Question

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?

Answer 1

Expected salary = Probability1*salary1 + Probability2*Salary2

Standard Deviation (Risk) = (probability1*(salary1-expected salary)2 + probability2* (salary2-expected salary)2)0.5

Job 1

Salary = $50000

Job 2

His probabilty of getting salary $48400 is 0.5

ans

His probability of getting $(48400+4500) is 0.5

Thus, expected salary= 0.5*48400 + 0.5*52900

= $50650

Risk = (0.5*(48400-50650)2 + 0.5* (52900-50650)2)0.5

Risk = (2131250 + 2531250)0.5 = $2159.30

Job 3

Expected Salary = 0.75*62500 + 0.25*40000

= $56875

Risk= (0.75*(62500-56875)2 + 0.25*(40000-56875)2)0.5 = (3,16,40,625+ 28,47,65,625)0.5

= $ 17787.81

b) Job 3 is most risky with highest standard deviation.

c) If she is risk neutral, she will choose the job having most expected salary i.e. Job 3

d) If she is risk loving, she will choose the job with higest standard deviation i.e. Job 3

e) U = I0.5

Utility for job 1 = 500000.5 = 223.60

Utility for job 2 = 506500.5 = 225.05

Utility for job 3 = 568750.5 = 238.48

f) She will choose the job offer which maximizes her utility, thus, Job 3

g) A risk premium of $ 6875 (56875-50000) is charged over job 1 as risk premium for job 3.

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