Risk + Insurance Flashcards
What 2 things do you need to Evaluate a Risky Prospect?
- Expected Income E(I)
- Expected Utility EU(I)- assume Individuals receive Utility U(I) from a given level of Income
How do you find Expected Income?
E(I) = pW + (1 - p) L
How do you find Expected Utility?
EU(I) = pU(W) + (1 - p) U(L)
What does Expected Utility show?
Shows that Individual’s Attitude to Risk is linked to their Utility Function
What does a Linear Utility Function mean?
Constant Marginal Utility of Income
Risk Neutral
U(I) = I^a , a = 1
As Income Increases–> Utility Increases proportionately
What does a Convex Upward sloping Utility Function mean?
Increasing Marginal Utility of Income
Risk Loving
U(I) = I^a , a > 1
As Income Increases–> Utility Increases More than proportionately
What does a Concave Upward sloping Utility Function mean?
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
Why would people Buy Insurance?
Insurance makes a Risky Situation–> a More Certain one
- Helps maintain Income/Wealth in a ‘Loss’ State
=> In Return for Paying a Premium
What is the purchase of Insurance a choice between?
Taking a Gamble + Having Certainty
What do we need to be able to represent to Analyse the Decision to Buy Insurance?
- Expected Utility from a Gamble- i.e. EU(I)
- Utility from Certainty
What does Expected Utility from a Gamble + Utility from Certainty together produce?
Demand for Insurance
What is the Max. a Consumer would pay for Insurance?
I from W - £x corresponding to EU(I)
What is the condition for a Consumer to buy Insurance?
Risk Averse- U(I) > EU(I)
What is the equation for Expected Profits for the Insurer?
E(Prof.) = sigma - (1 - p) (W - L)
sigma = Insurance Premium
(W - L) = Size of Loss
What is a Fair Price for the Insurer?
sigma
Insurer pays Size of Expected Loss
What is the Risk Premium in an Imperfect Market?
sigma(mp) = sigma(c) + theta [E(I) - £x]
What is Asymmetric Information?
One party knows more than another party
Why is Asymmetric Info a problem?
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
When are the 2 times Asymmetric Information can happen?
- Adverse Selection
- Moral Hazard
What is Adverse Selection?
Insured has Exogenous Probability of Loss but Insurer can’t see it
- e.g. Someone with a Genetic Illness
What is Moral Hazard?
Insured can Influence Probability of Loss by taking ‘care’ which is costly
- Why take care if Insured?
- e.g. Driving Carefully, Smoking
What is the problem with Adverse Selection?
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
What is a Solution for Adverse Selection?
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
What is the problem with Moral Hazard?
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
What is a Solution to Moral Hazard?
Signal
- e.g. Offer to pay first £500 of car damage
=> Excess
what is the issue with Excesses?
Excesses do NOT offer Full Coverage–> Issue NOT Fully Overcome
