Question

2. Consider an experiment involving the following two decision situations.

Decision 1:

• A: A chance of winning $4,000 with probability 20%.
• B: A chance of winning $3,000 with probability 25%.

Decision 2:

• C: A chance of winning $4,000 with probability 80%.
• D: A chance of winning $3,000 with certainty.

1. If a given subject has “neoclassical” preferences over lotteries, what should be his/her choices?
2. If, instead, subjects’ preferences over lotteries violate independence axiom, what kind of effect should we expect to happen here?

Answer 1

Solution :

Expected Value of a Lottery = Probability of Winning × Winning Amount

Decision 1 :

Expected Value of A : 20% × $4,000 = 20/100 × $4,000 = $800

Expected Value of B : 25% × $3,000 = 25/100 × $3,000 = $750

Therefore, total expected value of Decision 1 = $1550 ($800 + $750)

Decision 2 :

Expected Value of C : 80% × $4,000 = 80/100 × $4,000 = $3,200

Expected Value of D = $3,000

Part a :

Neoclassical preference means that a rational consumer will make his/her choice by comparing the values of given options and will choose the best among them, as in the option with highest benefit.

According to Neoclassical preferences, Decision 2 is the best because the expected winning from Decision 2 is more than expected value of Decision 1.

Part b :

Independence Axiom states that even if the subject is provided with a mix of the two Decisions(Decision 1 and 2), the subject will choose the better and the mixing of the two decisions will not affect his or her preference.

If the subject violates the Independence Axiom, then the subject might end up choosing Decision 1 instead of Decision 2 when he or she is provided with a mix of Decision 1 and 2, even when the subject's preference was Decision 2.