Economics of Information

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Chapter 12

• Economics of Information

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Uncertainty and Risk

• Imperfect information requires additional tools
  of analysis
• Uncertainty is present in a problem if some
  outcome has more than one possible value.
• The expected value can be calculated if the
  probability distribution is known.
• Random outcomes imply risk.

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Risk and Decision Making

• People have different attitudes about risk.
• Risk averse people avoid risk.
• Risk inclined people seek out risks.
• It is a matter of preferences.
• Risk can be measured using the variance.
• Uncertainty and risk have significant
  implications for economic decision making.

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Risk Neutrality

• X denotes the firms profits.
• X can be 1,000 with probability .90 and ?4,000
  with probability .10
• E(X) 1,000(.9) ? 4,000(.1) 500
• Some decisions can be based on the expected value
  of the random variable.
• A person who is risk neutral will take any gamble
  with positive expected value.

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Are You Risk Averse?

• Consider a gamble
• win 1,000,001 with probability ½,
• lose 1,000,000 with probability ½.
• Expected value is .50 gt 0
• A risk neutral person would eagerly take this
  gamble.

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Measuring Risk

• Variance is a measure of the risk of a gamble.
• ?2 (.9)(1,000 ? 500)2 (.1)(?4,000 ? 500)2
  2,250,000
• Sum of sqd deviations from the mean of each
  possible outcome multiplied by its probability
• The variance of an uncertain outcome will affect
  the decision-makers optimal choice.

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Taking Gambles

• If the expected value of a gamble is M, then a
  risk averse person prefers M for certain to the
  gamble.
• A risk loving person prefers the gamble to
  receiving M for certain.
• A person can be both risk averse and risk loving
  buy insurance and play the lottery.

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Risk Aversion in Consumers

• 1. New products have uncertain characteristics.
• Consumers are unwilling to pay the actual value
  of the product.
• Firms give out free samples to remove that
  uncertainty.
• 2. For traveling consumers local stores have
  uncertain quality.
• Chain stores and brand names remove uncertainty
  about product quality.

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• 3. Insurance removes risk of loss.
• Consumers pay more than the expected value of
  insurance in order to eliminate risk.
• 4. Many complicated products (cars, appliances,
  computers) have uncertain life due to breakdowns.
• Warranties and money-back guaranties remove this
  risk.

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Searching for the Best Price

• Many stores sell the same good.
• Consumer wants to find the lowest price.
• Consumer must decide when to stop looking and
  make a purchase.
• Consumer can buy a watch for a known price of PK
  or search for lower price.
• Consumers experience provides information about
  the distribution of prices.

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Using Experience

• Most stores, three quarters, sell at PK or
  higher.
• The others sell at discounted price PL, giving a
  saving of PK ? PL.
• The expected benefit of searching one more store
  is
• EB (1/4)(PK ? PL)

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Search is Costly

• Time spent searching has opportunity cost.
• If the cost of search is C, then search again if
• EB (1/4)(PK ? PL) gt C.
• Or PK gt 4C PL
• Keep searching as long as this is true.

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Stopping Decision

• A reservation price R is the known price PK at
  which search stops R 4C PL

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Changes in Reservation Price

• High PK implies more search.
• Higher C implies less search.

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Risk Aversion in Firms

• A firm with many independent product lines is
  diversified.
• It is risk neutral to the individual risks.
• Stockholders have diversified portfolios.
• Owners want to maximize the expected value of the
  firm.
• A manager will be risk averse if income is not
  diversified.
• Interests may conflict.

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Example

• Manager must choose between two projects for the
  firm.
• Project 1 has risky income 2m or 0 with equal
  probability.
• EV1 (.5)2 (.5)0 1m
• Project 2 income is certain .9 with prob. 1.
• EV2 .9 lt 1 EV1
• Stockholders prefer project 1.

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Managers Incentives

• Manager will be fired if project fails.
• Income from remaining hired is 100k and income
  from being fired is 0.
• If project 1 is chosen, expd income is 50k.
• If project 2 is chosen, income is 100k.
• Manager prefers project 2, even if risk neutral.
• This can lead to punishment of the manager.
• This is a form of moral hazard.

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Wrong Incentives

• Incentives are too strong.
• They induce conservative behavior.
• Could make managers income depend on value of
  stock.
• Manager still faces risks.
• Manager cannot control value of stock.
• Include base salary to reduce risk.

