Suppose you have a house worth $900,000. There are 25% chance that a burglar wil

Question

Suppose you have a house worth $900,000. There are 25% chance that a burglar will vandalize your house so that your house only worth $640,000 if it gets vandalized. To prevent this, you can buy home insurance at $5,000 cost. Your utility is given by W, where W is your wealth.

a) Show that you would prefer to insure your house than not to insure

Now, suppose there is deductible of $1,000 for the insurance. However, the insurance only cost $3,000 this time.

b) Show that you would prefer insurance with deductible to insurance without deductible

Explanation / Answer

Answer:

Utility function:

u = w ½   

Now it is given that there are 25% chances that burglars will vandalize house and that house will worth only $640000.

So there is 25 chance of a loss of ($900000-$640000= $260000) on wealth.

Therefore expected utility of wealth is given by:

Expected utility of wealth = e(w) = 25% x $640000 + 75% x $900000

                                                     = $160000 + $675000

                                                      = $865000

So expected losses = wealth – e(w)

Here wealth is the worth of house which is = $900000

And expected wealth is e(w) = $865000

So expected losses = $900000 - $865000 = $35000

Hence the price of the insurance policy = $35000

Whereas, we are paying $5000 for this policy. So we are better off purchasing insurance policy at $5000.

Price of policy = $5000 + $1000 = $6000

This is still less than the worth of the policy calculated above which is $35000

Therefore in this case still the insurance is worthy.

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