Insurance companies and risk neutrality

The requirements for the insurance market to be efficient are that the least risk adverse agent bears all the risk. This means that the agents will be bearing all the risk giving the insurance company a more certain outcome.

The market will also have to be in equilibrium, which means that two conditions will be have to be met. The first is the break even condition; this means that no contract makes negative profits. If the insurance company is not making profit off of a contract then this is inefficient and may mean the company would have to shut down depending on the profit made from other contracts. The market will also have an absence of unexploited opportunities for profit. If this is not that case then rival companies can exploit this opportunity and offer a better contract.

To be efficient the insurance market a firm will also have to be in perfect competition so they can offer a fair insurance (Risk premium = PR of loss x loss). If they do not offer fair insurance, another company can under-cut them and steal all their customers.

Finally, the market will need to have perfect information so they can offer the correct premium to everyone. Otherwise they will have to pool equilibrium as they will not know individual risk types. This would mean low risk people will be essentially paying for part of the high risk candidates insurance as well as their own which is not Pareto efficient. Pareto efficiency is when principal cannot be made better off without making the agent worse off. This condition must be met for the market to be efficient. If it is not met then they will be at a point where both parties can be made better off.

The insurance markets pretty much meet all the requirements above and so to an extent are efficient. Although of course perfect information is not quite possible.  Insurance companies reduce the amount moral hazard and adverse selection in the market by for example, making candidates fill out forms which void contracts if  information proves to be false and offer no claims bonuses.

To discuss whether risk neutrality is a necessary and sufficient condition for insurance to take place, we need to look at what would happen in the three possible scenarios: risk neutral, risk adverse and risk loving.

We can start by looking at a risk-neutral insurance company. In reality, large organisations such as insurance companies tend to be risk neutral for mainly two reasons: the risks are small relative to the organisations size and as they offer so many risk contracts, on average they all tend to cancel each other out. A risk neutral insurance company earn their profit from the fact that the value of premiums they receive is either greater than or equal to the expected value of the loss.

Even insurance companies that take on purely risky customers will still be risk neutral as they will raise the premiums to offset the extra risk. For example, some specialist  holiday insurance companies may only take on candidates who already have pre-existing medical conditions and find it difficult to get insured elsewhere. The companies will offset the extra risk however by charging much higher premiums. Again the value of premiums they receive will be either greater than or equal to the expected value of the loss.

An insurance company cannot be risk averse because of the nature of the insurance market. If the company is risk averse, then it will charge premiums much higher than the expected value of the loss. In the presence of perfect information and perfect competition, customers will not choose to insure with this company as there will be better alternatives elsewhere. Therefore the if the insurance company was risk averse it would get no customers and soon fail.

Finally, an insurance company will not work in the long run if it is risk loving. A risk loving firm would accept lower premiums from customers than a risk neutral firm would and hope that the gamble pays off. This would mean that they would be expected to make a loss overall as their premiums would be less than their expected loss. Therefore eventually they would be making a negative profit and would have to shut down. (Unless they are very, very lucky!)

So for all of these reasons, it’s necessary for an insurance company to be risk neutral for insurance to take place. It is also a sufficient condition for insurance to take place as they will be at a minimum, breaking even and so can continue to exist in a perfectly competitive market, and they can offer a competitive premium to survive in a market with perfect information. Being risk neutral will also allow the insurance company to be efficient, as they will be making the break even condition.

Are the assumptions of the Marshallian and Hicksian consumer optimisation problems plausible?

The assumptions made implicitly in the two models relate to the basic axioms of consumer theory which I have briefly described below.

Completeness – “for any pair of bundles, our consumer can say if one of the pairs is preferred to the other or is indifferent.” (M. Hoskins, pages 3)

Transitivity – “if APB and BPC then APC”. Also works with indifference – if A/B (A indifferent to B) and B/C then A/B (M. Hoskins, pages 4)

Continuity of preference – “for any bundle of goods, this requires another bundle ‘near it’ such that these two bundles and indifferent to each other.”  “This requires the divisibility of goods and allows us to define the marginal rate of substitution between x and y.” (M. Hoskins, pages 4)

Non satiation – “consumers always prefer more goods to fewer. This deduces that indifference curves slop down from left to right.” (M. Hoskins, pages 5)

Convexity of preference – “people prefer a mixture of bundles.” “This leads to the diminishing marginal rates of substitution. “(M. Hoskins, pages 7)

The assumptions are mainly the same for both the Hicksian and Marshallian consumer optimisation problems. We assume that both optimisation problems have the traits of completeness and transitivity as otherwise we would not know the consumers utility to work from. These two traits however can be seen an irrational when related to the real world. There may be situations in which decision making can be extremely difficult and so a consumer may not be able to decide if a bundle of goods are preferred to another or indifferent, rendering us unable to economically analyse the situation using this model. Also, it assumes that the customer knows their utility that they will receive from the product which is not always the case. The transitivity assumptions eliminate the possibility of intersecting indifference curves. At any one point in time, this could be true, for example, today I may prefer an apple to pear and a pear to an orange, and therefore I would prefer an apple to an orange. However, it does not take into account the time horizon. Tomorrow my preferences may change, and neither model takes that into account.

Continuity of preference is also assumed by both models and both assume that the marginal rate of substitution equals the price ratio (P1/P2). This however ignores quantity discounts; if you order in bulk then you are likely to get more for you money.

The non-satiation property also will not hold in reality. The consumer is always defined as per period and there is usually an upper limit on consumption of most goods in a specific time frame. This assumption also links in with the other assumption made in both models that that X1*>0 and X2*>0 (non-negativity). If there are two goods, for example, carrots and peas and the consumer does not like carrots, he does not prefer to have more as he does not like them. What also if one of the goods was pollution, which it would be rational to prefer none of.

The last assumption of the basic axioms I have listed is the convexity of preference which again for reasons listed before, may not hold in reality. People may prefer a mixture of bundles in some cases, but not in others. If they do prefer the mixture of goods then the diminishing marginal rates of substitution does makes sense in reality. For example, if the two goods were coke and water (and you preferred a mixture of the two) and you had loads of water and no coke, then eventually the enjoyment you would gain from an extra glass of water would fall. You would therefore be prepared to lose more water in comparison to the amount of coke you would gain.

Although the two optimisation problems share all the assumptions above, they also have individual assumptions. The Marshallian optimisation problem specifically assumes that the customer is a utility maximiser. This is in line with the rational theory of the consumer as he wants to maximise his utility according to his wealth. This is not always true of reality as it will depend on the type of consumer. Some consumers may well try to maximise their utility but this will mean exhausting income. For example, people who are hooked on drugs may spend all of the income on drugs which they believe gives them their maximum utility. Other consumers will want to save some of their income and in doing so happily forfeit the extra utility.

Finally, the Hicksian optimisation problem assumes that the consumer targets a utility and finds the most cost effective way to reach this. I think this is probably truer of reality than the Marshallian method; however again, it depends entirely on the consumer himself. Less wealthy consumers may decide they want a certain product and then search the internet and high street to find the best deal. A consumer who is a billionaire however may not have a target utility as money is not a worry. He may also not adhere to price ratios – if a good increases in price, he may buy more of that good as a symbol of status.