Economics, Coursework Example

Q2.

Expected Utility Theory
Suppose a consumer has an income of $30,000. If an adverse effect occurs (say
getting sick or having the house burn down), the person suffers a loss of $20,000
(leaving him with an income of $10,000). Suppose the probability of this event is
20%.
a) Calculate the consumer’s expected income E(I).
b) Suppose the person is risk averse with a concave utility function, where
U($10,000)=100, U($30,000)=500. Calculate the consumer’s expected utility E(U).
c) Make up a plausible value for U(E(I)). Is it greater than, equal to, or less than E(U)?
d) Suppose the consumer’s risk premium is $500, calculate the certainty income (Ic).
e) Now suppose the size of the loss is smaller, $5,000. How do E(I), E(U), U(E(I)), and
the size of the risk premium change? Explain your answer, you do not need to
perform any calculations.

Response:

(.8*30000)+(.2*10000)=26,000

(.8*500)+(.2*100)=450

460. It is greater than the EI due to the concave nature of the function.

26,000-500=25,500

In this case, with a smaller risk, expected income and utility, and U((E)I) would all increase as they would feature the same upside and probabilities, but lower downsides. The risk    premium will be lower, as people would the lower risk means a lower amount of money one   would be willing to accept for it.

Q3.

Moral Hazard
a) Briefly explain the difference between how health insurance reduces risk through a
coinsurance rate and how car insurance reduces risk.
b) In your own words describe Moral Hazard.
c) How does the size of the moral hazard welfare loss change as the coinsurance rate
falls? As the demand for health care becomes more elastic?
d) Refer to the numerical example on p.310 (also in lecture notes) about moral hazard.
Suppose all values are the same except.

I. f1=.4
II. f2=.1
III. C=.1
IV. Loading fee =20%

Calculate E(B), the expected benefit paid by the insurance company.
Calculate the premium charged by the insurance company.
Would the consumer be willing to purchase this insurance policy? If so what is the consumer’s net benefit. (don’t forget moral hazard).

Response:

a. Car insurance only covers large claims, but does no regular maintenance. Health insurance usually does cover not just catastrophic things of that nature, but does provide coverage to the insured for things such as checkups as well. Car insurance is reducing risk by spreading it out amongst many people while health insurance does that as well as tries to lower overall costs through preventive methods.

b. Moral hazard is the idea that people will take too many risks if they are not the ones responsible for the loss associated with that risk. In terms of health insurance that would mean that someone completely covered will take on too many health risks and also over consume healthcare if they do not have any copays.

c. As the coinsurance rate falls, the moral hazard goes up. The insured is facing less and less of the risk he creates by himself. As the demand for healthcare becomes more elastic, the moral hazard changes. Since the insured is going to take on more risk, seeing the marginal value of the healthcare to be much greater than the dollar in this situation.

d. E(B)=500*(.4*4)+(.1*9))*(1-.1)=1125

1125*1.2=1350, the premium.

The consumer, with a $220 risk premium, would be willing to pay $1345, or in other words, less than the premium being charged. This means a negative net benefit of negative seventy five dollars, once the $70 moral hazard welfare loss is considered.

Q5.

Adverse Selection (Genetic Testing)
Suppose geneticists discover an Alzheimer gene (“A” gene) that provides useful information about the chances of developing Alzheimer’s disease. The only way for an individual to know if he/she has the “A” gene is to get a genetic test. Otherwise everyone, individuals (and insurance companies) know that 20% of the population has the “A” gene. Furthermore, suppose the chance of developing Alzheimer’s disease is 10% if you don’t have the “A” gene and 50% if you do have the “A” gene. Everyone knows these odds. The dollar-valued loss of getting the disease is $40,000, and everyone has a risk premium of $2,000.

a) Calculate the actuarially fair premium for an insurance policy that protects against Alzheimer’s disease under the assumption that nobody has taken the genetic test?
b) Calculate the net benefit of a consumer buying this insurance?
c) What is the actuarially fair premium if the insurance company and I both know that I have the “A” gene?
d) What is the actuarially fair premium if the insurance company and I both know that I do not have the “A” gene?
e) If I learned that I do have the “A” gene would I be willing to reveal that information to the insurance company or would I prefer the insurance policy from part a) (hint: calculate the net benefit in both situations)
f) If I learned that I do not have the “A” gene would I be willing to reveal that information to the insurance company or would I prefer the insurance policy from part a) (hint: calculate the net benefit in both situations)
g) Suppose the cost of the genetic test is $500. Would I be willing to pay for the test if: a. It is mandatory for me to reveal the result to the insurance co. (hint: only the insurance contracts in part c) & d) would be offered)
b. I am forbidden from revealing the result to the insurance co. (hint: only the insurance contract in part a) would be offered)
c. It is optional for me to reveal the result to the insurance co. (hint: suppose all of the insurance contracts in part a), c), d) are offered, and which one I can get depends on whether or not I have taken the test, and whether or not I reveal information to the insurance company about the gene test results.) (show the calculations depicting how you arrived at your answers. Do not consider other non-financial motives for getting genetic testing, such as “peace of mind”)
h) If it is optional to reveal the results to the insurance co., explain why the insurance contract in part a) would not be offered.
i) The government must make decisions on two types of policies
a) taxing or subsidizing the genetic test
b) Forbidding, making mandatory, or making it optional for individuals to reveal the result of a test to insurance co.
In light of this example, what are the consequences of these policies? What are the distributional considerations? What do you think the best policy choices are in terms of maximizing individual’s welfare?

Response:

a. .5*.2=.1

.8*.1=.08

Total chance=18%.

.18*40,000=7200

b. A consumer buying this policy at this price would gain $2,000 of benefit through their risk premium.

c. 40000*.5=20,000

d. 40000*.1=4,000

e. You would prefer the insurance company not know.

f. In this case it should be revealed.

g. If the test saves $500 then you should not pay for it if it must be revealed. Your expected insurance premiums is still $7200 afterwards.

If it cannot be revealed, then the value of the test would fall outside of insurance. You would be paying $500 to retain the same premium. This could be worth it to someone who wants a better understanding of their risk, but it will not affect health insurance premia.

If it is optional, the test should be taken. The potential loss is only $500, as if the test says you have the A gene, you would be out the test fee, but not tell your insurance provider. The potential gain is $2,700, the potential savings minus the test fee. Considering that the gain is much more likely and larger, this makes the test a good idea.

h. Because in this situation, the insurance company can only lose money. They get no extra premium if the test is positive but lose if it is negative. Therefore, they must take away the first option and only offer coverage to those who take the test and reveal results.

i. I would mandate telling the insurance company if there is a test done. However, I would not subsidize the test. This gives people incentive to take it as their expected benefit exists. It would be a loss for those with the gene and a gain for those without. Insurance companies would also more accurately be able to price their policies.