We proposed in Individual choice that people have diminishing marginal utility: Successive equal increments in consumption yield progressively less additional utility. This concept is central to understanding behaviour towards risk.
Suppose you have a specific sum of money and you are offered a fair gamble in the sense we described above – you have an equal chance of winning or losing a fixed amount – suppose $1,000. While this game is by definition fair in the probabilistic sense it might not be fair in the utility sense. Diminishing marginal utility means that the additional utility associated with the gain of $1,000 is less than the utility change associated with losing $1,000: The more money we have, the less is the utility value placed on it at the margin; the less we have, the greater is the value placed on an additional unit. In consequence, risk-averse individuals devote resources to reducing risk; this is why insurance forms such a sizable sector in the economy. Furthermore, those who take on risk (insurers) have to be rewarded for doing so, and many economic activities consist of the more risk-averse individuals paying insurers to bear risk.
Insurance companies always insure a multitude of individuals or households. Hence, while these companies pay out claims to many customers each year the companies have so many customers that it is rare that they encounter a year when the insurance claims and the insurance premiums paid to the company do not balance out. We sometimes call this the law of large numbers.
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