investment, growth in
  share value --gt capital gains for shareholders
• Different taxation of dividends K gains can
  encourage or discourage retention
• Chosen policy depends on beliefs about how firms,
  investors choose to invest funds

13
Why does investment fluctuate?

• Lumpy capital
• Much productive building equipment can be paid
  for over time but must be acquired all at once
• Innovation
• New product to be produced or new process
• Expectations
• Better to invest when strong demand expected
• Firms tend to invest when others are investing
• Acceleration and deceleration
• Intensifies booms and slumps

14
Portfolios of investments

• hedge reduce overall risk by spreading
  investment over many independent projects
• The word risk from sailors word for steep rock
  merchants could lose all their investment in one
  cataclysm
• So they invented insurance

15
What is insurance?

• To make sure. To remove uncertainty and protect
  against risk.
• People prefer certainty they have an aversion to
  risk.
• In particular people would not like to see income
  (or rather consumption) dip below a certain
  minimum.
• Willing to pay to smooth consumption

16
Risk, uncertainty, and insurance

• Economists use lotteries to think about uncertain
  situations
• Example 1 say you pay 10 to get
• 10 chance of winning 100
• 90 chance of losing (winning 0)
• Example 2 (real life uncertainty --- no charge)
• 5 chance of losing 1,000 in a burglary
• 95 chance of no burglary, so loss 0
• Example 3 Plaintiff is injured in an accident
  and files a lawsuit. She has a
• 70 chance of winning damages of 10,000.

17
Expected Value

• Example 1 EV .10(100) .90(0) 10
• Note this lottery is fair, because the cost of
  the lottery ticket equals the EV of what the
  buyer will get.
• Example 2 EV .05(-1,000) .95(0) -50.
• Example 3 EV .70(10,000) 7,000

18
Attitudes toward risk

1. Risk neutral a risk neutral person is
   indifferent about fair bets. She doesnt care
   how much uncertainty she bears. So s/he gets
   equal utility from having 10 or having a 10
   chance of receiving 100 and a 90 chance of
   receiving 0 (the winnings in example 1).
2. Risk averse a risk averse person prefers
   certainty over fair bets. So s/he prefers to
   have 10 over having the lottery in example 1.
3. Risk loving a risk loving person prefers fair
   bets over certainty. So s/he prefers having the
   lottery in example 1 to having 10.

19
Utility and Uncertainty EU

• Utility in each state is weighted by its
  probability of occurring EU is weighted sum.
• Example 2
• Suppose the persons initial wealth is W.
• She faces two possible outcomes
• If the burglary occurs, her wealth falls from W
  to W-1000, and her utility is U(W-1000), which is
  lower than...
• If no burglary occurs, and her utility is U(W).
• Situation (1) occurs with probability .05 and
  (2) occurs with probability .95.
• So her expected utility (the expected value of
  her U) isEU .05 U(W-1000) .95 U(W)

20
Expected Wealth

• Still Example 2
• The persons expected wealth (or the expected
  value of her wealth) isEW .05(W-1000) .95
  (W) W 50
• Risk neutral people act as though they are
  maximizing their expected wealth.
• They are indifferent to more/less uncertainty and
  only care about the expected value of their
  wealth.

21
Relationship of wealth to utility
The slope is the additional utility that
individuals receive from an extra dollar of
(expected) wealth.
22
Relationship of wealth to utility

• Utility from wealth leads to risk preferences
• For risk neutral people, the slope is constant.
• This means that they get the same increase in
  happiness/utility from an additional dollar,
  regardless of whether they are poor or rich.
• For risk averse people, the slope declines as W
  rises.
• Therefore they get a larger increase in
  happiness/utility from an additional dollar when
  they are poor than when they are rich.
• Because of this, they dont like uncertainty.

23
Relationship of wealth to utility risk averse
people

• Suppose that instead of W, they have either
  W100 or W-100, each with .5 probability.
• The value of the extra 100 in additional utility
  is less than the cost in lost utility of losing
  100.
• So they gain less from having an additional 100
  than they lose from having 100 fewer dollars.
• Their utility level when they have W with
  certainty is U(W), and their expected utility
  level if they have W100 or W-100, each with
  equal probability, is .5U(W100) .5U(W-100).
• So U(W) gt .5U(W100) .5U(W-100).
• So if they face uncertainty, they will want
  insurance.

