5. You prefer a fifty-fifty chance of winning either $100 or $10 to a lottery in

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.

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