Tennessee just instituted a state lottery. The initial jackpot is $100,000. If t

Question

Tennessee just instituted a state lottery. The initial jackpot is $100,000. If the first week yields no winners, the next week’s jackpot goes up, depending on the number of previous players who placed the $1 lottery bets. The probability of winning is one in a million (1.0 * 10^–6 = 1/1,000,000). What must the jackpot be before the expected payoff is worth your $1 bet? Assume that the state takes 60% of the jackpot in taxes, that no one else is a winner, and that you are risk neutral (i.e., you value the lottery at its expected value).

Explain the calculation and the steps please:

Explanation / Answer

Let x = the jackpot needed.

Hence,

P(win) x(win) + P(loss) x(loss) = 0 = E(x)

(1.0*10^-6)*(x(1-0.60)) + (1-1.0*10^-6)*(-1) = 0

(1.0*10^-6)*(0.40x) - 0.999999 = 0

(1.0*10^-6)*(0.40x) = 0.999999

0.40x = 999999

x = $ 2,499,997.50 [ANSWER]

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