24
Relationship of wealth to utility

• Risk loving people are the opposite of risk
  averse people.
• They get a larger increase in happiness/utility
  from an additional dollar if they are rich than
  if they are poor.
• As a result, they prefer having W1 or W-1, each
  with the same probability, to always having W.
• So U(W) lt .5U(W100) .5U(W-100).
• Most people are risk averse.

25
A role for insurance

• Insurance helps reduce or eliminate uncertainty.
• Example 2 with burglary insurance
• Suppose there are 20 people who face the same
  risk of losing 1000 with 5 probability.
• They each put 50 into a cigar box, so 1000 is
  collected in total.
• Over the next year, one of them has a burglary
  and the 1000 is paid to her.
• So the insurance provides coverage of 1000 for
  losses in return for a premium of 50/year.

26
Fair insurance

• Fair insurance if the insurance premium (50)
  just equals the expected value of each insured
  persons loss, which is (1000)(.05) 50.
• So the insurance company makes zero profit.
• With the insurance, the person no longer faces
  uncertainty. She has wealth of
• W 50 if no burglary occurs or
• W- 50 1000 1000 W - 50 if a burglary occurs.
• So her utility is U(W-50), regardless of whether
  a burglary occurs or not.
• Suppose the fair insurance premium is called f.

27
Risk preferences and premiums

• risk neutral indifferent between certainty or
  uncertain situation with same expected wealth, as
  in the burglary example.
• Indifferent to fair insurance against the risk
  expected wealth EW is W-50, regardless
• risk averse prefer certainty over uncertain
  situation with same expected wealth.
• Better off buying fair insurance.
• Means that they would be willing to pay more than
  the fair insurance premium of 50 to get the
  insurance.

28
Risk preferences and premiums

• risk loving prefer uncertainty over facing an
  uncertain situation with same expected wealth.
• If offered fair insurance, better off not buying
  it.
• Means they would be willing to pay less than the
  fair insurance premium of 50 to get the
  insurance.

29
Risk aversion and willingness to pay

• Assume U vW
• Risk from example 2 5 chance of a burglary and
  loss of 1000.
• If no insurance, then EU .05 U(W-1000) .95
  U(W)
• Initial wealth, W, is 2,000.
• EU .05(v 1000) .95(v 2000) 44.066 utils
• Say person buys fair insurance for a premium of f
  50
• then her wealth is always 1950 and her utility
  is
• U v(1950) 44.159 utils (higher)

30
Maximum premium

• Utility if no insurance is U 44.06.
• The maximum insurance premium that she would be
  willing to pay would leave her with same utility
  as no insurance 44.06 utils.
• Suppose the max insurance premium is denoted m.
• If she buys insurance for m, then she always will
  have wealth of 2000 m and her utility will be U
  v(2000 m) with certainty.
• So U v(2000 m) 44.06 and m 58.15.
• This is more than the fair insurance premium of
  50.

31
Conclusions on premiums

• a risk averse person is better off if she can buy
  full insurance for a fair premium than if she
  goes uninsured.
• a risk averse person is willing to pay more than
  the fair premium to obtain insurance, so m gt f.
• Note People can be more/less risk averse. The
  closer their utility functions are to straight
  lines, the less risk averse they are and the
  closer m is to f.

32
Who buys insurance? Who sells?

• Risk averse people willing to buy insurance for
  more than the fair insurance premium.
• So selling insurance is profitable. (Selling
  fair insurance means making zero profit.)
• So risk neutrals sell insurance to risk averses.
• Risk neutral people absorb risk
• but are made better off they receive premiums
  that are higher than the fair level.
• Risk averse people pay more than the fair
  insurance premium
• but are better off because they get rid of risk.

33
Problems w/ storys assumptions

• Many insurance buyers w/ identical risks.
• In our example, all have a 5 chance/year of
  losing 1000 in a burglary.
• The law of large numbers allows the insurance
  company to predict risks very accurately.
• Insured persons risks of loss independent
• one persons probability of a loss unaffected by
  whether another person has a burglary.
• Examples of non-independent risks
• Burglars who steal from several apartments in a
  building. Hurricane or earthquake insurance.
• These risks are positively correlated.

