Risk + Insurance

Question 1

What 2 things do you need to Evaluate a Risky Prospect?

Answer 1

• Expected Income E(I)

- Expected Utility EU(I)- assume Individuals receive Utility U(I) from a given level of Income

Question 2

How do you find Expected Income?

Answer 2

E(I) = pW + (1 - p) L

Question 3

How do you find Expected Utility?

Answer 3

EU(I) = pU(W) + (1 - p) U(L)

Question 4

What does Expected Utility show?

Answer 4

Shows that Individual’s Attitude to Risk is linked to their Utility Function

Question 5

What does a Linear Utility Function mean?

Answer 5

Constant Marginal Utility of Income
Risk Neutral
U(I) = I^a , a = 1
As Income Increases–> Utility Increases proportionately

Question 6

What does a Convex Upward sloping Utility Function mean?

Answer 6

Increasing Marginal Utility of Income
Risk Loving
U(I) = I^a , a > 1
As Income Increases–> Utility Increases More than proportionately

Question 7

What does a Concave Upward sloping Utility Function mean?

Answer 7

Diminishing Marginal Utility of Income
Risk Averse
U(I) = I^a , 0 < a < 1
U(I) = ln(I) , I > 1
As Income Increases--> Utility Increases Less than proportionately

Question 8

Why would people Buy Insurance?

Answer 8

Insurance makes a Risky Situation–> a More Certain one
- Helps maintain Income/Wealth in a ‘Loss’ State
=> In Return for Paying a Premium

Question 9

What is the purchase of Insurance a choice between?

Answer 9

Taking a Gamble + Having Certainty

Question 10

What do we need to be able to represent to Analyse the Decision to Buy Insurance?

Answer 10

• Expected Utility from a Gamble- i.e. EU(I)

- Utility from Certainty

Question 11

What does Expected Utility from a Gamble + Utility from Certainty together produce?

Answer 11

Demand for Insurance

Question 12

What is the Max. a Consumer would pay for Insurance?

Answer 12

I from W - £x corresponding to EU(I)

Question 13

What is the condition for a Consumer to buy Insurance?

Answer 13

Risk Averse- U(I) > EU(I)

Question 14

What is the equation for Expected Profits for the Insurer?

Answer 14

E(Prof.) = sigma - (1 - p) (W - L)
sigma = Insurance Premium
(W - L) = Size of Loss

Question 15

What is a Fair Price for the Insurer?

Answer 15

sigma

Insurer pays Size of Expected Loss

Question 16

What is the Risk Premium in an Imperfect Market?

Answer 16

sigma(mp) = sigma(c) + theta [E(I) - £x]

Question 17

What is Asymmetric Information?

Answer 17

One party knows more than another party

Question 18

Why is Asymmetric Info a problem?

Answer 18

Buyer knows more about Risky Prospect than Insurer

• Buyer might hide True Probability of Loss State- to get lower Risk Premium
• -> Harder for Insurer to set Premium

Question 19

When are the 2 times Asymmetric Information can happen?

Answer 19

• Adverse Selection

- Moral Hazard

Question 20

What is Adverse Selection?

Answer 20

Insured has Exogenous Probability of Loss but Insurer can’t see it
- e.g. Someone with a Genetic Illness

Question 21

What is Moral Hazard?

Answer 21

Insured can Influence Probability of Loss by taking ‘care’ which is costly

• Why take care if Insured?
• e.g. Driving Carefully, Smoking

Question 22

What is the problem with Adverse Selection?

Answer 22

High Risk can lie to receive Lower Premium
=> Insurer can’t tell who is High + Low Risk
==> Insurer bases Price on Average Likelihood- in between probability of Win + Loss
–> More Expensive than fair Price for Low risk–> Low Risk do not Buy

Question 23

What is a Solution for Adverse Selection?

Answer 23

Low Risk need to be able to send Signal that High Risk can’t send
-e.g. Offer to pay first £500 of Medical Bill
=> Excess

Question 24

What is the problem with Moral Hazard?

Answer 24

Insurer can’t see who takes ‘care’
People buy Insurance for Price with taking ‘care’ –> Enjoy Insurance cover + save on Cost of ‘caring’
=> Insurer Loses–> Insurer raises Price–> Naturally Careful stop Buying Insurance

Question 25

What is a Solution to Moral Hazard?

Answer 25

Signal
- e.g. Offer to pay first £500 of car damage
=> Excess

Question 26

what is the issue with Excesses?

Answer 26

Excesses do NOT offer Full Coverage–> Issue NOT Fully Overcome