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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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- 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)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 utility
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