The theory of risk aversion and its utilization by the insurance companies - Essay Example

Microeconomics Risk averse means is a situation whereby individuals are willing to pay some money in order to avoid playing a risky game; this takesplace even when the expected game value is in this individuals favor. Risk aversion is thus a theory that explains why people are always willing to buy insurance. There is a greater potential in this island of Aversia for the booming Insurance market this is mainly due to the fact that the residents of this small island are always willing to pay the insurance premiums so that they can be compensated in the occurrence of an event insured against. In dollar terms we can say that taking an insurance cover is a gamble whose expected value gives a negative figure. A risk averse individual tends to pay more than the expected value of a game that will let him or her avoid a risk. For example, if an individual faces a 4/100 chance of losing 20,000 pounds risk aversion means that the individual will pay more than the expected value of 800pounds for an insurance policy that will reimburse him for that 20,000 pounds loss if it happens. Indemnity is a principle of insurance that states puts it clearly that an insured person will only get compensation if there is a risk occurrence. On the other hand if the event does not occur then the insured will not get any compensation whether money or property. In this case the insurance company will benefit a lot since all the premiums paid will remain as the company's revenue. Many people in this small island will pay for insurance which will result into a lump sum insurance pool. Out of the risk insured against the likely hood of an event occurring will be very minimal a suggestion that the insurance company will stand to gain because it will pay out less money as compensation a thing that makes it stay in business. The pay off expected by the insured is always less than the premiums he pays; this puts the insurance company in a better position making it a booming business with minimal chances of loss occurrence. For the highly regarded health insurance schemes, for example, the Blue Cross expected health insurance scheme value is about -10% in relation to the sum insured meaning that they have a 90% medical loss ratio. With some companies they sell policies to people with medical loss ratio of 60% or even a lesser percentage. The big advantage with the insurance company is that it can play games severally and leap much benefits associated with the law of large numbers. The more people the insurance company insures the more it the more it will collect money to cater for administrative costs as well as profits. To the insured it is also obvious that the bigger the pool the smaller the individuals risk of losing large amount of money ,at the same time the less the expected premiums. The Friedman-Savage sought to know why is it that people will buy both insurance and lottery tickets against losses. His view was that this behavior of people was making them both risk averse and risk loving. The answer to this is the fact that a section of the utility function is convex while the other part is concave. Individuals wish to play it safe across the lower range but very much willing to take gambling on the lower and upper parts Illustration A group of thirty people are willing to pay 120 pounds to avoid a risk of losing 15000 pounds. The group can all join together to form a mutual insurance company, collect 120 pounds from each member and pay 15000 pounds to anyone amongst the group who is unlucky and loses coming out ahead. The more people join this mutual insurance company the more the money for its administrative costs and more returns will be realized. By joining this mutual insurance company it shows that the participants are risk averse. The individual's elasticity is . Utility is an indicator of how many percentage points one thing changes as a result of a one percent change in something that affects it. In this functional form; U=M1/2 where u=utility M=money (income) The exponent is the elasticity of U (utility) with respect to M (income) When income changes by one percent utility will change by a half percent. For risk averse people elasticity is less than one and therefore the individual discussed in this question is risk averse because he has an elasticity of which is less than one. In this case utility is relatively inelastic with respect to changes in income a thing that will lead to a curve which is convex. (Dominick, 1990) We can conclude that the individual is averse to risk taking because his utility function shows that the individual is willing to pay price P1 which makes him face a 8/10 chance of winning or a 2/10 chance of losing . This means that the individual will pay more than the expected value of 500. For the smallest value of money 2500 pounds there is a large increase in satisfaction as compared to the second figure of 2500000 pounds and the last figure of twenty five million pounds. The individual has accumulated a certain amount of wealth such that there is almost no increase in utility for additional pounds earned. The theories by Von Neumann-Morgenstern entails that various people have different attitudes towards risk. The points out that individuals choice is influenced not by the different amounts of pounds but by the different amount of satisfaction that are likely to be achieved. Their notion is that one will always choose alternatives that have the highest pound value attached to them. Philip (1990) gives an example where, an individual is to spin two wheels(x and y) so as to win some money with each wheel having 150 numbers on it. For each wheel the chances that any particular number will come up on any one spin is 1/150.one has to play these game only once with the following as the wheel payoffs For wheel x Numbers one through twenty pays two million pounds Numbers twenty one through 150 does not pay anything For wheel y Numbers one through twelve pays ten million pounds Numbers 13 through 150 pay nothing This indicates that wheel x will be having a more better chance of winning while the other wheel may not be having better chances of winning though one can win a lot of money from the it. Choosing the wheel to play will depend on the various attitudes people has towards risk. Being risk averse the individual will always be willing to pay more than the expected value of the game which lets him avoid the risk. In lottery 1; the individual can win 2,500 pounds with a 0.8 chance of winning and a 0.2 chance of losing. In this case his expected value will be 2/10 x 2,500 = 500 This individual is willing to pay a higher price than 500 Thus, P1 =2,500-500=2,000 In lottery 2; the individual has a chance of winning 250000 pounds the probability being 0.008 and that of losing being 0.002. Expected value will be calculated as follows, 2/1,000x 250,000= 500 The individual is willing to pay a higher price than 500. Thus P2 equals 250,000-500=249,500 In lottery 3; The individual has a chance of wining 25,000,000 with 0.00008 chances of winning and a 0.00002 chance of losing Expected value will be 2/100,000x25, 000,000=500 This shows that the individual is willing to pay a higher price than 500 Thus P2 equals 25,000,000-500= 24,999,500 Prices P1, P2 and P3 are not consistent with the choices made by a typical consumer because the expected value is constant. The consumers being risk averse and for small value of money there is a large increase I satisfaction. However, after a certain amount of money there is almost no increase in utility for additional pounds earned making the individual take very little care about pounds earned. (Bradley, 1989) References Bradley, R. (1989): The Micro Economy Today, Ravelon House, New York Philip, H. (1990): An introduction to modern Economics, Longman group, England Dominick, S. (1995): International Economics, Prentice hall, New Jersey. Hanson, J. (1997): A text book if Economics Macdonald and Evans, London. Brumo, M. and Sachs, J. (1985): The economics of worldwide stagflation, Harvard University Press, Cambridge Read More