Question

What is a von Neumann-Morgenstern expected utility function? An individual’s von
Neumann-Morgenstern (vNM) utility function is given by
U(M) = √
where M denotes money. Assume this individual has Rs 4 with him. A lottery ticket that will be
worth Rs 12 with probability 1
2
and zero otherwise is available in the market. What is the
maximum price he would pay to obtain it?

Answer 1

Answer:

In 1947, John von Neumann and Oskar Morgenstern proved that any individual whose preferences satisfied four axioms has a utility function;[1] such an individual's preferences can be represented on an interval scale and the individual will always prefer actions that maximize expected utility. That is, they proved that an agent is (VNM-)rational if and only if there exists a real-valued function u defined by possible outcomes such that every preference of the agent is characterized by maximizing the expected value of u, which can then be defined as the agent's VNM-utility (it is unique up to adding a constant and multiplying by a positive scalar). No claim is made that the agent has a "conscious desire" to maximize u, only that u exists.

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