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Review Session 3 Risk and insurance

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### Review Session 3Risk and insurance

Catalina Martinez

Office hours: Tuesdays 6-8pm Rigot 27

Economics and Development

MDev 2012-2013

THE GRADUATE INSTITUTE | GENEVA

Probability

- The probability of a repetitive event happening is the relative frequency with which it will occur
- probability of obtaining a head on the fair-flip of a coin is 0.5

- If a lottery offers n distinct prizes and the probabilities of winning the prizes are i (i=1,n) then

Expected Value

- For a lottery (X) with prizes x1,x2,…,xn and the probabilities of winning 1,2,…n, the expected value of the lottery is

- Theexpected value is a weighted sum of the outcomes
- the weights are the respective probabilities

Example

- Suppose that Smith and Jones decide to flip a coin
- heads (x1) Jones will pay Smith $100
- tails (x2) Smith will pay Jones $100

- From Smith’s point of view,
- Games which have an expected value of zero (or cost their expected values) are called actuarially fair games

Risk

- Uncertainty about possible states of the world.
- Variability of the outcomes of some uncertain activity
- Variance

- We need to understand how people behave and choose under uncertainty, since many (or all) economic decisions involve risk:
- Prices change
- Income fluctuates
- Bad stuff happens…

Example

- Smith and Jones change the price from $100 to $1,000
- The two games may have the same expected value (mean) but differ in their riskiness (variance).
- Game 2 is more risky.

Game 1

Game 2

Risk Aversion

- When faced with two gambles with the same expected value, individuals will usually choose the one with lower risk
- In general people will be less willing to play game 2.

- If people tend to prefer game 1 it means that game 1 gives more ‘utility’ than game 2.
- As a general rule, certain prospects are worth more in utility terms than uncertainones, even when expected tangible payoffs are the same.

Risk Aversion

- Aflip of a coin for $1,000 promises a gain in utility if you win, but a large loss in utility if you lose
- The negative impact that the loss has on utility tends to be bigger than the positive impact of the gain.
- The marginal utility from wealth is decreasing: It is higher when wealth is low than when wealth is high.

- A flip of a coin for $1 is inconsequential as the gain in utility from a win is not much different as the drop in utility from a loss

Expected Utility

- Expected utility can be calculated in the same manner as expected value

- A rational individual will choose among gambles based on their expected utilities

Suppose that W* is the individual’s current

level of income

U(W*)

U(W*) is the individual’s

current level of utility

W*

Graphical representation: Risk AversionUtility (U)

U(W)

Wealth (W)

Risk Aversion

- Suppose that the person is offered two fair gambles:
- a 50-50 chance of winning or losing $h
Uh(W*) = ½ U(W* + h) + ½ U(W* - h)

- a 50-50 chance of winning or losing $2h
U2h(W*) = ½ U(W* + 2h) + ½ U(W* - 2h)

- a 50-50 chance of winning or losing $h

The expected value of gamble 1 is Uh(W*)

Uh(W*)

W* - h

W* + h

Risk AversionUtility (U)

U(W)

U(W*)

Wealth (W)

W*

The expected value of gamble 2 is U2h(W*)

U2h(W*)

W* - 2h

W* + 2h

Risk AversionUtility (U)

U(W)

U(W*)

Wealth (W)

W*

Risk Aversion

The person will prefer current wealth to a fair gamble

The person will also prefer a small gamble over a large one

Utility (U)

U(W*) > Uh(W*) > U2h(W*)

U(W)

U(W*)

Uh(W*)

U2h(W*)

Wealth (W)

W* - 2h

W* - h

W*

W* + h

W* + 2h

W ” provides the same utility as

participating in gamble 1

W ”

Risk Aversion and insuranceUtility (U)

U(W)

U(W*)

Uh(W*)

The individual will be

willing to pay up to

W* - W ” to avoid

participating in the

gamble

Wealth (W)

W* - h

W*

W* + h

Risk Aversion and Insurance

- In general, external shocks can determine fluctuations in income and consumption patterns of individuals.
- Typically, individuals like to smooth out income fluctuations (and consumption), as this tends to increase their utility.
- A risk averse individual will be willing to pay to avoid taking fair bets
- There are several ways in which this goal can be achieved:
- Savings (self-insurance)
- Credit
- Mutual insurance: two (or more) individuals agreeing to pay a certain amount to those being in a bad period (to a fund) when they are in a good period.

Asymmetric information in insurance

- Limited information about what led to the outcome (moral hazard).
- Relevant because full insurance reduces the incentives to act optimally (underprovision of inputs).
- The effort that a farmer exerts might be reduced if he is insured…

- Limited information about the final outcome (adverse selection).
- There is the risk that individuals ask for transfers while providing deliberately wrong or misleading information (fraud).

- Informational constraints pose a real problem to effective insurance.
- Better access to the information increase the probability of successful mutual insurance.

Final 2011 – Q1

- Credit schemes in village economies are often informal. How can we explain this?
- Think about the case where in a village economy the interest rate is equal to zero. This should strongly reduce the incentive to lend. What would be the role of the credit market in this type of village economy?

Answer – Q1.1

- Market failure – information asymmetries
- Adverse selection (hidden characteristic: ability, type of borrower) - trust
- Moral hazard (hidden action: effort)
- Formal banks do not have the same information (have less info) than informal lenders do. This is always less than the info that borrowers have.
- Credit rationing (Stiglitz & Weiss): banks raise the interest rate to incorporate the probability of default. As a result the optimal credit is smaller.
- The main problem is that even if some people are willing to pay more (higher interest rates), the banks won’t offer them credit
- Informal creditors have closer contact with the community and may be able to solve this problems better.
- Suboptimal: higher costs, unreliability…

Answer – Q1.2

- If the interest rate is zero, lenders have no incentive to offer money. They may choose another economic activity.
- There is an excess demand of credit.
- The market system in this scenario would increase prices.
- The market equilibrium price and quantity would be reached: demand=supply.
- The main idea is that the market would be able to match lenders with borrowers, allocating money to its most efficient use.
- Nevertheless, information asymmetries may still persist…

Final 2009 – Q2

- “If households within a village provide perfect insurance to each other, variation in household consumption should not be related to variations in household income”. Please comment.

Answer

- If there is perfect insurance,the community of this village will help households going through a bad time.
- If a given household faces an income shock, it would be provided a transfer by the community insurance system.
- This implies that each household will be able to maintain a smooth path of consumption, i.e. one that does not move sharply (in response to own income shocks).
- All households in the community would be subject to the same shocks, i.e. to the shocks to the community income. Therefore, only these shocks will affect households’ consumption.
- Problems:
- Moral hazard: perfect insurance diminishes households’ incentives to exert effort.
- Adverse selection: it is difficult to determine objectively when a household income shock occurs.

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