6.1. Suppose there are two islands. The total population on the two islands is 500 people. The initial stock of fiat money is $500. The money stock increases according to M, = 1.1M-1. The probability that a person is on Island 1 is 1/4 and the probability that a person is on Island 2 is 3/4. Let I(p) = 4 (so that labor supply does not depend on price). a. Write down the money market-clearing condition for each island. b. Solve for the equilibrium price level in date 1. c. Write down the per-person transfer that the government gives to each old person. d. Compute the value of the transfer.
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- a. Suppose that you took part in a lottery that has a chance to increase, decrease or have no effect on your level of income. With probability 0.5, your income remains at it original level K500; with 0.2 probability, your income increases to K700; and with probability 0.3, your income decreases to K400. The utility function is.u(1) =I^0.7where I denote income leveli.Using the utility function show that the consumer's risk preference is averse. (2marks)ii.Calculate both the EU and EV of the income. (4marks)iii.Using the results in (il) above, indicate the attitude to risk of this consumer. (2marks)Question 4 Suppose a prosecutor expects to convict a defendant with probability 0.5 and that the sentence on conviction is 10 years in prison. Assume the prosecutor values prison time at $1,000 per year (its value as a deterrent of crime), and incurs a cost of trial equal to $2,000. a. What is the minimum prison sentence the prosecutor will o er as part of a plea bargain if her objective is to maximize the expected value of the sentence imposed, less the cost of trial (ignore the information provided in b. below to answer this question a.)? b. Suppose the defendant believes his chances of being convicted are 0.3, his cost of prison time is $5,000 per year, and his cost of a trial is $1,000. Will he accept the plea bargain in a.?Leo needs one unit of capital from a bank to launch a business. His profits depend on the interest rate of the contract r and the level of effort. Leo can either put high effort in the project, in which case his profits 7 equal y -r with probability 1/2 and 0 with probability 1/2. H | Leo incurs a cost of high effort c=2- Otherwise Leo can put low effort, in which case his profits 7 equals y,-r with probability 1/3 and 0 with probability 2/3. Leo incurs a cost of low effort L c=0: %3D Leo's utility function is 271/2- c where A represents his profits and c the cost of efforts. For a given an interest rate r, the risk-neutral bank receives r if the entrepreneur is successful or -1 if he is not. The bank knows that there are many entrepreneurs like Leo who either make high or low effort. It then proposes two types of loans. The first loan is designed for entrepreneurs who make high effort, with an interest rate r=r,. The second loan is designed for entrepreneurs who make low effort, with…
- 2. Alice believes that her car would cost £12500 to replace if it was stolen or damaged. Based on crime statistics for the area she lives in, she believes that the probability of her car being stolen or damaged is 0.15. (i) Alice's utility function is given by U(w) = ln(w) for w > 0 and she as £35000 in the bank. Calculate how much Alice would be prepared to pay (in a single payment) to insure her car against theft or damage (ii) Repeat the calculation in the previous part but now assume Alice has £500000 in the bank.The manager of XYZ Company is introducing a new product that will yield N$1000 in profits if the economy does not go into a recession. However, if a recession occurs, demand for normal good will fall so sharply that the company will lose N$4000. If economists project that there is a 10 percent chance the economy will go into a recession, what are the expected profits to XYZ Company of introducing the new product? How risky is the introduction of the new product?Online sale Suppose a student is considering selling their used smartphone online. They can sell it now for $p or wait and sell it next month for a different price. If they wait, they will receive a random offer with an equal probability of being either $300 or $100. The student can only receive one offer and cannot sell the phone after the second month. 1. Calculate the expected price in the next month. 2. Suppose that the current price p is equal to 200. (a) Give a reason why selling today could be a good idea. (b) Give a reason why selling next month could be a good idea.
- A person has wealth of $500,000. In case of a flood her wealth will be reduced to $50,000. The probability of flooding is 1/10. The person can buy flood insurance at a cost of $0.10 for each $1 worth of coverage. Suppose that the satisfaction she derives from c dollars of wealth (or consumption) is given by u(c) = √c. Let C denote the contingent commodity dollars if there is a flood (horizontal axis) and CNF denote the contingent commodity dollars if there is no flood (vertical axis). 1 Determine the contingent consumption plan if she does not buy insurance. 2 Assume that the person has von Neumann-Morgenstern utility function on the contingent consumption plans. Write down the expected utility U(CF, CNF) and derive the MRS. 3 Solve for optimal (CF, CNF). To this end, first use the tangency condition (TC) to find the relation between the two contingent commodities (CF, CNF). Next, use (BC) to solve for their values. What is the optimal amount of insurance K the person will buy? (Note:…4) You are a financial professional working in a corporate loan department. A company named Mitch Hedberg Inc. (MH) comes to you for a loan. MH has debt from a previous loan (given by a different firm than yours) of 200. Your company analysts say that MH is likely to earn either 180, 240, or 300 this year - each with a probability of 1/3. MH wants you to lend them 100. MH could use this borrowed 100 to do either project X or project Y. Project X has a guaranteed return of 125 if the 100 is put there. Project Y may return either 0 or 210; each has probability of 1/2 and also costs 100 to do. a) Which project, X or Y, has the larger expected value? b) If you lend MH the 100, what will they do with the money? Why? Show your math. c) Should you lend MH the money or not? Show your math. d) Why did I choose the letters "MH" for this problem? What financial economic concept with initials "MH" is important in this problem?Donna just paid $800 for a new iPhone. Apple offers a two year extended warranty for $200 and Donna is considering purchasing it. She has utility given by U(X)=√X. Without the extended warranty, the iPhone becomes worthless if it breaks. What is the minimum probability, p, that the iPhone breaks in the next two years that will cause Donna to prefer to purchase the extended warranty? p=_____________ If the probability that her phone breaks is p=0.25, will Donna will prefer to buy or not buy the warranty?
- Bob earn 60,000 a year and an accounting firm each year he receives Reyes Bob has determined that the probability that he receives a 10% raise is .7 the probability that he earns a 3% raise is .2 and the probability that he earns a 2% raise is .1 a competing company has offered Bob a similar position for 65,000 a year Bob wonders if he should take the new job or take his chances with his current job. a. Find the mathematical expectation of the dollar amount of his raise at his current job b.# 4 Consider an individual with a utility function of the form u(w) = √w. The individual has an initial wealth of $4. He has two investments options available to him. He can eitffer keep his wealth in an interest-free account or he can take part in a particularly generous lottery that provides $12 with probability of 1/2 and $0 with probability 1/2. Assume that this person does not have to incur a cost if he decides to take part in the lottery. (a) Will this individual participate in the lottery? (b) Calculate this individual's certainty equivalent associated with the lottery. What is his risk premium?A person has wealth of $500,000. In case of a flood her wealth will be reduced to $50,000. The probability of flooding is 1/10. The person can buy flood insurance at a cost of $0.10 for each $1 worth of coverage. Suppose that the satisfaction she derives from c dollars of wealth (or consumption) is given by u(c) = √c. Let CF denote the contingent commodity dollars if there is a flood (horizontal axis) and CNF denote the contingent commodity dollars if there is no flood (vertical axis). (a) Determine the contingent consumption plan if she does not buy insurance. (b) Determine the contingent consumption plan if she buys insurance $K. (c) Use your answer in (b) to eliminate K and construct the budget constraint (BC) that gives the feasible contingent consumption plans for different amounts of insurance K. Determine the slope of budget line (both graphically and by forming the price ratio).