(a) Given a utility function of an individual is U(x) = x² - 4x, determine his risk attitude. (b) With a utility function of U(x) = x - 3x², where x is the amount invested. determine if this function satisfy the two properties of utility functions. (i) (ii) compute the utility when the amount invested is 3 and 5 respectively.
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- 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…Safety and risk are subjective concepts which depend on the followingfactors, except a. voluntary vs. involuntary risk b. occasional vs. frequent accidentsc. delayed vs. immediate risk d. expected probability What is the answer ?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…
- A health economist is conducting the analysis and making a choice between the following two choices: Choice A: there is a certain outcome that the patient will stay in chronic health state X for the rest of his life T Choice B: the treatment has two possible outcomes, either the patient is returned to full Health (1) of the rest of his life T with probability p; the patient dies (0) immediately with the remainig probability What is the utilty value of the health state X? X=P X=PT X=(1-P)/P X=PT/(1-P)If the option doesn't match, no worries you can submit your answer then also . Not necessary to match the option, but make sure you have done correctlySuppose that the point spread for a particular sporting event is 10 points and that with this spread you are convinced you would have a 0.60 probability of winning a bet on your team. However, the local bookie will accept only a $1000 bet. Assuming that such bets are legal, would you bet on your team? (Disregard any commission charged by the bookie.) Remember that you must pay losses out of your own pocket. Your payoff table is as follows: STATE OF NATURE DECISION ALTERNATIVES YOU WIN YOU LOSE BET $1000 -$1000 DON’T BET $0 $0 What decision does the expected value approach recommend? What is your indifference probability for the $0 payoff? (Although this choice isn't easy, be as realistic as possible. It is required for an analysis that reflects your attitude toward risk.) What decision would you make based on the expected utility approach? In this case are you a risk taker or a risk avoider? Would other individuals assess the same…
- The following profit payoff table was presented in Problem 1: The probabilities for the states of nature are P(s1) 5 0.65, P(s2) 5 0.15, and P(s3) 5 0.20.a. What is the optimal decision strategy if perfect information were available?A manager must decide how many machines of a certain type to buy. The machines will be used to manufacture a new gear for which there is increased demand. The manager has narrowed the decision to two alternatives: buy one machine or buy two. If only one machine is purchased and demand is more than it can handle, a second machine can be purchased at a later time. However, the cost per machine would be lower if the two machines were purchased at the same time. The estimated probability of low demand is .30, and the estimated probability of high demand is .70. The net present value associated with the purchase of two machines initially is 950,000 if demand is low and 1,300,000 if demand is high. The net present value for one machine and low demand is 900,000. If demand is high, there are three options. One option is to do nothing, which would have a net present value of 1,000,000. A second option is to subcontract; that would have a net present value of 1,400,000. The third option is to…Explain probability and nonprobability samplingtechniques.
- You hold an oral, or English, auction among three bidders. You estimate that each bidder has a value of either $40 or $50 for the item, and you attach probabilities to each value of 50%. The winning bidder must pay a price equal to the second highest bid. The following table lists the eight possible combinations for bidder values. Each combination is equally likely to occur. On the following table, indicate the price paid by the winning bidder. Combination Number Bidder 1 Value Bidder 2 Value Bidder 3 Value Probability Price ($) ($) ($) 1 $40 $40 $40 0.125 2 $40 $40 $50 0.125 3 $40 $50 $40 0.125 4 $40 $50 $50 0.125 5 $50 $40 $40 0.125 6 $50 $40 $50 0.125 7 $50 $50 $40 0.125 8 $50 $50 $50 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 would not be willing to bid against each…Discuss how one is able to describe the riskiness of the decision-taker’s situation in ways which are intuitively appealing and analytically tractable.3. (True, False, or Uncertain) The satisficing procedure is unlikely to perform well in an environment where the decision maker is learning about the options as she samples them.