Please help me with this question

John works for company A and earns$10000 per annual. One of John's friends attempts to bribe John for some private information of company A. John is assured that he can ask for any pricezupto$4000.

If John accepts the bribe without getting detected by company A, he can keep the money received from his friend. However, if John gets caught, he has to return the money from his friend and pay a penalty, which is double the amount of the bribery. And the probability of getting caught isP.

(a)Draw a Hirshleifer-Yaari (HY) diagram, measuring John's wealth in the event that he gets caught on the horizontal axis, and his wealth in the event that he does not get caught on the vertical axis. On your diagram, sketch theline segmentcorresponding to the lotteries associated with the different possible values ofzthat John can choose. (Hint: the slope of the line segment is 1/2)

(b)Assume John is risk averse andP >1/3, explain why John won't accept the bribe. (You can use the HY diagram to illustrate your answer.)

(c)Suppose John is an expected utility maximiser with von Neumann-Morgenstern utility functionv(w) =wandP=1/5, will John accept the bribe? If John accepts the bribe, how much will he ask for from his friend?