Suppose you have a mutually exclusive investment choice to make: you can choose

Question

Suppose you have a mutually exclusive investment choice to make: you can choose A or B. If you choose to invest in A, your income, m, will be 5 with certainty. If you choose B, you may end up earning m=400, but there is only a 1% chance of this event. Otherwise, given that you choose B, you will earn 2. Suppose your value of whatever income actually occurs from your investment choice is given by U = 1 - (1 / m) where m represents the (expected) income from the chosen asset. This implies the that the expected value (or utility) of the income from investment choice “i” is given by EUi = kj=i pj (1 / mj), where pj is the probability of event j, and K is the number of possible outcomes. Naturally, kj=i pj = 1

Given the above information, what is the rational choice, asset A or B? Explain.

Explanation / Answer

For A

The income is always 5 therefore m =5

For B

Expected income is m=0.01(400)+0.99(2)= 1.98+0.04=2.02

Value from investment A= 1-(1/5)=0.8

Value from investment B= 1-(1/2.02)=0.505

Then if we check for every outcome then

0.01(1-(1/400))+0.99(1-(1/2))=

0.01-1/40000+0.99-0.495=0.505-0.000025=0.504975

As the Value of A >Value of B that is 0.8>0>504975

Therefore A is the better option

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