By Karl Hendrik Borch
The description for this booklet, The Economics of Uncertainty. (PSME-2), may be forthcoming.
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Additional resources for The Economics of Uncertainty. (PSME-2)
Sample text
Distributions of the type er(x) = 0 x ¥= r er(x) = 1 x = r. If we apply our formula to this prospect, we obtain U{er(x)} = u(r). This means that u(x) is the utility assigned to the prospect which will give us the amount x of money with certainty. From this it follows that the function u(x) can be interpreted as the utility of money-a concept which played a very important part in classical economic theory. Some people consider this very surprising and have created considerable confusion trying either to explain or to deny the validity of the result.
Let us now assume that preferences can be represented by a convex utility function, of the shape indicated by Fig. , a function such that u(px) < (1 - p)u(O) + pu(x). In this case our person is willing to gamble, even if the terms are not quite fair. , a prospect with utility u(px), he will be willing to stake his cash on a chance of increasing it to x with probability p, or losing it with probability I - p. It is usual to say that a person with a concave utility function has a risk aversion. He will not by his own choice gamble if odds are fair.
However, if we force the problem into this pattern, we may lose something essential. It seems a little naive to quote a premium just on the merits of the contract, without considering both how much the ship-owner is willing to pay for insurance coverage and the premium which competing companies may quote. If the ship-owner is prepared to pay $400,000 for insurance, and no other company is willing to take the risk at this price, there is no reason why our company should quote a lower premium. This illustrates the point made in Chapter I, that we cannot-or should not-consider a decision problem in isolation.