34
Problems w/assumptions (cont.)

• No moral hazard.
• Refers to increases in the probability of an
  event occurring if it is insured against.
• Example of moral hazard people with burglary
  insurance may become careless about locking their
  doors.
• Or, if there is moral hazard, then insurance
  companies have perfect information.
• Example an insured person doesnt lock his door.
  So his probability of loss rises from 5 to 20.
• The insurer observes this and raises the premium
  from 50 to 200.

35
Real world insurance

• In actuality, the assumptions for fair insurance
  arent met.
• So insurance companies use deductibles and
  co-insurance to reduce moral hazard.
• Deductibles if a loss occurs, the insured person
  pays the first 100.
• Co-insurance if a loss occurs, the insured
  person pays 10.
• Sometimes insurance isnt available, particularly
  when risks are positively correlated.
• Example is earthquake insurance, which is only
  available as a government program. Why?

36
Adverse selection

• Imperfect information sometimes leads to good
  risks dropping their insurance coverage.
• Example there are healthy people with 1 chance
  of getting a disease and unhealthy people with 5
  chance of getting the same disease.
• People know their types, but insurance companies
  cant observe individuals types.
• So it charges all insureds the same premium of
  .03L, where L is the cost of treating the
  disease.
• So the healthy subsidize the unhealthy and this
  causes some healthy people to drop the coverage.

37
Adverse selection (cont.)

• The proportion of unhealthy people in the group
  of people buying insurance rises.
• So the insurance company must raise the price of
  insurance in order to avoid losing money.
• But the unhealthy people may not be willing to
  pay the high premium.
• If so then the insurance disappears completely.

38
Breakdowns in the system

• If buyer of insurance knows more than seller of
  insurance, there could be adverse selection or
  moral hazard
• If buyer of labor knows less than sellers, could
  be group-based discrimination
• Works the same way in deciding loans
• Among results redlining (not selling insurance
  or awarding loans in particular areas or for
  particular populations)

39
Lemons example used car market

• Two types of used cars good cars and lemons
• Sellers know if their used cars are lemons or
  not.
• Value of a lemon is L, and value of a good used
  car is G G gt L.
• Buyers cant find out if individual used cars are
  lemons or not.
• They only know the overall probability of used
  cars being lemons p.
• Buyers willingness-to-pay for used cars is the
  expected value of a used carEV pL (1-p)G

40
Lemons example continued

• Sellers incentives
• keep good cars because G gt EV
• sell lemons because L lt EV.
• Adverse selection makes good used cars disappear.
• Buyers eventually learn this
• so p rises and EV falls.
• This makes sellers incentives to keep good cars
  even stronger.
• The market for used cars turns into a market for
  lemons only.

41
Bankruptcy example

• Suppose a person borrows an amount B and
  promises to repay B(1r) next year.
• Next year, with probability p she will lose her
  job. In this case, her income falls from Y to Y.
• Her expected utility without bankruptcy isEU
  (1-p)U(Y-B(1r)) pU(Y-B(1r))
• Introduce bankruptcy If she files for bankruptcy
  her debt will be discharged.
• No obligation to repay from future earnings.
• Now her expected utility with bankruptcy isEU
  (1-p)U(Y-B(1r)) pU(Y)

42
Bankruptcy example continued

• Bankruptcy makes borrower better off by partially
  insuring against job loss.
• Bankruptcy may cause problems
• lenders raise the interest rate on loans, since
  borrowers who lose their jobs dont repay. This
  makes those who repay their debts worse off.
• Bankruptcy is estimated to cost the average
  debtor who repays 400/yr in extra interest
  payments.
• borrowers may work less hard and become more
  likely to lose their jobs, since the bad outcome
  isnt so bad (moral hazard).
• What problems caused w/no bankruptcy laws?

43
Workarounds the breakdowns

• Signaling (costly)
• Pay to reveal your type or
• Undertake activity that is less costly for your
  type of person
• Examples university degrees, resume paper
• Social capital
• Investments in reciprocal relationships
• Form of insurance, loan guarantees

44
More workarounds

• Conditionality
• Often imposed by banks
• (doesnt change underlying motivations)
• Loan sharks
• Loan to populations thought to be bad risks and
  charge high premiums
• Often use inside knowledge sometimes threat of
  violence