1. Consider a lottery P that offers $40 with probability 1 and $80 with probability and…

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.