New York University BUSF-SHU BUSF-SHU 304 O 2. (30 points; substantially modified from number 14 on Problem…

New York University BUSF-SHU BUSF-SHU 304 O 2. (30 points; substantially modified from number 14 on Problem…

Suppose that there are two states of the world, s1 and s2, and that an individual who knows the probabilities, p1 and p2, of the two states chooses among state-contingent consumption bundles to maximize the expectation of a state-independent, strictly increasing von Neumann-Morgenstern utility function.
(a) Suppose that the individual is risk-neutral, and that he is indifferent between (8, 2) and (4, 4).  What must the value of p1 be?
(b) Now suppose that the individual may be either risk-averse or risk-loving.  What is the lowest possible value of p1 for which the individual could weakly (or strictly) prefer the state-contingent consumption bundle (6, 2) to the bundle (2, 6)?
(c) Now suppose that the individual is risk-averse, and that he is indifferent between (6, 2) and (2, 6).  Show (graphically or algebraically) that he must weakly prefer (4, 4) to either of these bundles.

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