Chapter 7: Income Security
We now take a closer look at the risk of losing one’s income before retirement, either temporarily or permanently, the most common reasons being illness and unemployment. We begin with some general comments on income insurance and then turn to unemployment insurance, sickness insurance, and disability insurance. INSURANCE: THEORETICAL BACKGROUND Income security is a classical topic in the economics of insurance. Modern utility theory started with Daniel Bernoulli’s claim, in 1738, that an individual’s utility from income, u(Y), is increasing but at a decreasing rate, uЈ(Y)Ͼ 0, uЉ(Y)Ͻ0. He used this postulate to explain the demand for insurance in a model where individuals were supposed to maximize expected utility, Eu(Y). This approach was advanced in 1944 when John von Neumann and Oscar Morgenstern developed a method to measure utility as a function of income/wealth. This was done in the following way: 1. 2. 3. Deﬁne a relevant interval for income/wealth. Assign particular values to the endpoints of the interval, for example u(Y min)ϭ0 and u(Y max)ϭ50. In order to evaluate an intermediate point, say Y ϭY*, ask the individual whether he or she prefers this income with certainty to a lottery with the outcome Ymax with probability , and the outcome Ymin with probability (1 Ϫ ). Let vary and ﬁnd out at which value of the probability, *, the individual is indiﬀerent between the lottery and the certain income Y*. The expected utility theorem implies that u(Y *)ϭ*u(Y max)ϩ(1...
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