5. You prefer a fifty-fifty chance of winning either $100 or $10 to a lottery in
ID: 3184096 • Letter: 5
Question
5. You prefer a fifty-fifty chance of winning either $100 or $10 to a lottery in which you win $200 with a probability 01%, $50 with a probability of ¼, and $10 with probability of ½. You also prefer a fifty-fifty change of winning either $200 or $50 to receiving $100 for sure. Are your preferences consistent with von Neumann and Morgenstern's a (1/2, $100; 1/2, $10) b (1/4, $200; 1/4, $50; 1/2, $10) c (1/2, $200; 1/2, $50) d (1.0, $100) Assume , ( 1.0, $10) (using NM) 1/2 : ac + (1-a)a_ (1/4, $200; 1/4, $50; 1/2, $10) ~ b 1/2 : ad + (1-0) a. (1/2, $100; 1/2, $10)" a Then considering from c d--> b a : there is a conflict.Explanation / Answer
Solution:
Option 1: Winning $100 lotter with p = 0.5
So expected value = 100* 0.5 = $50
Option 2: Winning a lottery with $10
Expected value = 200*1/4 + 50*1/4 + 10*1/2 = 130
Expected profit = 130-10 = $120
In second case,
For $ 200 lottery,
Expected value = 200*1/2 = 100
For $50 lottery,
Expected value = 100*1 = 100
In first case I will choose, option 2.
In second case I will choose $100 for sure.
In the second case there is no risk, so people may tend to take this option. So preferences are consistent with
von Neumann and Morgenstern’s axioms.