Decision making under uncertainty

Question 1

What is the difference between uncertainty and risk?

Answer 1

Uncertainty is when any state of the world can occur and there is no information about which will arise.
Risk is when a probability of a state of the world occuring can be estimated.

Question 2

What does Savage say about uncertainty and risk?

Answer 2

Savage (1954) argues that all uncertainties can become risks, as choices have subjective probabilities that can be inferred from the choice made. This probability does not have to be empirical.

Question 3

What is a fair gamble?

Answer 3

When the expected value of a gamble is 0

Question 4

What are the three attitudes to risk? Describe them.

Answer 4

Risk averse - these individuals get utility from certainty.
Risk neutral - these individuals get no additional utility from certainty nor risk
Risk loving - these individuals get utility from uncertainty

Question 5

How do calculate expected utility?

Answer 5

Question 6

Describe expected utility theory.

Answer 6

Theorised by von Neumann and Morgenstern (1944).
It predicts that a rational individual will rank risky prospects based on expected utility, and choose the one that returns the highest expected utility.

Question 7

Six

What are the axioms of rational choice?

Answer 7

1. Completeness - any option can be compared to any option.
2. Transitivity - If A is preferred to B, and B is preferred to C, then A must also be preferred to C
3. Dominance - A choice would not be made that was worse in one aspect and no better in any other aspect.
4. Independence of common factors - If there are any components of each choice that are identical, they should not alter the decision.
5. Continuity - There is always an equivalent gamble to certain outcomes. E.g. If A is preferred to B, and B is preferred to C, there will be a probability that B is preferred to a gamble between A and C
6. Invariance - it is irrelevant how the question is posed if the outcome would be the same (e.g. 90% of winning or 10% chance of losing)

Question 8

Describe the Allais paradox.

Answer 8

Developed by Allais (1953).
It demonstrates an inconsistency between observed choices and expected choices based on expected utility theory, based on choices between two hypothetical lotteries.

Lottery A: 100% chance of £1m or 1% chance of £0, 89% chance of £1m and 10% chance of £5m
Lottery B: 89% chance of £0 and 11% chance or £1m or 90% chance of £0 and 10% chance of £5m.

These probabilities can be separated to be two choices that are exactly the same. If A1 is preferred to A2 but B2 is preferred to B1 then the common factors axiom has been violated.

Question 9

Why do risk-averse individuals seek insurance?

Answer 9

1. Risk averse individuals have diminishing utility to income
2. Healthcare is uncertain, so risk-averse individuals essentially pay to have a certain cost of their healthcare
3. There is a utility gain from fair insurance

Question 10

Draw the expected utility function for each risk attitude.

Answer 10

1. Risk loving
2. Risk averse
3. Risk neutral

Question 11

Demonstrate graphically that risk averse individuals get a welfare gain from insurance.

Answer 11

The loss in utility caused by buying insurance is not as great as the difference between the utility of ‘winning’ and the expected utility.

Question 12

What would happen if insurance companies started charging more than the fair premium?

Answer 12

According to this graph, insurance companies can charge between W-premium and W-Q and the utility from having insurance will still be greater than being uninsured. If the company charged more than W-Q, individuals would have more utility out of being uninsured.

Question 13

What are sources of uncertainty in the healthcare market?

Answer 13

• Timing of ill-health is unpredictable
• The success and adverse events associated with treatment is unknown
• The final cost of healthcare is unknown
• Healthcare has a demand derived from health, which is contributed to by more variables than just healthcare

Question 14

Why can’t the healthcare market reach Pareto efficiency?

Answer 14

Pareto efficiency is underpinned by the assumption that consumers and producers have perfect information. The uncertainty in healthcare makes this impossible.

Question 15

How does society react to the failure of the healthcare market?

Answer 15

• Regulation of supply of healthcare (e.g. qualifications required to permit medical practice)
• Expected ethical behaviour from healthcare professionals
• Regulations of the providers surrounding advertising

Question 16

How does the market react to the failure of the healthcare market?

Answer 16

• Insurance markets to insure against the cost of ill-health
• Information about medical care is a commodity

Question 17

What are the challenges surrounding the insurance market in reality?

Answer 17

1. Individuals do not know their own risk
2. Insurers do not know individual risk
3. There is no perfect competition between insurance companies
4. Moral hazard

Question 18

What is adverse selection?

Answer 18

Described by Akerlof (1970) in his seminal paper “a market for lemons”.

Insurers offer the same insurance to everyone regardless of risk. The individuals with high risk pay less than their risk, but those with low risk pay more. The insurer is relying on low-risk individuals from covering the costs of insuring high-risk individuals.

If the price is too high, low-risk individuals will drop out of the market. The price may then increase for high-risk individuals, which exacerbates the issue of adverse selection.

Question 19

What are strategies of dealing with adverse selection?

Answer 19

• Insurers gathering more information on insurees (e.g. medical examinations, more rigourous questioning on applications)
• Compulsory insurance
• Co-payments and deductibles

Question 20

How does insurance still work despite aysmmetric information?

Answer 20

Rothschild and Stiglitz (1976).
High-risk and low-risk individuals will self-select different prices of insurance packages.

Both high risk and low risk individuals would be happy to purchase insurance package A.
Only high risk individuals would pick package C, because this package is on a lower indifference curve than the low-risk curve, but higher than the high-risk.
Only low risk individuals would pick package B, because it is on a lower curve than the high-risk curve but higher than the low-risk curve.

Question 21

What work supports the Rothschild and Stiglitz (1976) paper

Answer 21

Cohen and Siegelman (2010) conducted an analysis of literature looking at a correlation between coverage and risk. They found that the majority of papers confirmed the presence of adverse selection across a range of insurance markets.

Shepard (2016) also found that adverse selection may not be just linked to risk, but also insuree’s preference for expensive treatment at ‘star hospitals’. Insurers opt not to cover care at these hospitals. Individuals who want care at these hospitals will select higher coverage plans to be insured, but this leads to inefficiently low access to these hospitals.

Question 22

What is moral hazard?

Answer 22

Defined by Arrow (1963)

Where individuals have already purchased their insurance package, and so the cost of them making a claim is effectively zero. As a result, insured individuals may take more risks as the potential utility loss is lower.

Question 23

Demonstrate how moral hazard leads to a welfare loss.

Answer 23

The price to the insuree is much lower than the market price so they demand more, but the suppliers still have to supply at the lower price. Therefore, there is a welfare loss associated.

Question 24

How may insurers deal with moral hazard?

Answer 24

Some outlined by Pauly (1968)
- No claims bonuses
- Co-payments
- Excesses/deductibles
- Rationing
- User-based insurance

Question 25

What is supplier moral hazard?

Answer 25

If doctors know that a patient is insured, the doctor will be more inclined to offer or recommend expensive options compared to if the patient is paying out-of-pocket.

Question 26

Why is obtaining empirical evidence about moral hazard and adverse selection challenging?

Answer 26

Cohen and Siegelman (2010) find that adverse selection and moral hazard, while are distinct reasons for insurance markets failing, are difficult to disentangle in data as they both lead to a correlation between coverage and risk.

Question 27

What does economic theory suggest about the use of user-based insurance? Why does this differ from the actual demand of UBI?

Answer 27

Holzapfel et al. (2023).
They predict that demand for user-based insurance should be high as they offer incentives for low-risk individuals to demonstrate they are low-risk, however demand for these are low.
They find this is because individuals want insurers to have accurate monitoring of their information, and not because of high start-up costs or privacy concerns. However I would argue this assumes individuals are rational with regards to privacy concerns, and there is a difference between telling a company where you live and allowing them to track your car.