Suppose we have the following situation: Our current wealth stock is $150,000. I

Question

Suppose we have the following situation:

Our current wealth stock is $150,000.

If an illness occurs, our wealth stock will decrease by $100,000.

The probability of getting ill is 25%.

The utility function is U(W)=log 4W , where W=wealth; log= logarithm base 10.

1. Compute the expected wealth, expected utility (use up to 4 decimal places) and expected loss.

2. Calculate the maximum amount that we would be willing to pay to get rid of our loss. If we could buy an insurance policy for $30,000, which would completely pay for the medical treatment that we may need, should we purchase this insurance policy? Explain.

3. Graph it.

4. Do parts 1-3 again with the following utility functions: U(W)= 3.2W ; U(W)=W2

Explanation / Answer

1) Expected wealth = 150,000*.75+100,000*.25 = $137,500

Expected utility = .25*log(4*100,000)+.75*8log(4*150,0000) = 5.7341

Expected loss = probability of losss*(given loss when getting ill) = .25*(150,000-100,000) = $12500

2)

since the expected loss is $12,500, maxm amount that we can pay is $12,500

we should not purchase policy for $30,000 because this amount is greater than our expected loss.

4) repeat above calculation with U = 3.2W and U = 2W

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