Week 4/5 - Risk and Uncertainty

Question 1

Risk

Answer 1

• We know the probability distribution

Question 2

Uncertainty

Answer 2

• We don’t know the probability distribution

Question 3

Expected Value

Answer 3

EV = Σ πi(xi)

Question 4

Expected Utility

Answer 4

Under some assumptions, we can represent
preferences via Expected Utility functions, i.e.
𝑈 (𝑥1, 𝑥2) = 𝜋1 𝑢(𝑥1) + 𝜋2 𝑢(𝑥2)

Question 5

Risk Averse

Answer 5

• Will not play an actuarially fair game
• Preference for certainty over uncertainty.
• Is the most common attitude - we tend to prefer certainty.
• The function is concave
• The utility of the expected value is greater than the expected utility.
• U(π1W1+ π2W2) > π1U(W1) + π2U(W2)
• If you are risk averse, you will simply take the value of the expected value E(V) instead of gambling.

Question 6

Risk Seeking

Answer 6

• Will play actuarially fair game
• If the expected utlity is greater than the utility of the expected value, then this person is risk seeking.
• U(π1W1+ π2W2) < π1U(W1) + π2U(W2)

Question 7

Neutral

Answer 7

• Indifferent between playing and not playing.
• That is, the utility of the expected value is equal to the expected utility.

Question 8

Neutral

Answer 8

• Indifferent between playing and not playing.
• That is, the utility of the expected value is equal to the expected utility.

Question 9

Certainty equivalent

Answer 9

How much money you have to give me for me to be indifferent between entering the gamble and the value of the certainty equaivalent.
- Where the certainty equivalent is Expected utility reverse enginereed through utility funciton.
- That is, if the expected utlity is 5 and the utlity function is x^1/2, then the CE is 5^2

Question 10

When is insurance actuarially fair

Answer 10

• When the expected value of the gamble remain unchanged.
• We assume that the price of unit of insurance = the probability something bad happens
• A risk averse individual will therefore fully insure their good. That is optimal units of insurance A* is equal to the value of the damage D. A* = D
  Thereby keeping our expected value constant.

Question 11

Risk Premium

Answer 11

• ## Risk averse individuals who pay above perfectly competitive price, where price = probability of damage.

Question 12

Assymetric information

Answer 12

missing information which affect other adversely because it can be used take advantage of uniformed agent.
Can lead to;
- Adverse selection (hidden information)
- Moral hazard (Hidden action)

Question 12

Assymetric information

Answer 12

missing information which affect other adversely because it can be used take advantage of uniformed agent.
Can lead to;
- Adverse selection (hidden information)
- Moral hazard (Hidden action)

Question 13

Adverse selection

Answer 13

Students who buy insurance impose a negative externality in the market by raising the AC of insurance (and the premium)
- Therefore, a market equilibrium doesn’t exist

Question 14

How to determine if event is risk averse or risk seeking with no values

Answer 14

• If second derivative of utility function is less than 0, the person is risk averse
• if second derivative of utility function is grater than 0 is risk seeking

Question 15

Actuarially fair premium

Answer 15

The premium charged is equal to the expected loss. That is the probaility of the damage occuring multiplied by the value of the damage.