1. Francesca has the utility function U = 10 ln(M+1). ( ln(x) is the natural log
ID: 3066937 • Letter: 1
Question
1. Francesca has the utility function U = 10 ln(M+1). ( ln(x) is the natural logarithm of x.) Francesca has initial wealth of 60 and can make an investment that loses 40 with probability 0.4 or gains 40 with probability 0.6. (Utility calculations should be written out to at least one decimal place.)
a.If she does this alone, will she want to invest?
b.If she can pool risk with an equal partner who makes half of the investment, takes half of the gains and pays half of the losses, will she want to invest with pooled risk?
Explanation / Answer
The expected utility of Francesca is
0.4*10ln(41)+0.6*10ln(41) = 1.612
Therefore her certainty equivalent is 10ln(1.612+1) = 0.417
This value shows that she has chances of loses when she invests alone. Hence she would not invest alone, which is the solution to Part a. of the question.
Part b:
If this investment is done with a partner, who can take half gain and pay half loss, then Francesca's certainty of utility will be
0.5*10ln (41) = 0.806
This shows that her probability to invest in a pooled risk is 0.806 as the loss that she will have to pay off will be less and that will be less than half of the investment.
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