3. George is seen to place an even-money bet of $100,000 on the Bulls to win the

Question

3. George is seen to place an even-money bet of $100,000 on the Bulls to win the NBA Championship (i.e. if the Bulls win he gains $100,000, if they loose he looses $100,000). George’s current wealth is one million dollars.

(a) If George estimates that the probability of Bull will win is p what is the income lottery that he faces when he places his bet?

(b) George is an expected utility maximizer with a logarithmic utility of wealth (i.e. he maximizes E(ln(x)) ). From the fact that he chooses to bet, what can we deduce about his probability estimate p?

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Explanation / Answer

a.

Amount of bet (X) = $100,000

Probability = P

Income lottery could be calculated by using the formula of expectation (PX).

PX = $100,000 × P = 100,000P

Answer: The income lottery is 100,000P.

b.

If the person is utility maximizer, his expectation of wining the bet is the highest. Highest expectation indicates getting the full amount of money, $100,000. It could only be possible if the probability (P) is 1, since it is multiplied with 100,000.

Answer: The required probability, P = 1.

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