Welfare State Economics lecture summary
Welfare State Economics lecture 2: Insurance Theory
- Demand for insurance
o Why interested?
- Supply of insurance
o 4 conditions
o 2 problems: moral hazard and adverse selection
- Empirical analyses of the two problems
Demand for insurance: may be beneficial for individuals if uncertainty causes disutility →
risk aversion.
This means there are two conditions for insurance demand:
- Uncertainty about utility outcomes.
- Decreasing marginal utility of income.
Insurance provides certainty … Slide 3
Suppose U(y) denotes the utility U as a function of income/wage y.
When you want insurance:
U(y)>0 : utility is positive
U’(y)>0 : utility increases with income
U’’(y)<0 : increase in utility smaller for higher income
Definitions/assumptions:
- Suppose there are two possible outcomes:
o With probability p, you receive income y1
o With probability 1-p, you receive income y2
o
o There is a utility loss because of uncertainty. In a world without uncertainty
you can follow the green line, with
o Willingness to pay for insurance is determined by the distance between:
▪ Utility of expected income
▪ Expected utility of income
, o Example:
▪ U(y) = wortel van y -> concave slope
▪ Income of 225 with probality 0.8 and 25 with probability 0.2
▪ Expected amount (E(y)): 185 = 225*0,8 + 25*0,2
▪ 0,8 wortel225 + 0,2*wortel25 = 12+1=13 expected utility
▪ Certainty equivalent of this utility level
• y2=169
• difference between straight line vs concave
▪ willingness to pay for insurance?
▪ Fair premium 225-185=40
▪ Plus willing to pay for certainty: 185-169=16
• So 56 willingness
▪ Characteristics for utility:
• Positive
• Going up
• Decreasing
o
o
-
Supply side of insurance:
- Insurers essentially pool risks to reduce risks for individuals. The average risks of
individuals decreases.
- The four conditions to step into this market:
o 1. Risk probabilities are independent: individual risks, not common shocks.
The law of large numbers doesn’t work anymore, diversifications needed.
Unemployment risk correlated with business cycle, which applies to large
groups of workers
o 2. Probabilities less than one. Risk, not certainty. Medical insurance for the
elderly.
o 3. Known probabilities. Risk not uncertainty. Rare events: natural disasters.
Complexity of problem: insurance for pension indexing against future
inflation? Long term contracts: in the long term, risks may become unknown,
like long term care due to medical advances.
o 4. No asymmetric information. There has to be a plain field.
▪ Hidden actions (to increase your risks) causes moral hazard.
, ▪Hidden knowledge causes adverse selection: individuals with high risks
are contracted, rather than low risks
▪ Moral hazard: this behaviour wouldn’t have been there because of the
insurance.
o Outcome is over-insurance.
▪ Deadweight loss due to elastic demand (due to moral hazard) P*xQ**-
Q*=DWL
▪ Endogeneity (individuals can change risks) is a necessary but not
sufficient condition for moral hazard
• Four cases of endogenous risks:
o 1.
o 2. Low psychic costs of moral hazard (ignore being sick)
o 3. High gains of moral hazard: insured event is
deliberate act, you exploit it. (childbirth, hair transplant)
o Not risk but costs are endogenous (supply side; third
party problem)
▪ No incentive to prevent high costs
▪ Another way to classify:
• Reduced precaution (car
• Increased odds of staying in the adverse state (unemployment
• Increased costs when in adverse state (third party)
▪ How can we fight moral hazard?
• Regulation/inspection: getting more information that causes
moral hazard
• Less insurance: taking away the incentive. Providing less
insurance.
o Experience rating: determined by past behaviour.
o Deductibles: fixed amount of the costs
o Co-payments: proportional amount of the costs
o Stricter eligibility conditions: where is the problem of
moral hazard the biggest?
▪ Adverse selection:
• Individuals have private information on certain risks and this
information is not available for the insurer
• → consequence: there can be no market, or incomplete market
(with underinsurance)
• One drastic solution: one single pooling contract with
compulsory participation.
• Examples:
o 2nd hand cars
o Medical insurance
o Car insurance (drives like a madman)
▪ Voluntary pension contracts
o Model of adverse selection:
▪ Two types of risks, high and low
▪ Individuals types are unknown, but the distribution of risks is observed.
