Charlie has von Neumann-Morgenstern utility function u(x) = ln x and has wealth W = 250, 000. She is offered the opportunity to purchase a risky project for price P = 160, 000. 1 1 With probability p = 2 the project will be a success and return V > 160, 000. With probability 1 −p = 2 the project will fail and be worthless (i.e. it returns 0). For simplicity assume there is no interest between the time of the investment and the time of its return, that is r = 0 . How large must V be in order for Charlie to want to purchase the risky project? [Hint: What is Charlie’s expected utility is she does not purchase the project? What is Charlie’s expected utility is she purchases the project?]
Exercise 3: Risky Investment
Charlie has von Neumann-Morgenstern utility function u(x) = ln x and has wealth W = 250, 000.
She is offered the opportunity to purchase a risky project for price P = 160, 000.
1 1
With probability p = 2 the project will be a success and return V > 160, 000. With probability 1 −p = 2
the project will fail and be worthless (i.e. it returns 0).
For simplicity assume there is no interest between the time of the investment and the time of its return, that is r = 0 .
How large must V be in order for Charlie to want to purchase the risky project?
[Hint: What is Charlie’s expected utility is she does not purchase the project? What is Charlie’s expected utility is she purchases the project?]
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