6. Expected Utility. Consider a Princeton student who feels that a "normal" year on campus is like gaining SA, compared to taking the year off, which gives utility u(woff). But she fears Princeton will renege on its promise of a normal year, and move everything online; she feels that this is like losing $L (compared to a normal on-campus year). If she expects this to happen with probability p, (a) Write out the expected utility from enrolling. (b) Write out the expected utility from taking the year off. (c) Show: if the student chooses to take the year off, and is risk-loving, it must be that L>A/p.
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- : Suppose that Charlene has an income of $110,000 per year and that there is a 1 QUESTION in 5 (20%) chance that she will get sick in a given year. Let's suppose that the cost of the illness (in terms of lost work time and medical bills) is $80,000 which leaves her with an income of only $30,000 in that particular year. Utility UHealthy UE = UR Usick $30,000 $88,000 $94,000 $110,000 Income a) What is the actuarially fair premium for Charlene's situation? b) Continue to assume the given information. Suppose that the figure above represents Charlene's utility over various income levels. What is Charlene willing to pay for insurance? c) Continue to assume the given information. We know that Charlene would buy actuarially fair insurance but if the insurance company applied a 20% loading fee would Charlene still purchase the health insurance?Suppose that there is a 45 percent change that George's coffee shop will make $10000 in profits in January and a 45 percent chance it will make 0 profits and a 10 percent chance that it will make -$1000 in profits (i.e., it will lose $1000). Calculate the coffee shop's expected profits3.Suppose that you observed the following set of data: Average Business School tuition: $30,000 Average Salary for non-MBA’s: $50,000 per year Average MBA salary: $90,000 per year. The length of an MBA program is 2 years and is assumed that and MBA will have a working career of 20 years after graduation. Further, suppose that, instead of going to get an MBA,2you could keep your current non-MBA job and invest what you could have used to pay for tuition, risk free, at 4% per year.SHOW ALL YOUR WORKING.a) Is this set of data consistent with market equilibrium? Explain.b) If your answer to (a) is no, how will markets adjust?
- 5. Consider a weather forecaster who is paid based on her performance. Each day, she forecasts the probability q = [0, 1] that it will rain the following day. She is given a bonus that depends on her forecast and whether it rains. Assume that the forecaster knows the true probability, p, and when choosing her forecast, q, cares only about maximizing her bonus for that day (in particular, she may lie about the probability if doing so increases her pay). (a) Suppose the bonus is equal to the percentage the forecast assigns to what actually happens. For example, if the forecaster says there is a 72% chance of rain (i.e. q = 0.72), then she is paid $72 if it rains and $28 if it does not rain. If the forecaster is a risk neutral expected utility maximizer, what forecast will she make (as a function of p)? (b) Suppose instead that the bonus is equal to 100(1 − (1 − q)2) dollars if it rains and 100(1-q²) dollars if it does not rain. For example, if the forecaster says there is an 80% chance…Assume that an individual expects to work for 40 years andthen retire with a life expectancy of an additional 20 years.Suppose also that the individual’s earnings increase at a rateof 3 percent per year and that the interest rate is also 3 percent(the overall price level is constant in this problem). What(constant) fraction of income must the individual save ineach working year to be able to finance a level of retirementincome equal to 60 percent of earnings in the year just priorto retirement?3. Consider a home energy storage (battery) system that can store up to 2 units of energy. At every time step, there is a demand for energy in the home which is drawn from 0,1,2 units with equal probability independent of the demands in the previous time steps. At every point in time, you have to satisfy the demand either by discharging the needed energy from the battery or purchasing power from the grid (or a combination of the two). You could also choose to purchase power from the grid to charge your battery. The grid energy price is either H(igh) or L(ow) according to a Markov chain (Price moves from H to L with probability p, and from L to H with probability q). (a) Model the decision making as an infinite horizon MDP where the objective is to minimize the discounted cost of energy purchased over an infinite horizon. (b) Write down a policy a of your choosing. Perform two steps of the operator T, for your policy, followed by one step of T..