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Maximizing Uncertain Profits

• Firm faces uncertain price
• P 2 with probability .3
• P 1 with probability .7
• Costs are known
• TC 200 .0005Q2

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• A risk neutral firm will maximize expected
  profits
• E? 2Q(.3) 1Q(.7) ? 200 ?.0005Q2
• Set dE?/eQ .6 .7 ?.001Q 0
• To get 1.3 .001Q
• This is just expected P MC
• Optimal Q 1,300.
• E? 1.3(1,300) ? 200 ? .0005(1,300)2.
• This is valid as long as the firm is risk neutral.

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Asymmetric Information

• Some people have better information than others
  do.
• Adverse selection happens when there are hidden
  characteristics.
• Sometimes informed party will not divulge
  information.
• Uninformed may then choose not to trade leading
  to missing markets.

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Market for Lemons

• Used car may be good or a lemon.
• Seller knows cars characteristics, buyer does
  not.
• There are potential gains from trade.

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Decision to Buy

• Buyer believes that the proportion of good cars
  is ?, where 0 ? ? ? 1.
• Expected value to buyer is
• EVB 1,000 ? 200 (1??)
• Buyer will get a good car only if the
• EVB 1,000 ? 200 (1??) gt 800 VS(good)
• or 800 ? gt 600 or ? gt 3/4.

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Missing Market

• If ? ½, then half of the used cars are good and
  EVB 600.
• Offering 600 will not get a good car, only a
  lemon.
• If the buyer understands that no one would sell
  a good car for 600, then no trade in good cars
  takes place.
• This is known as adverse selection the offer
  attracts only the unwanted deals.

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Other Examples

• Raising the interest rate on loans attracts bad
  investments (more likely to default)
• Firms offer of paid sick days but at a lower
  salary attracts workers most likely to use them.
• Offer of health insurance at higher premiums
  attracts only the least healthy.
• Offer of accident insurance at higher premiums
  attracts only worst drivers.

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Example of Car Insurance

• Assume 20 of drivers are bad drivers
• Probability of accident no accident
• for good drivers 0.1 0.9
• for bad drivers 0.8 0.2
• Claim per accident 1,000
• Probability of a claim
• Prob(good)Prob(acc?good) Prob(bad)Prob(acc?bad)

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Expected Claim

• Expected claim
• E(claim) (.8)(.1) (.2)(.8)1,000 240
• If premium is 240, then expected value of the
  policy to a good driver is
• EV(accident) EV(no acc.) ? premium
• EVG (.1)(1,000 ? 1,000) (.9)0 ? 240
• ? 240 lt EVG(no policy) (.1)1,000

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Adverse Selection Again

• Good drivers would not voluntarily carry
  insurance.
• Only bad drivers would buy insurance
• EVB ? 240 gt EVB(no policy)
• (.8)1,000.
• In that case, premium must be higher.
• E(claim) (.8)1,000 800 only bad drivers will
  pay to be covered.

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Moral Hazard

• Moral hazard is also a case of asymmetric
  information
• Due to hidden actions after the transaction.
• The principal-agent problem is an example.
• If employees income does not depend on actions,
  employee will not work hard.

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Managerial CompensationFrom Appendix of Ch. 4

• Manager faces choice between labor and leisure
• By giving up one hour of leisure, income
  increases by the wage
• This gives budget line with slope equal to the
  wage
• Optimum choice is where MRS between leisure and
  income equals wage.

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(p. 139 Ch. 4)
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Fixed Salary or Profit Sharing

• Manager who earns salary whether working or
  shirking chooses to shirk.
• Bonus is a percentage b of profits ?.
• This changes budget line that determines how
  leisure can be traded for income.
• Budget line is share of increasing profits from
  greater effort e with slope equal to b?d?/de.
• Less shirking (moral hazard) than with fixed
  salary.

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(Appendix of Ch. 6)
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Moral Hazard and Insurance

• The insured party can affect the probability of
  an accident and claim.
• If a driver with accident insurance drives more
  recklessly than without insurance, this is moral
  hazard.
• If all losses are covered, then there is no cost
  of reckless driving.
• Deductibles put some of the cost of an accident
  back on driver.

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Moral Hazard and HMOs

• If health insurance pays full cost of care to the
  doctor, doctors use too many tests and procedures
  to prevent malpractice suits.
• Health maintenance organizations do not pay
  doctors the full cost of care to provide
  incentive for doctors to reduce the number of
  tests and procedures.
• Since patients pay little of the cost of care,
  they want more procedures than doctors are
  willing to supply.