After Hurricane Katrina in 2005, the government offered subsidies to people whose houses were destroyed. How does the expectation that the government will offer subsidies for future major disasters affect the probability that risk-averse people will buy insurance and the amount they buy? Use a utility function for a risk-averse person to illustrate your answer. (Hint: See Solved Problem 16.5 for example, included below)

Solved Problem 16.5

The local government collects a property tax of 20 on Scott's home. If the tax is collected whether or not the home burns, how much fair insurance does Scott buy? If the tax is collected only if the home does not burn, how much fair insurance does Scott buy? Answer 1. Determine the after-tax expected value of the house with and without insur- ance. If the tax is always collected, the house is worth 480 = 500 - 20 if it does not burn and -20 if it does burn. Thus, the expected value of the house is 380 = [0.2 x (-20)] + [0.8 x 480]. If the tax is collected only if the fire does not occur, the expected value of the house is 384 = [0.2 x 0] + [0.8 x 480]. 2. Calculate the amount of fair insurance Scott buys if the tax is always collected. Because Scott is risk averse, he wants to fully insure so that the after-tax value of his house is the same in both states of nature. If the tax is always collected, he pays a premium of x such that 500 - x - 20 = 4x - 20, so x = 100. If no fire occurs, his net wealth is 500 - 100 - 20 = 380. If a fire occurs, the insurance company pays 500, or a net payment of 400 above the cost of the insurance, and Scott pays 20 in taxes, leaving him with 380 once again. That is, he buys the same amount of insurance as he would without any taxes. The tax has no effect on his insurance decision because he owes the tax regardless of the state of nature. 3. Calculate the amount of fair insurance Scott buys if the government collects the tax only if a fire occurs. With this tax rule, Scott pays a premium of x such that 500 - x - 20 = 4x, 50 x = 96. Scott pays the insurance company 96 and receives 480 if a fire occurs. With- out a fire, Scott's wealth is 500 - 96 - 20 = 384. If a fire occurs, the insur- ance company pays 480, so Scott's wealth is 480 - 96 = 384. Thus, he has the same after-tax wealth in both states of nature. Comment: Because the tax system is partially insuring Scott by dropping the tax in the bad state of nature, he purchases less private insurance, 480, than the 500 he buys if the tax is collected in both states of nature