Question: You wish to construct your personal utility function U(M) for receiving M thousand dollars. After setting U(0) = 0, you next set U(1) = 1

You wish to construct your personal utility function U(M) for receiving M thousand dollars. After setting U(0) = 0, you next set U(1) = 1 as your utility for receiving $1,000. You next want to find U(10) and then U(5).
(a) You offer yourself the following two hypothetical alternatives:
A1: Obtain $10,000 with probability p.
Obtain 0 with probability (1 – p).
A2: Definitely obtain $1,000.
You then ask yourself the question: What value of p makes you indifferent between these two alternatives? Your answer is p = 0.125. Find U(10).
(b) You next repeat part (a) except for changing the second alternative to definitely receiving $5,000. The value of p that makes you indifferent between these two alternatives now is p = 0.5625. Find U(5).

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