Consider a farmer who is trying to choose between a coinsurance policy and a deductible policy...

Consider a farmer who is trying to choose between a coinsurance policy and a deductible policy to protect
against damage to her farming lands. The value of the loss, and the corresponding probabilities of each
value, are given as follows:
L =
0 with prob. 0:4
10; 000 with prob. 0:2
20; 000 with prob. 0:05
40; 000 with prob. 0:05
60; 000 with prob. 0:05
80; 000 with prob. 0:05
100; 000 with prob. 0:15
220; 000 with prob. 0:05
The farmer's initial wealth is W = 280; 000.
The Coinsurance policy o ers to pay = 0:75 fraction of any loss incurred. Under the Deductible policy,
the insurance company pays nothing if the loss is less than D = $19; 000, then pays any losses incurred
beyond D; that is, the insurance company pays L ?? D if L > D. Both policies are o ered for a premium
amount P = $12; 000.

(a) Which contract would the farmer choose if she is an expected utility maximizer with u(x) = x0:4? (Keep
5 decimal places throughout) (3 points)

(b) Which contract would the farmer choose if she is an expected utility maximizer with u(x) = x0:8? Is the
answer di erent than in (a)? If so, explain why. (3 points)

Expert Solution

Rahul Sunny answered 2 years ago

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