Tasha is choosing between 3 job offers. Job 1 is a salaried position that will pay $50,000 with certainty. Job 2 is also a salaried job that pays slightly less, $48,400, but also includes a 50% chance that she will get a $4,500 bonus at the end of the year. Finally, Job 3 is paid on commission. Tasha expects that with probability 0.75 she will earn $62,500 and with probability 0.25 she will only earn $40,000.
a) Calculate the expected value of each job offer.
b) Which job is the riskiest choice for Tasha?
c) If Tasha is risk neutral, which job offer will she take?
d) If Tasha is risk loving, which job offer will she take?
Suppose Tasha’s utility function for income is given by U=the square root of I
e) Calculate Tasha’s expected utility from each job offer.
f) Which job offer will Tasha choose?
g) What is Tasha’s risk premium for Job #3?
In: Economics
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A sequential game A local bee-keeper derives net revenue z(h) from choosing a level of production (number of hives) h given by z(h) = 4h − 2h 2 .
A nearby apple farmer also benefits from being next to the bee-keeper, because the bees help to polinate fruit trees. The value of the bees to the apple farmer is given by y(h) = 12h − 2h 2 .
(a) Show that the bee-keeper maximizes their net benefit by choosing h = 1, while the sum of benefits, y(h) + z(h), is maximized at h = 2.
(b) Suppose that the government has the power to impose a transfer from the farmer to the bee-keeper in amount t. The level of t is chosen after the bee-keeper decides on h. Additionally, the government wishes to maximize the sum of the logarithms of the payoffs of the the two parties, so that it solves max t ln(12h − 2h 2 − t) + ln(4h − 2h 2 + t).
i. Show that by choosing t taking h as given, the government optimally sets t = 4h.
ii. Show that this transfer scheme leads to the bee-keeper wishing to maximize z˜(h) = 8h − 2h 2 .
iii. What level of h will be chosen by the bee-keeper if they anticipate this payment? Show your reasoning.
(c) Would your answer to part (b)(iii) change if the government put less weight on the bee-keeper’s utility so that it solved, instead, max t ln(12h − 2h 2 − t) + 1 2 ln(4h − 2h 2 + t) ?
Justify your answer.
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