Question

1. Consider a lottery P that offers $40 with probability 1 and $80 with probability and $100 with probability Compare this against a lottery Q that offers $39 with probability and $90 with probability and $120 with probability (a) Prove that neither lottery first-order stochastically dominates the other. (b) Find a non-decreasing utility function such that if a DM had that utility function, she would prefer P to Q (c) Find a non-decreasing utility function such that if a DM had that utility function, she would prefer Q to P.

Answer 1

a) Random variable A has first-order stochastic dominance over random variable B if for any outcome x, A gives at least as high a probability of receiving at least x as does B, and for some x, A gives a higher probability of receiving at least x. In notation form, $P[A\geq x]\geq P[B\geq x]$ for all x, and for some x, $P[A\geq x]>P[B\geq x]$ .

b) In economics, utility function is an important concept that measures preferences over a set of goods and services.