Microeconomic Theory
Microeconomic Theory
12th Edition
ISBN: 9781337517942
Author: NICHOLSON
Publisher: Cengage
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Chapter 7, Problem 7.1P
To determine

To find: Minimum probability to win.

Expert Solution & Answer
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Explanation of Solution

Given the even money placed on bulls = $100,000

The current wealth = $1,000,000

Let the probability of winning = pThus, expected utility, EU(bet) = p×U(1100000) + (1 - p)×U(900000)Expected utility in the case of no bet.EU(no bet) = U(1000000)

Since the utility function is logarithmic, expected utility from betting and not betting should be equal.

EU(bet) = EU(no bet)p×U(1100000) + (1 - p) × U(900000) = U(1000000)p×ln(1100000) + (1 - p) × ln(900000) = ln(1000000)p×ln(11/9) = ln(10/9)p = 0.525

The minimum probability to win is 0.525.

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