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Economics for CED. Noémi Giszpenc Spring 2004 Lecture 5: Micro: Markets and Information Investment and Insurance March 30, 2004. What is investment?. Investment means to apply resources in ways that you hope will produce more resources later. “Wealth creation”

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economics for ced

Economics for CED

Noémi GiszpencSpring 2004Lecture 5: Micro: Markets and InformationInvestment and Insurance

March 30, 2004

what is investment
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

Economics for CED: Lecture 5, Noémi Giszpenc

how do firms decide to invest
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

Economics for CED: Lecture 5, Noémi Giszpenc

a detour into accounting
A detour into accounting
  • Basic accounting equation:Assets = Liabilities + Equity
  • Can be seen as a description of capital’s Uses and Sources
  • Different (combos of) uses bring different returns
  • Different sources have different costs

Economics for CED: Lecture 5, Noémi Giszpenc

structure of a balance sheet
Structure of a balance sheet

Economics for CED: Lecture 5, Noémi Giszpenc

uses sources returns costs
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

Economics for CED: Lecture 5, Noémi Giszpenc

4 sources of capital
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

Economics for CED: Lecture 5, Noémi Giszpenc

calculating return 5 ways
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

Economics for CED: Lecture 5, Noémi Giszpenc

calculating return 5 ways cont
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.

Economics for CED: Lecture 5, Noémi Giszpenc

calculating return 5 ways cont10
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

Economics for CED: Lecture 5, Noémi Giszpenc

example bonds vs pine trees
Example: Bonds vs. Pine trees

Economics for CED: Lecture 5, Noémi Giszpenc

effects of different tax regimes
Effects of different tax regimes
  • Net profit split between dividends to shareholders and retained earnings
    • Retained earnings lead to investment, growth in share value --> 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

Economics for CED: Lecture 5, Noémi Giszpenc

why does investment fluctuate
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

Economics for CED: Lecture 5, Noémi Giszpenc

portfolios of investments
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

Economics for CED: Lecture 5, Noémi Giszpenc

what is insurance
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

Economics for CED: Lecture 5, Noémi Giszpenc

risk uncertainty and insurance
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.

Economics for CED: Lecture 5, Noémi Giszpenc

expected value
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

Economics for CED: Lecture 5, Noémi Giszpenc

attitudes toward risk
Attitudes toward risk
  • Risk neutral: a risk neutral person is indifferent about “fair” bets. She doesn’t 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).
  • 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.
  • Risk loving: a risk loving person prefers “fair” bets over certainty. So s/he prefers having the lottery in example 1 to having $10.

Economics for CED: Lecture 5, Noémi Giszpenc

utility and uncertainty eu
Utility and Uncertainty: EU
  • Utility in each state is weighted by its probability of occurring; EU is weighted sum.
  • Example 2
    • Suppose the person’s 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) is:EU = .05 U(W-1000) + .95 U(W)

Economics for CED: Lecture 5, Noémi Giszpenc

expected wealth
Expected Wealth
  • Still Example 2:
    • The person’s expected wealth (or the expected value of her wealth) is:EW = .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.

Economics for CED: Lecture 5, Noémi Giszpenc

relationship of wealth to utility
Relationship of wealth to utility

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

Economics for CED: Lecture 5, Noémi Giszpenc

relationship of wealth to utility22
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 don’t like uncertainty.

Economics for CED: Lecture 5, Noémi Giszpenc

relationship of wealth to utility risk averse people
Relationship of wealth to utility: risk averse people
  • Suppose that instead of W, they have either W+100 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 W+100 or W-100, each with equal probability, is .5U(W+100) + .5U(W-100).
  • So U(W) > .5U(W+100) + .5U(W-100).
  • So if they face uncertainty, they will want insurance.

Economics for CED: Lecture 5, Noémi Giszpenc

relationship of wealth to utility24
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 W+1 or W-1, each with the same probability, to always having W.
    • So U(W) < .5U(W+100) + .5U(W-100).
  • Most people are risk averse.

Economics for CED: Lecture 5, Noémi Giszpenc

a role for insurance
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.

Economics for CED: Lecture 5, Noémi Giszpenc

fair insurance
“Fair insurance”
  • “Fair insurance” if the insurance premium ($50) just equals the expected value of each insured person’s 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.

Economics for CED: Lecture 5, Noémi Giszpenc

risk preferences and premiums
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.

Economics for CED: Lecture 5, Noémi Giszpenc

risk preferences and premiums28
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.

Economics for CED: Lecture 5, Noémi Giszpenc

risk aversion and willingness to pay
Risk aversion and willingness to pay
  • Assume U= √W
  • 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*(√ 1000) + .95*(√ 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 = √(1950) = 44.159 utils (higher)

Economics for CED: Lecture 5, Noémi Giszpenc

maximum premium
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 = √(2000 – m) with certainty.
  • So U = √(2000 – m) = 44.06 and m = $58.15.
    • This is more than the fair insurance premium of $50.

Economics for CED: Lecture 5, Noémi Giszpenc

conclusions on premiums
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 > 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.

Economics for CED: Lecture 5, Noémi Giszpenc

who buys insurance who sells
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.

Economics for CED: Lecture 5, Noémi Giszpenc

problems w story s assumptions
Problems w/ story’s 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 person’s 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.

Economics for CED: Lecture 5, Noémi Giszpenc

problems w assumptions cont
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 doesn’t 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.

Economics for CED: Lecture 5, Noémi Giszpenc

real world insurance
Real world insurance
  • In actuality, the assumptions for fair insurance aren’t 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 isn’t available, particularly when risks are positively correlated.
      • Example is earthquake insurance, which is only available as a government program. Why?

Economics for CED: Lecture 5, Noémi Giszpenc

adverse selection
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 can’t 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.

Economics for CED: Lecture 5, Noémi Giszpenc

adverse selection cont
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.

Economics for CED: Lecture 5, Noémi Giszpenc

breakdowns in the system
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)

Economics for CED: Lecture 5, Noémi Giszpenc

lemons example used car market
“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 > L.
  • Buyers can’t 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 car:EV = pL + (1-p)G

Economics for CED: Lecture 5, Noémi Giszpenc

lemons example continued
“Lemons” example continued
  • Sellers’ incentives:
    • keep good cars because G > EV
    • sell lemons because L < 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.

Economics for CED: Lecture 5, Noémi Giszpenc

bankruptcy example
Bankruptcy example
  • Suppose a person borrows an amount B and promises to repay B(1+r) 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(1+r)) + pU(Y’-B(1+r))
  • 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(1+r)) + pU(Y’)

Economics for CED: Lecture 5, Noémi Giszpenc

bankruptcy example continued
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 don’t 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 isn’t so bad (moral hazard).
  • What problems caused w/no bankruptcy laws?

Economics for CED: Lecture 5, Noémi Giszpenc

workarounds the breakdowns
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

Economics for CED: Lecture 5, Noémi Giszpenc

more workarounds
More workarounds
  • Conditionality
    • Often imposed by banks
    • (doesn’t 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

Economics for CED: Lecture 5, Noémi Giszpenc

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