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### Economics for CED

Noémi GiszpencSpring 2004Lecture 5: Micro: Markets and InformationInvestment 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”
- 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?

- 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

- 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

Economics for CED: Lecture 5, Noémi Giszpenc

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

- 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)

- 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.)

- 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 (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

Economics for CED: Lecture 5, Noémi Giszpenc

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?

- 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

- “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?

- 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

- 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.

- Example 1: say you pay $10 to get:

Economics for CED: Lecture 5, Noémi Giszpenc

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

- 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 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

- 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

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 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

- 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 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

- 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” 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 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 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

- 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

- 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

- 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?

- 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.

- Risk neutral people absorb risk

Economics for CED: Lecture 5, Noémi Giszpenc

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.)

- 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

- 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?

- So insurance companies use deductibles and co-insurance to reduce moral hazard.

Economics for CED: Lecture 5, Noémi Giszpenc

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.)

- 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

- 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

- 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

- 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

- 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 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).

- 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.
- What problems caused w/no bankruptcy laws?

Economics for CED: Lecture 5, Noémi Giszpenc

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

- 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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