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Flashcards in Risk + Insurance Deck (26)
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1
Q

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

A
  • Expected Income E(I)

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

2
Q

How do you find Expected Income?

A

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

3
Q

How do you find Expected Utility?

A

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

4
Q

What does Expected Utility show?

A

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

5
Q

What does a Linear Utility Function mean?

A

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

6
Q

What does a Convex Upward sloping Utility Function mean?

A

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

7
Q

What does a Concave Upward sloping Utility Function mean?

A
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
8
Q

Why would people Buy Insurance?

A

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

9
Q

What is the purchase of Insurance a choice between?

A

Taking a Gamble + Having Certainty

10
Q

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

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

- Utility from Certainty

11
Q

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

A

Demand for Insurance

12
Q

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

A

I from W - £x corresponding to EU(I)

13
Q

What is the condition for a Consumer to buy Insurance?

A

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

14
Q

What is the equation for Expected Profits for the Insurer?

A

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

15
Q

What is a Fair Price for the Insurer?

A

sigma

Insurer pays Size of Expected Loss

16
Q

What is the Risk Premium in an Imperfect Market?

A

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

17
Q

What is Asymmetric Information?

A

One party knows more than another party

18
Q

Why is Asymmetric Info a problem?

A

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
19
Q

When are the 2 times Asymmetric Information can happen?

A
  • Adverse Selection

- Moral Hazard

20
Q

What is Adverse Selection?

A

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

21
Q

What is Moral Hazard?

A

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

  • Why take care if Insured?
  • e.g. Driving Carefully, Smoking
22
Q

What is the problem with Adverse Selection?

A

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

23
Q

What is a Solution for Adverse Selection?

A

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

24
Q

What is the problem with Moral Hazard?

A

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

25
Q

What is a Solution to Moral Hazard?

A

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

26
Q

what is the issue with Excesses?

A

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