x J A u L 2. There is a town with 100 identical residents with initial wealth of $1000 and a utility function u = V wealth. Every person owns a car and there is a probability p = .2 that a person's car will need a costly repair in a given year. If a person needs a repair, they must pay $500 to x it. (a) What is the maximum amount that a person would be willing to pay to insure against the cost of repairing their car? (b) Suppose a single company exists to offer these insurance policies. What price do they charge? What are their expected prots? 3. Consider the following two lotteries: $20 p = 0.5 L1 = $10 p = 0.25 $0 p = 0.25 $25 10 = 0.5 L2 = $4 p = 0.25 $0 p = 0.25 (a) Calculate the Expected Monetary Value - ]E(L) for each lottery. (b) Olivia and Taylor have the following utility functions: 1450(3) = 93%, ux) = . Calcu- late each person's expected utility - E(u(L)) - for both lotteries. How does Olivia rank the lotteries? Taylor? (c) Calculate each persons' certainty equivalent for each lottery. How do they compare? Is this ndinE consistent with the findingr from (bl? 1. Suppose you have $100,000 and you want to invest in real estate. There are two houses available on the market and both of these houses are, conveniently, priced at $100, 000. One of these houses is close to the urban area, and the other one is in the suburbs. Suppose you don't care much where you live, you just want to buy the house that will increase in value the most. The value of the house next year depends on the state of the economy. If the economy in the following year is booming, the value of houses in the urban area will increase by 7% while the values in the suburban area will increase by 10%. If the economy is tanking, values in the urban area will drop by 5%, while values in the suburban area will drop by 12%. If the economy is stable, the values in the urban area will increase by 2%, while values in the suburban area will increase by 1%. You believe the chance of a booming economy is 18%, the chance of a tanking economy is 12%, and the chance of a stable economy is 70%. (a) First, we need to gure out the distribution of possible values. To do so, calculate the value for each house in each state of the world (that is, under each economic condition). You'll want to ll out a table that looks like this: l booming tanking stable l I urban l I suburban ' Hint. If something worth $1 grows by 55%, then its final value is $1 X (1 + 1%). (b) Each potential investment can be viewed as a probability distribution over possible values. Write out these distributions. (c) Calculate the expected value of each house based on your current information about the economy. (d) Now, suppose the government is preparing to release a report on national employment. For simplicity, let's suppose the report can be \"good\" or \"bad\" (say jobs were added or jobs weren't added). You believe based on past data that if the economy is booming, there will be a positive report with 100% probability. Similarly, if the economy is tanking, there will be a negative report with 100% probability. Finally, if the economy is stable, you get a positive report with 50% probability and a negative report with 50% probability. (e) Suppose you get a positive report. Use Bayes' rule to calculate new probabilities for the states of the economy. That is, calculate (i) P(booming|postve), (ii) P(tankng|positiee), (iii) P(stable|positive). (f) Recalculate the expected values of each home using these new probabilities