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Would you like this assignment to be marked?YESNOMA103 Lab Report 6 - Derivative ApplicationsName:Student Number:Spring 20181. [5marks] In financial mathematics, investors use utility functions to compare the “joy” of earning money on aninvestment to the “pain” of losing money on the same investment.Suppose that an investor using the utilityu= lnxhas $1000 and is trying to determine how much of this amount to invest in a stock (i.e. $1000xwhere 0x1).Assuming that when $1000xis invested there is a 60% chance it doubles in value and a 40% chance that half theinvestment is lost,then the expected utility can be shown to be:y=35ln (1000 + 1000x) +25ln(1000-500x).(a) Determine the critical values ofyonx(0,1).

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