Suppose Peter is trying to decide whether to put his money in a regular savings that will make 100,000 pesos in one year or in a special fund that depends on market condition over the year. If the market goes up, the special fund will make 150,000 pesos. If the market goes down, the special fund will make 50,000 pesos. a. Make a decision matrix for this problem. b. Make a decision tree for this problem c. What will a conservative (maximin) decision maker do?
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- We learned that we can use choice between a gamble over someone's best and worst outcomes and getting an outcome of interest (like getting pizza) for certain as a way to assign numeric values to utility (on a scale of 0 to 1). Using this method, if you are indifferent between the following: A gamble that has a 0.3 chance of your best possible outcome (and no lower chance), and a 0.7 chance of your worst possible outcome. Getting pizza for certain. it means that your utility for getting pizza is:Which of the following are examples of common behavioral errors in decision making (multiple correct answers; check all that apply). A. Always paying more than true willingness to pay. B. Letting unrecoverable sunk costs influence ongoing decisions for when such costs have no bearing on benefits and costs going forward. C. Making different decisions when an identical problem is framed in two different ways, especially when one is framed in terms of gains and the other in terms of losses. D. Always saving too little. E. Generally spending too little on high-quality, high-priced items. F. Settling on a default alternative in the face of a difficult or complex decision G. Considering the average cost and average benefit, instead of the marginal cost and marginal benefit, When choosing whether a little more or less should be bought or produced.Text of the problem from 'An introduction to decision theory' by Martin Peterson: You prefer a fifty-fifty chance of winning either $100 or $10 to a lottery in which you win $200 with a probability of 1/4, $50 with a probability of 1/4, and $10 with a probability of 1/2. You also prefer a fifty-fifty chance of winning either $200 or $50 to receiving $100 for sure. Are your preferences consistent with von Neumann and Morgenstern’s axioms? The book proposes as solution 'No. Your preferences violate the independence axiom.' without proposing the steps to reach that solution and I don't know why it is correct.
- Suppose that there are only 10 individuals in the economy each with the following utility function over present and future consumption: U (c1, c2) = c1 +C2, where ci is consumption today, and c2 is consumption tomorrow. Consumption tomorrow is less valued because people are impatient and prefer consuming now rather than later. Buying 1 unit of consumption today costs $1 today and buying 1 unit of consumption tomorrow costs $1 tomorrow. All individuals have income of $10 dollars today and no income tomorrow (because they will be retired) but they can save at the market interest rater> 0. How much of his or her income will an individual consume today given that the interest rate is 0.3? O. Less than half of it O. Exactly half of it O. The individual is indifferent between consuming today and saving O. More than half of it O. All of it O. None of it How much of his or her income will an individual consume today given that the interest rate is 0.5? O. Less than half of it…The conventional wisdom for urban economic development is: “Don’t put all your eggs in one basket. Diversify the economy.” To explain the idea of diversification, consider old McDonald, who must carry a dozen eggs from the barn to the house. The ground between the barn and the house is slippery, so there is a 50 percent chance that McDonald will slip on a given trip and break all the eggs in his basket. Consider two strategies: a one-basket strategy (a single trip with all 12 eggs) and a two-basket strategy (two trips, with 6 eggs per trip). INDEPTH ANSWERS. Questions= (1.)List all of the possible outcomes under each of the strategies. Question (2.)What is the expected number of delivered (unbroken) eggs under each strategy ? Question (3.)What are the trade-offs between the two strategies? If you were McDonald, which strategy would you adopt? Question (4.)What are the lessons for economic development strategies?A woman with current wealth X has the opportunity to bet an amount on the occurrence of an event that she knows will occur with probability P. If she wagers W, she will received 2W, if the event occur and if it does not. Assume that the Bernoulli utility function takes the form u(x) = with r > 0. How much should she wager? Does her utility function exhibit CARA, DARA, IARA? Alex plays football for a local club in Kumasi. If he does not suffer any injury by the end of the season, he will get a professional contract with Kotoko, which is worth $10,000. If he is injured though, he will get a contract as a fitness coach worth $100. The probability of the injury is 10%. Describe the lottery What is the expected value of this lottery? What is the expected utility of this lottery if u(x) = Assume he could buy insurance at price P that could pay $9,900 in case of injury. What is the highest value of P that makes it worthwhile for Alex to purchase insurance? What is the certainty…
- Assume that someone has inherited 2,000 bottles of wine from a rich uncle. He or she intends to drink these bottles over the next 40 years. Suppose that this person’s utility function for wine is given by u(c(t)) = (c(t))0.5, where c(t) is each instant t consumption of bottles. Assume also this person discounts future consumption at the rate δ = 0.05. Hence this person’s goal is to maximize 0ʃ40 e–0.05tu(c(t))dt = 0ʃ40 e–0.05t(c(t))0.5dt. Let x(t) represent the number of bottle of wine remaining at time t, constrained by x(0) = 2,000, x(40) = 0 and dx(t)/dt = – c(t): the stock of remaining bottles at each instant t is decreased by the consumption of bottles at instant t. The current value Hamiltonian expression yields: H = e–0.05t(c(t))0.5 + λ(– c(t)) + x(t)(dλ/dt). This person’s wine consumption decreases at a continuous rate of ??? percent per year. The number of bottles being consumed in the 30th year is approximately ???Consider two individuals whose utility function over wealth I is ?(?) = √?. Both people face a 10 percent chance of getting sick, and foreach the total cost of illness equals $50,000. Suppose person A has a total net worth of $100,000, and person B has a total net worth of $1,000,000. Both people have the option to buy an actuarially fair insurance contract that would fully insure them against the cost of the illness. a. Using expected utility calculations, show that person A would certainly buy full, actuarially fair insurance. b. Suppose an insurance company wants to maximize profits and wants to charge each customer the maximum price they are willing to pay. How much should the insurance company charge each client so that both buy the contract? c. What is surprising about your result in part b? What does this tell you about how insurance companies may be pricing health insurance contracts in the real world?Cost-Benefit Analysis Suppose you can take one of two summer jobs. In the first job as a flight attendant, with a salary of $5,000, you estimate the probability you will die is 1 in 40,000. Alternatively, you could drive a truck transporting hazardous materials, which pays $12,000 and for which the probability of death is 1 in 10,000. Suppose that you're indifferent between the two jobs except for the pay and the chance of death. If you choose the job as a flight attendant, what does this say about the value you place on your life?
- Let b(p,s,t) be the bet that pays out s with probability p and t with probability 1−p. We make the three following statements: S1: The CME for b is the value m such that u(m)=E[u(b(p,s,t))]. S2: A risk averse attitude corresponds to the case CME smaller than E[b(p,s,t))]. S3: A risk seeking attitude corresponds to a convex utility function. Are these statements true or false?If a risk-averse individual owns a home worth $100,000, and that individual is willing to pay $1,000 for an annual fire insurance policy that covers the entire loss in the event of a fire, then we know that?Scenario 2 Tess and Lex earn $40,000 per year and all earnings are spent on consumption (c). Tess and Lex both have the utility function ( sqrt c) . Both could experience an adverse event that results in earnings of $0 per year. Tess has a 1% chance of experiencing an adverse event and Lex has a 12% chance of experiencing an adverse event. Tess and Lex are both aware of their risk of an adverse event. Refer to Scenario 2 Calculate Lex’s and Tess' expected utilities without insurance. (each one separated) Round to two decimal places for both