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2. A real estate developer must decide on a plan for developing a certain piece of property. After careful consideration, the developer has two acceptable alternatives: residential proposal or commercial proposal. The main factor or state of nature that will influence the profitability of the development is whether or not a shopping center is built close by and the size of the shopping center. There is a 20% chance of no center being built, a 50% chance of a medium shopping center built, and a 30% chance of a large shopping center.
- If the developer selects the residential proposal and no center is built, he has a further set of options: do nothing $400,000 payoff; build a small shopping center himself $700,000 payoff; or put in a park resulting in $800,000 payoff. Should a medium shopping center be built nearby, his payoff for residential would be $1,600,000 and large shopping center results in a $1,200,000 payoff.
- If the developer selects the commercial proposal and no center is built, he also has the set of options: do nothing but payoff would be $-50,000; build a small shopping center himself for $1,400,000 payoff; or put in a park resulting in $1,000,000 payoff. Should a medium shopping center be built nearby, his payoff for commercial would be $400,000 and large shopping center results in a $1,500,000 payoff.
Draw a decision tree for this problem.
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- 12. Over the last decade, robotic-drone a research and development company has researched in new drone technology for home delivery. Their sales department considers that they could sell as many as $90 million per year with a probability of 20%. With a most likely value of $76 million with a probability of 45% and a lowest value of $50 million. a. Determine the expected value of their sales. b. The sales department estimates that they could maintain this sales rhythm for 4 years with a probability of 67% or that this sales rhythm could be maintained for 8 years. Determine the Expected Value for the PW if the company considers a yearly interest rate of 10%6. A risk-averse individual is offered a choice between a gamble that pays $1000 with probability of 25% and $100 with probability of 75% or a pay- ment of $325. (a) Which gamble would he choose? (b) What is the payment was $320Q3/ The probability that a consumer will rate a new antipollution device for cars What are the probabilities that it will rate the device (a) very poor, poor, fair, or good; (b) good, very good, or excellent? Rate Poor Fair Very good Excellent Very poor Good Probability 0.07 0.12 0.17 0.32 0.21 0.11
- 1. A dealer decides to sell a rare book by means of an English auction with a reservation price of 54. There are two bidders. The dealer believes that there are only three possible values, 90, 54, and 45, that each bidder’s willingness to pay might take. Each bidder has a probability of 1/3 of having each of these willingnesses to pay, and the probabilities for each of the two bidders are independent of the other’s valuation. Assuming that the two bidders bid rationally and do not collude, the dealer’s expected revenue is approximately ______. 2. A seller knows that there are two bidders for the object he is selling. He believes that with probability 1/2, one has a buyer value of 5 and the other has a buyer value of 10 and with probability 1/2, one has a buyer value of 8 and the other has a buyer value of 15. He knows that bidders will want to buy the object so long as they can get it for their buyer value or less. He sells it in an English auction with a reserve price which he must…1. Individual Problems 18-1 You hold an oral, or English, auction among three bidders. You estimate that each bidder has a value of either $88 or $110 for the item, and you attach probabilities to each value of 50%. The winning bidder must pay a price equal to the second highest bid. The following table lists the eight possible combinations for bidder values. Each combination is equally likely to occur. On the following table, indicate the price paid by the winning bidder. Combination Number Bidder 1 Value Bidder 2 Value Bidder 3 Value Probability Price ($) ($) ($) 1 $88 $88 $88 0.125 2 $88 $88 $110 0.125 3 $88 $110 $88 0.125 4 $88 $110 $110 0.125 5 $110 $88 $88 0.125 6 $110 $88 $110 0.125 7 $110 $110 $88 0.125 8 $110 $110 $110 0.125 The expected price paid is . Suppose that bidders 1 and 2 collude and would be willing to bid up to a maximum of their values, but the two bidders…Determine whether or not to stock a large supply of steel. There is uncertainty in the price of steel. Based on past history the following data are available Price (future) Prob (Price) PW if stocked PW if not stocked High 0.3 100000 0 Medium 0.5 -10000 0 Low 0.2 -50000 0 What is the probability that stocking steel will result in a negative present worth (PW)?
- Assume you are faced with two decision alternatives and two states of nature whose profit payoff table is shown below. Decision Alternative State of Nature 1 State of Nature 2 Decision 1 25 30 Decision 2 45 15 The probability of state of nature 1 is 0.4.(a) Compute the expected value of each alternative.(b) Which decision is the optimal decision?(c) Compute the expected value with perfect information.(d) Compute the expected value of perfect information.A lottery system has balls numbered 1 to 65 and randomly selects 6 of the lottery balls. There is only one prize of $ 10,000,000.00 which is awarded only it a lottery player selects the correct set of 6 lottery balls. a) If a lottery ticket costs $ 5.00, what is a lottery player's expected value? b) How much would the lottery prize have to be worth if it was to be a fair game? (Note: Include dollar signs in your answer)Philippines You're the manager of global opportunities for a U.S. manufacturer that is considering expanding sales into Asia. Your market research has identified the market potential in Malaysia, the Philippines, and Singapore as described in the following table: Success Level Big Mediocre Failure Malaysia Probability 0.3 0.2 0.5 Units 1,100,000 352,000 0 Philippines Probability 0.3 0.3 0.4 Units 1,300,000 650,000 0 Singapore Probability 0.7 0.1 0.2 Units 600,000 360,000 0 The product sells for $20, and each unit has a constant marginal cost of $16. Assume that the (fixed) cost of entering the market (regardless of which market you select) is $500,000. In the following table, enter the expected number of units sold, and the expected profit, from entering each market. Market Expected Number of Units Sold Expected Profit Malaysia Philippines Singapore If you were to…
- Many decision problems have the following simplestructure. A decision maker has two possible decisions, 1 and 2. If decision 1 is made, a sure cost of c isincurred. If decision 2 is made, there are two possibleoutcomes, with costs c1 and c2 and probabilities p and1 2 p. We assume that c1 , c , c2. The idea is thatdecision 1, the riskless decision, has a moderate cost,whereas decision 2, the risky decision, has a low costc1 or a high cost c2.a. Calculate the expected cost from the riskydecision.b. List as many scenarios as you can think of thathave this structure. (Here’s an example to get youstarted. Think of insurance, where you pay a surepremium to avoid a large possible loss.) For eachof these scenarios, indicate whether you wouldbase your decision on EMV or on expected utility4. $1000 with of $325. (a) (b) Adam is risk averse. He is offered a choice between a gamble that pays a probability of 25% and $100 with a probability of 75%, or a sure payment What is the expected payment of the gamble? Will Adam prefer gamble over sure payment? Would he change his mind if the sure payment is $320 instead of $325? (c) If this individual has a utility function u(x) = lnx, would he prefer the payment of $320 or the gamble? (d) In the CRRA utility family u(x) = x¹-7. If this individual has a utility where y = 0.01, would he prefer the payment of $320 or the gamble?An oil company is considering drilling in the Gulf at a current cost of $400,000 with an expected profit of $500,000 in three years. The current market rate of interest is 10 percent. Should the company make the investment? Multiple Choice No, the present value of the profit is less than the present value of the cost.. No, the future value of the profit is less than the present value of the cost. Yes, the present value of the profit is greater than the present value of the cost.. Yes, the future value of the profit is greater than the present value of the cost.