Consider the payoff matrix below with actions, states of nature, and prior probabilities. 0.20 0.30 0.50 S1 S2 S3 a1 az 1 a3 4 4 -1 gnore the prior probabilities. Which action should be taken based on the Hurwicz criterion with an index of optimism 0.6? O only a3 O none since the Hurwicz criterion does not apply O only a2 O only a1
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- At the beginning of each day, a patient in the hospital is classifed into one of the three conditions: good, fair or critical. At the beginning of the next day, the patient will either still be in the hospital and be in good, fair or critical condition or will be discharged in one of three conditions: improved, unimproved, or dead. The transistion probabilities for this situation are Good Fair Critical Good 0.65 0.20 0.05 Fair 0.50 0.30 0.12 Critical 0.51 0.25 0.20 Improved Unimproved Dead Good 0.06 0.03 0.01 Fair 0.03 0.02 0.03 Critical 0.01 0.01 0.02 For example a patient who begins the day in fair condition has a 12% chance of being in critical condition the next day and a 3%…Consider a public project with the cost of 500. There are three individuals with the following benefits for the public good: v1=400, v2=200 and v3=0. Which of the following statement is false about the VCG (Vickrey-Clarke-Groves) mechanism? None of the options The budget deficit is 200 VCG mechanism is strategy-proof The tax for individual 3 is equal to 0 The tax for individual 1 is equal to 300A store owner must decide whether to build a small or a large facility at a new location. Demand at a location can be either small or large, which probabilities estimated to be 0.4 and 0.6, respectively. If small facility is built and demand proves to be high, the manager may choose not to expand (payoff=P235,000) or to expand (payoff=P275,000). If a small facility is built and demand is low, there is no reason to expand and the payoff is P220,000. If a large facility is built and demand proves to be low, the choice is to do nothing (P60,000) or to stimulate demand through local advertising. The response to advertising may be either modest or sizable, with their probabilities estimated to be 0.3 and 0.7, respectively. If it is modest, the payoff grows to P230,000 if the response is sizable. Finally, if a large facility is built and demand turns out to be high, the payoff is P900,000.a.) Draw a decision tree.b.) Determine the expected payoff for each decision and event node.c.)…
- Given the following payoff table with the profits ($m), a firm might expect alternative investments (A, B, C) under different levels of interest rate. (Attached)(a) Which alternative should the firm choose under the maximax criterion? (b) Which option should the firm choose under the maximin criterion? (c) Which option should the firm choose under the LaPlace criterion? (d) Which option should the firm choose with the Hurwicz criterion with α = 0.2? (e) Using a minimax regret approach, what alternative should the firm choose? (f) Economists have assigned probabilities of 0.35, 0.3, and 0.35 to the possible interest levels 1, 2, and 3 respectively. Using expected monetary values, what option should be chosen and what is that optimal expected value? (g) What is the most that the firm should be willing to pay for additional information? Use Expected Regret (h) Use the alternative method to verify EVPI Part 2 Assume now that the pay offs are costs answer the following: (a) Using an…A manager is deciding whether to build a small or a large facility. Much depends on the future demand that the facility must serve, and demand may be small or large. The manager knows with certainty the payoffs that will result under each alternative, shown in the following payoff table. The payoffs (in $000) are the present values of future revenues minus costs for each alternative in each event. Possible Future DemandAlternative Low HighSmall facility 200 270Large facility 160 800Do nothing 0 0What is the best choice if future demand will be low?Suppose that you want to invest $10,000 in the stock market by buying shares in one of two companies: A and B. Shares in company A though risky, could yield a 50% return on investment during the next year. If the stock market if conditions are not favorable (bear market) the stock may lose 20% of it value. Company B provides safe investments with 15% return in a bull market and only 5% in a bear market Ali the applications you have consulted are predicting a 60% chance for a bull market and 40% for a bear market. Where you invest your money? Construct a decision tree.
- On Monday, a certain stock closed at $10 per share. Before the stock market opens on Tuesday, you expect the stock to close at $9, $10, or $11 per share, with respective probabilities 0.3, 0.3, and 0.4. Looking ahead to Wednesday, you expect the stock to close 10 percent lower, unchanged, or 10 percent higher than Tuesday’s close, with the following probabilities. Tuesday's Close 10 Percent Lower Unchanged 10 Percent Higher $9 0.4 0.3 0.3 10 0.2 0.2 0.6 11 0.1 0.2 0.7 Early on Tuesday, you are directed to buy 100 shares of the stock before Thursday. All purchases are made at the end of the day, at the known closing price for that day, so your only options are to buy at the end of Tuesday or at the end of Wednesday. You wish to determine the optimal strategy for whether to buy on Tuesday or defer the purchase until Wednesday, given the Tuesday closing price, to minimize the expected purchase price. Develop and evaluate a decision tree. a-1. Determine the optimal…The expected value of perfect information is the A. Same as the expected profit under certainty B.Sum of the conditional profit (loss) for the best event of each act times the probability of each events occurring. C. Difference between the expected profit under certainty and the expected opportunity loss D. Difference between the expected profit under certainty and the expected monetary value of the best act under uncertainty.Consider the following information for the Alachua Retirement Fund, with a total investment of $4 million. [5] Stock Investment Beta A $ 400,000 1.2 B 600,000 -0.4 C 1,000,000 1.5 D 2,000,000 0.8 The market required rate of return is 12 percent, and the risk-free rate is 6 percent. What is its required rate of return? Stock A has the following probability distribution of expected returns: [5] Probability Rate of Return 0.1 -15% 0.2 0 0.4 5 0.2 10 25 What is Stock A’s coefficient of variation? What is Stock T’s coefficient of…
- A manager wants to expand summer resort facilities now or wait at least another year. If he expands now and the upcoming summer season is good, the profit will be K246 000; and if not good, the loss will be K60 000. If he delays the expansion for at least a year and the upcoming summer season is good, the profit will be K120 000; if the season is poor, the profit will be K12 000. Required: Assuming the probability of a good summer in both cases is 1/3, use Bayesian analysis to aid the manager.An investor has a certain amount of money available to invest now. Three alternative investments are available. The estimated profits, in Kwacha, of each investment under each economic condition are indicated in the following payoff table: Event Investment selection A B C Economy declines 500 -2000 -7000 No charge 1000 2000 -1000 Economy Expand 2000 5000 20,000 Based on his own past experience, the investor assigns the following probabilities to each economic condition: P (Economy declines) = 0.30 P (No Change) = 0.50 P (Economy expands) = 0.20 i. Compute the coefficient of variation for each investment. ii. Compute the return-to-risk ratio (RTRR) for each investment. iii. Based on (i) and (ii), what investment would you choose? Why?Martha and Ken Allen want to sell their house. At thebeginning of each day, they receive an offer. We assume thatfrom day to day, the sizes of the offers are independentrandom variables and that the probability that a given day’soffer is for j dollars is pj . An offer may be accepted duringthe day it is made or at any later date. For each day thehouse remains unsold, a maintenance cost of c dollars isincurred. The house must be sold within 30 days. Formulatea dynamic programming recursion that Martha and Ken canuse to maximize their expected net profit (selling price -maintenance cost). Assume that the maintenance cost for aday is incurred before the current day’s offer is received andthat each offer is for an integer number of dollars.