Uncertainty

Question 1

What is expected value?

Answer 1

• The average outcome from an uncertain gamble

- EV = P(X)X + P(Y)Y

Question 2

What is true about fair gambles and expected value?

Answer 2

EV = 0 OR the initial income i.e. nothing earned or lost

Question 3

How can we explain risk aversion?

Answer 3

Utility v Income - straight line under U curve between win and lose

• Despite being fair, the gamble provides less utility than when you know you will receive for sure

Question 4

What are contingent commodities?

Answer 4

A commodity whose level depends on which state of the world occurs

Question 5

What is a contingent commodity bundle?

Answer 5

• The point on the graph defined by (consumption if success, consumption if lose) given the bet/situation
• i.e. work out what consumption will be if success and if lose and this combination is the contingent consumption bundle

Question 6

What are the characteristics of an AFBL?

Answer 6

• EV = P(Y)Y + P(X)X = 0
• Slope: P(X)/P(Y), P/(1-P)
• The expected value of consumption is equal at every bundle along a fair odds line

Question 7

What is risk aversion?

Answer 7

• Prefer sure thing to a gamble with the same expected value
• MRS = P(X)/P(Y)
• Greater: more towards perfect comp. shape
• Always at endowment point - bet not taken, unless can be on higher utility curve

Question 8

What is risk neutral?

Answer 8

Indifferent between sure thing and gamble with same expected value

Question 9

What is risk loving?

Answer 9

Prefer a fair gamble to sure thing with the same expected value

Question 10

What is the form of an AFBL?

Answer 10

• CL = P(X)/P(Y).Cw + b
  
  • CL: consumption if lose
  • m: odds ratio P(X)/P(Y)
  • Cw: consumption if win
• Plug in endowment for y-int

Question 11

What are the steps to determining whether a gamble will be taken?

Answer 11

1. Draw certainty
2. Determine AFBL
3. Determine contingent commodity bundle for taking bet
4. Compare to utility curve

Question 12

What is implied if the contingent commodity bundle falls below the AFBL?

Answer 12

unfair gamble

Question 13

When will a risk lover take an unfair gamble?

Answer 13

Dependent on the shape of their curve, NEVER more than 90 degrees

Question 14

When will a risk averse person take a gamble?

Answer 14

• A more than fair gamble, EV > 0

- i.e. a higher utility curve than tangential

Question 15

What is a risk premium?

Answer 15

• Extra return necessary to compensate for risk

- i.e. making the EV greater

Question 16

What will different people do if the EV of a risk (B) is the same as certainty (A) i.e. both are a fair gamble?

Answer 16

• A risk loving individual will take B (C.C. Bundle)
• A risk natural individual will be indifferent
• A risk averse individual will take A (tangent point)

Question 17

What does the risk premium =

Answer 17

The vertical = horizontal distance between the C.C bundle and a risk averse persons utility curve

Question 18

What is the relationship between how risk averse someone is as the risk premium?

Answer 18

More risk averse: higher R necessary to meet indifference curve

Question 19

What is actuarily fair insurance?

Answer 19

Premium = EV of payout, r = p(payout) (probability x $1)

EVcompenstation = AFpremium!!!

Question 20

What is fully insured?

Answer 20

same consumption in both world states, i.e at certainty equivalent

Question 21

What is true of risk aversion and fair insurance?

Answer 21

If you are risk averse, and offered fair insurance, you will fully insure yourself

Question 22

What is unfair insurance?

Answer 22

For every $ pay as premium

Question 23

What is the contingent commodity bundle we are interested in when considering insurance?

Answer 23

Y-Int (i.e. if fire, if injured) (Cfire = 0) (i.e. you get nothing)

Question 24

What is important about investigating unfair insurance?

Answer 24

Must compare to AFBL (P/(1-P))

Question 25

What is true of risk aversion and unfair insurance?

Answer 25

• If risk averse fully insuring would put us on a lower indifference curve
• Partially insure (i.e. not down to AFBL endowment point)

Question 26

What is true of fair insurance in regards to the BC?

Answer 26

AFBL = AFinsurance

Question 27

What are the steps to a gamble question?

Answer 27

1. Determine contingent commodity bundle values
2. Determine EV of risk - ONLY lies on AFBC if 0 or ∆0
3. Draw indifference curve to suit outcome

Question 28

What is true if the expected (total) value of a contingent commodity bundle is greater than endowment?

Answer 28

Only that the point is not on the AFBL, whether the risk is taken depends solely on the indifference curve type and then shape

Question 29

What are the steps to an insurance question?

Answer 29

1. IF FAIR: EVcompensation = AFpremium
2. Commodity bundle point
3. Endowment = EV of situation
4. Determine AFBL
5. Commodity bundle point - Endowment should = AFpremium

Question 30

What is the most important thing about insurance questions?

Answer 30

The endowment point is an ideal where the highest U curve would be tangent to the AFBL - the expected bundle (CCB) is the actual situation

Question 31

How can a risk premium be shown on the I vs U graph?

Answer 31

The utility derived from the expected value of the risk is higher on certainty (normal curve) than the risk line (straight line connecting high outcome and low). Where the utility of the straight line at the expected value intersects the normal curve is x. The risk premium therefore is EV - x

Question 32

What is true of the bundle in insurance?

Answer 32

Will never be certainty

Question 33

What is true of the unfair insurance line?

Answer 33

Must pass through the bundle

Question 34

Who desires insurance?

Answer 34

ONLY risk averse

Question 35

When will a risk averse person need a risk premium?

Answer 35

If fair and below indifference
If fair but not tangent
If unfair