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EC325 Exam Solutions (2014/15/16)
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Social Insurance2016, Q5:
Social insurance systems to cover disability risks traditionally offer less insurance coverage for individual’s
subject to mental disorders than to individual’s subject to other physical disabilities. Explain under what
conditions this reduced coverage might be socially optimal.
Model answer
1. Direct answer: if cost of mental disorder is smaller than the cost of physical disabilities → socially
optimal to offer less insurance for disorders than physical disabilities → because this reduces moral
hazard and increases utility gain from insurance
2. Applied definitions: Asymmetric information - patients know more than the insurers about their own
health (e.g. whether they actually have a mental disorder); Moral hazard - when an agent takes on
risk because agent knows they’re protected from the consequences (e.g. by buying insurance);
Coinsurance - when consumers pay a share of medical bill (and insurer pays rest)
3. In-depth explanation with maths and graphs: Moral hazard is a problem with health insurance → if
health insurance is provided → consumers will reduce precautions against health risks because they
know they’re covered + overconsume health care because they don’t foot the cost + producers will
overprescribe medication because they know the insurers will have to cover the costs
So providing full health insurance can lead to overconsumption.
So Feldstein suggests a “Major Risk Insurance Plan” → 50% coinsurance on “small events” (until
medical bill reaches 10% of income) → full insurance only after that!
, Optimal because moral hazard is much lower for big events: e.g. physical disabilities → consumers
aren’t going to overconsume hip replacement surgery unless they really need it → so only provide
insurance for big events when moral hazard is low
And only co-insure for small events: e.g. mental disorders → consumers may overconsume
therapy/antidepressants even if they don’t need → so bad idea to fully insure → better idea to just
co-insure → so agents still feel 50% of cost to deter overconsumption
Also optimal because utility gain from insuring big events > utility gain from insuring small events →
best to fully insure big events
INSERT DIAGRAM & EXPLANATION
4. Link back: Feldstein shows insuring big events > insuring small events because it reduces the moral
hazard problem and increases the utility gain from insurance → so if physical disability is more
serious “big event” > mental disorders → makes sense to fully insure physical disability + co-insure
mental disorders
5. Extra: this is supported by RAND → elasticity = 0.2 → people insured more, on more generous
programmes BUT no improvement in health + criticisms: but RAND was only for small event and SR
window, might not have external validity, risk of measurement error (misreporting) + moral hazard --
/→ DWL if positive externalities
This reduced coverage may be socially optimal if the probability of ending up with mental disorders is low -
with more low risk types. The lower the variation and risk in getting a mental disability means the lower the
utility gains from full insurance. Can show this from lower utility differences from CV when there is a larger
risk spread in diagram.
Less than full insurance occurs when there is asymmetric information present in insurance markets - i.e.
observable risks are not realistic and risk types are only known to the individual and not the insurer.
Therefore, as the insurer is unable to make individuals reveal preferences - they have to offer coverage at the
same price for all types. This adverse selection problem makes worst risk types buy more which pushes
prices up and there are no longer full insurance as low risk types are unable to afford the contract. In this
context, mental disorders may have reduced coverage for these reasons. Therefore, there is a case for partial
insurance where the insurer provides several contracts with difference price-coverage combinations to
induce self-revelation. An equilibrium exists with lower priced partial insurance and higher prices full
insurance which is better than no insurance for the low risk types.
,2015, Q11:
a) A risk averse individual faces a diminishing marginal utility curve. This tells us that they get higher
marginal utility from not being in a bad state (unemployed) than being in a good state (employed) - ie. they
are very worried of losing but don't care as much for winning. This would not be the same for risk-neutral
individuals.
Their expected return with certainty is therefore higher than playing the “lottery” of facing employment or
unemployment. This expected return that they get is the full insurance they would receive at actuarially fair
, prices and therefore risk averse individuals would purchase it with a risk premium equivalent to the
difference between the expected value and certainty equivalent (the individual is indifferent in getting a
lower amount of consumption for sure than expected value of playing lottery of being employed or
unemployed - showing that they want to consumption smooth between both good and bad states). This
would not be true for risk neutral individuals as they face an upward sloping linear utility curve which is not
diminishing - they are indifferent between insurance and the lottery - hence risk “neutral”.
b) The inefficient provision of unemployment insurance is due to asymmetric information and the problem of
adverse selection. Insurers cannot observe everyone's types in a way that determines who faces a higher risk
of becoming unemployed - this is private information only known to the individual. Adverse Selection is
defined as one party having more information than the other on a transaction.
Risky types would by insurance first but insurance firms are unable to distinguish between the high and low
risk individuals as these risks are unobservable. Without revelation of types, insurers will charge the same
price based on the average risk across populations. Since risky types demand insurance coverage the most,
the price would be higher as insurance companies average cost increases with the risky types - hence
eliminating the demand for the low risk types as it is now too costly to buy insurance based on the fact that
they have a low probability of entering the adverse state (not actuarially fair prices).
Akerlof argued this and the new equilibrium reached is inefficient as more of the low risk types opt out -
hence no full insurance. This equilibrium is inefficient as there are welfare gains to be made but the
unobservability of characteristics leave the equilibrium point at P=AC where MB>MC.
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