Question 1 :
John Doe is a rationale person whose satisfaction or preference for various amounts of money can be expressed as a function U(x) = (x/100)2, where x is in $. How much satisfaction does $20 bring to John?
If we limit the range of U(x) between 0 and 1.0, then we can use this function to represent John's utility (i.e. U(x) becomes his utility function). How does his utility function look like?
What does U(x) show about John's incremental satisfaction with respect to x?
The shape of John''s utility function shows that he is willing to accept _______ risk than a risk-neutral person.
John is considering a lottery with a payoff of $80, 40% of the time, and $10, 60% of the time. If John plays this lottery repeatedly, how much will be his long-term average satisfaction?
For John, what certain amount would give him satisfaction equal to this lottery? Express your answer to nearest whole $.
Question 2 :
Frodo, a junior engineer at Baggins Metal Works is considering the introduction of a new line of products. In order to produce the new line, the company needs either a major or minor renovation of the current plant. The market for the new line of products could be either favorable or unfavorable, each with equal chance of occurrence. The company has the option of not developing the new product line at all.
With major renovation, the company's payoff from a favorable market is $100,000, from an unfavorable market, $ -90,000. Minor renovation and favorable market has a payoff of $40,000 and an unfavorable market, $-20,000. Not developing the new product line effectively has $0 payoff.
Frodo realizes that he should get more information before making his final decision. He contracted with Gandalf Market Research to conduct a market analysis to determine for certain if the market will be favorable or unfavorable. How much is the maximum amount Frodo should be willing to pay for this accurate information? (Please indicate your answer to the nearest whole number)
Question 3 :
An engineer is trying to determine the suitability of two metal alloys (alloy A and alloy B) in fabricating industrial machinery fuse elements - the part of the fuse which melts after reaching a certain temperature or current. Samples are taken from batches of alloys and are subjected to laboratory test where the melting temperatures are recorded. The melting temperatures for both alloys are provided in the excel file. The engineer had asked your help describing the extremely high and extremely low melting temperatures of the alloys by using G-I plot for minima and maxima. (for all numeric questions, please specify your answers in one decimal places of accuracy, ###.# - format, using standard convention in rounding of values)
For alloy A, what is the plotting position v for the largest of the minimal values?
For Alloy A, what is the plotting position v for the largest of the maximal values?
What is the asymptotic distribution of the minimal melting temperature of alloy A?
What is the asymptotic distribution of the maximal melting temperature of alloy A?
For alloy B, what is the plotting position v for the largest of the minimal values?
For alloy B, what is the plotting position v for the largest of the maximal values?
What is the asymptotic distribution of the minimal melting temperature of alloy B?
What is the asymptotic distribution of the maximal melting temperature of alloy B?