- (1) Do you think you currently have the disciplineneeded to control your spending in order to free upcash for regular investing? If not, what changes couldyou make? (2) If someone gave you a “hot tip” on astock, how would you go about researching theopportunity before making an investment decision?3. Which lottery payout scheme is better? Suppose you win a raffle held at a minor league baseball game and are given the choice between two different ways to be paid. You can either accept the money in a lump sum immediately or in a series of payments over time. If you choose the lump sum payout, you receive $3,000 today. If you choose to collect payments over time, you receive three payments: $1,000 today, $1,000 1 year from today, and $1,000 2 years from today. At an interest rate of 6% per year, the winner would be better off accepting the value. , since that choice has the greater present O The lump sum is always better. The payments over time are always better. O It will depend on the interest rate; advise her to get a calculator. O None of these answers is good advice. At an interest rate of 10% per year, the winner would be better off accepting A couple years after you win the raffle, you and your friend are back at the same event. This time, your friend gets lucky and wins the…3. Which lottery payout scheme is better? Suppose you win a raffle held at a neighborhood elementary school fundraiser and are given the choice between two different ways to be paid. You can either accept the money in a lump sum immediately or in a series of payments over time. If you choose the lump sum payout, you receive $3,100 today. If you choose to collect payments over time, you receive three payments: $1,000 today, $1,000 1 year from today, and $1,000 2 years from today. At an interest rate of 7% per year, the winner would be better off accepting the value. At an interest rate of 9% per year, the winner would be better off accepting since that choice has the greater present O The lump sum is always better. O The payments over time are always better. O It will depend on the interest rate; advise her to get a calculator. O None of these answers is good advice. , since it has the greater present value. A couple years after you win the raffle, you and your friend are back at the…
- Suppose Dalia is a sports fan and buys only football tickets. Dalia deposits $3,000 into a savings account that pays an annual nominal interest rate of 5%. Assume this interest rate is fixed, and so it will not change over time. On the day she makes her deposit, suppose that a football ticket has a price of $15.00. Initially, Dalia's $3,000 deposit has a purchasing power of 200 football tickets. For each of the annual inflation rates given in the following table, first determine the new price of a football ticket, assuming it rises at the rate of inflation. Then enter the corresponding purchasing power of Dalia's deposit after one year in the first row of the table for each inflation rate. Finally, enter the value for the real interest rate at each of the given inflation rates. Hint: Round your answers in the first row down to the nearest football ticket. For example, if you find that the deposit will cover 20.7 football tickets, you would round the purchasing power down to 20 football…3. Which lottery payout scheme is better? Suppose you win a raffle held at a neighborhood elementary school fundraiser and are given the choice between two different ways to be paid. You can either accept the money in a lump sum immediately or in a series of payments over time. If you choose the lump sum payout, you receive $3,100 today. If you choose to collect payments over time, you receive three payments: $1,000 today, $1,000 1 year from today, and $1,000 2 years from today. At an interest rate of 7% per year, the winner would be better off accepting the value. At an interest rate of 9% per year, the winner would be better off accepting I O The lump sum is always better. The payments over time are always better. O It will depend on the interest rate; advise her to get a calculator. None of these answers is good advice. since that choice has the greater present since it has the greater present value. A couple years after you win the raffle, you and your friend are back at the same…Assume you can invest in 2 projects whose payoff depend on the state of the economy. The profits from each project for each state of the economy are presented below. What are the expected payoffs of each project if there is a 50% chance of a recession and a 50% of no recession? Profit under recession Profit under normal conditions Project 1100,000 150,000 Project 2 50,000 240,000 O Project 1: $120,000 and Project 2: $150,000 Project 1: $125,000 and Project 2: $115,000 Project 1: $145,000 and Project 2: $145,000 O Project 1: $125,000 and Project 2: $145,000