Question

Suppose when Joan is healthy, she earns $50,000 which generates utility of 100 utils.When sick, the cost of treatment is $30,000 and her utility falls to 60 utils. The probability of illness occurring is 25%. Income of $32,500 produces actual level of utility of 90. Income of $42,500 produces actual utility of 98.

i. Find Joan’s expected income and expected utility without health insurance.

ii. Would Joan buy health insurance, given the insurance policy offered sells at an actuarial fair premium (i.e., reflects only expected costs of medical care to treat illness). Explain your answer carefully.

b). One of the problems resulting from health insurance is moral hazard.

i. What is moral hazard? What are 2 different types of moral hazard? Please explain carefully.

ii. How does Nyman’s (2003) view on moral hazard differ from the conventional view of moral hazard?

iii. What are 2 examples of responses to reducing the moral hazard problem? Explain briefly.

Answer 1

a.1) Joan's income without insurance will be 50,000$ with a probability of 75% (no illness) and 20,000$ with a probability of 25% (Illness costing 30,000 in treatment)
Therefore Joan's expected income = 0.75*50,000 + 0.25*20,000 = 42,500$

Joan's utility without insurance will 100 with a probability of 0.75 and 60 with a probability of 0.25, so her expected utility is 0.75*100+60*0.25 = 90

2) Yes Joan will buy health insurance given the insurance policy offered wells at an actuarial fair premium. Since if it is a fair premium and only reflects expected costs of medical care, her expected income will remain the same. However her expected utility will increase. This can be determined by the fact that her utility curve is a typical upward sloping curve with decreasing slope i.e. diminishing return with income. Therefore she will have a higher utility with the utility associated with guaranteed income of 42,500(the utility will be higher than 90) than a 75% chance of 100 utility and 25% chance of 60 utility which gives a utility of 90.

b) 1) Moral hazard is when an individual/agent has incentive to change their behavior and engage in risky behavior knowing that they will not have to bear the full cost of the outcome. The two types of moral hazard are ex ante and ex post moral hazard. Ex ante moral hazard can be described as the behavior of the individual before the outcome of the event has occured and ex post as after the event has occured. For example in the case of an insurance which is going to end at the end of the year and the event is the insurance getting over and the outcome his final health, if the individual takes more risks for his health knowing that insurance will pay for it, it goes under ex ante moral hazard as the behavior is before the insurance ends, however an individual who is perfectly healthy but tries to defraud the insurance company by lying about their health will be ex post moral hazard.

2) Nyman's view is different from conventional view of moral hazard as the conventional view is of the opinion that moral hazard always leads to reduction in welfare. He proposes that the insurance acts as a transfer of income from the healthy to the sick,and if there is more moral hazard, more money will be made available to the sick, i.e. it makes the healthcare industry more affordable.

3) Since moral hazard is mostly a problem in case of asymmetric information i.e. the private actions of an agent affects the probabiltiy of the outcome, it can be avoided by an approach that allows to monitor the behavior of the individual in response to getting the insurance. There can be conditions put to discourage the individual from engaging in risky behavior and his behavior can be monitored.

Another way this can be achieved is by deductibles and co-pay for example. In this case the individual will have to bear part of the cost and insurance will not pay the full, hence the individual still has incentive to not engage in risky behavior as he will still have to bear some cost.

Hope it helps. Do ask for any clarifications if required.