▪ A is income when working
Welfare State Economics lecture 2: Insurance Theory
- Demand for insurance
o Why interested?
- Supply of insurance
o 4 conditions
o 2 problems: moral hazard and adverse selection
- Empirical analyses of the two problems
Demand for insurance: may be beneficial for individuals if uncertainty causes disutility →
risk aversion.
This means there are two conditions for insurance demand:
- Uncertainty about utility outcomes.
- Decreasing marginal utility of income.
Insurance provides certainty … Slide 3
Suppose U(y) denotes the utility U as a function of income/wage y.
When you want insurance:
U(y)>0 : utility is positive
U’(y)>0 : utility increases with income
U’’(y)<0 : increase in utility smaller for higher income
Definitions/assumptions:
- Suppose there are two possible outcomes:
o With probability p, you receive income y1
o With probability 1-p, you receive income y2
o
o There is a utility loss because of uncertainty. In a world without uncertainty
you can follow the green line, with
o Willingness to pay for insurance is determined by the distance between:
▪ Utility of expected income
▪ Expected utility of income
, o Example:
▪ U(y) = wortel van y -> concave slope
▪ Income of 225 with probality 0.8 and 25 with probability 0.2
▪ Expected amount (E(y)): 185 = 225*0,8 + 25*0,2
▪ 0,8 wortel225 + 0,2*wortel25 = 12+1=13 expected utility
▪ Certainty equivalent of this utility level
• y2=169
• difference between straight line vs concave
▪ willingness to pay for insurance?
▪ Fair premium 225-185=40
▪ Plus willing to pay for certainty: 185-169=16
• So 56 willingness
▪ Characteristics for utility:
• Positive
• Going up
• Decreasing
o
o
-
Supply side of insurance:
- Insurers essentially pool risks to reduce risks for individuals. The average risks of
individuals decreases.
- The four conditions to step into this market:
o 1. Risk probabilities are independent: individual risks, not common shocks.
The law of large numbers doesn’t work anymore, diversifications needed.
Unemployment risk correlated with business cycle, which applies to large
groups of workers
o 2. Probabilities less than one. Risk, not certainty. Medical insurance for the
elderly.
o 3. Known probabilities. Risk not uncertainty. Rare events: natural disasters.
Complexity of problem: insurance for pension indexing against future
inflation? Long term contracts: in the long term, risks may become unknown,
like long term care due to medical advances.
o 4. No asymmetric information. There has to be a plain field.
▪ Hidden actions (to increase your risks) causes moral hazard.
, ▪Hidden knowledge causes adverse selection: individuals with high risks
are contracted, rather than low risks
▪ Moral hazard: this behaviour wouldn’t have been there because of the
insurance.
o Outcome is over-insurance.
▪ Deadweight loss due to elastic demand (due to moral hazard) P*xQ**-
Q*=DWL
▪ Endogeneity (individuals can change risks) is a necessary but not
sufficient condition for moral hazard
• Four cases of endogenous risks:
o 1.
o 2. Low psychic costs of moral hazard (ignore being sick)
o 3. High gains of moral hazard: insured event is
deliberate act, you exploit it. (childbirth, hair transplant)
o Not risk but costs are endogenous (supply side; third
party problem)
▪ No incentive to prevent high costs
▪ Another way to classify:
• Reduced precaution (car
• Increased odds of staying in the adverse state (unemployment
• Increased costs when in adverse state (third party)
▪ How can we fight moral hazard?
• Regulation/inspection: getting more information that causes
moral hazard
• Less insurance: taking away the incentive. Providing less
insurance.
o Experience rating: determined by past behaviour.
o Deductibles: fixed amount of the costs
o Co-payments: proportional amount of the costs
o Stricter eligibility conditions: where is the problem of
moral hazard the biggest?
▪ Adverse selection:
• Individuals have private information on certain risks and this
information is not available for the insurer
• → consequence: there can be no market, or incomplete market
(with underinsurance)
• One drastic solution: one single pooling contract with
compulsory participation.
• Examples:
o 2nd hand cars
o Medical insurance
o Car insurance (drives like a madman)
▪ Voluntary pension contracts
o Model of adverse selection:
▪ Two types of risks, high and low
▪ Individuals types are unknown, but the distribution of risks is observed.
▪ A is income when working
