You participate in a coin-toss gamble with a weighted coin. The coin has a 70% chance of landing heads and a 30% chance of landing tails. If the coin lands heads, you receive $1000; if lands tails, you lose $2000. Your initial level of wealth is $3000 and your utility of wealth function can be modeled using the function U(wealth) = In(wealth).

Microeconomic Theory
12th Edition
ISBN:9781337517942
Author:NICHOLSON
Publisher:NICHOLSON
Chapter7: Uncertainty
Section: Chapter Questions
Problem 7.1P
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You participate in a coin-toss gamble with a weighted coin. The coin has a 70%
chance of landing heads and a 30% chance of landing tails. If the coin lands heads,
you receive $1000; if lands tails, you lose $2000. Your initial level of wealth is $3000
and your utility of wealth function can be modeled using the function U(wealth) =
In(wealth).
a) What is the utility of your expected wealth following this game?
b) At what wealth level will you be indifferent between playing and not playing this
game?
Transcribed Image Text:You participate in a coin-toss gamble with a weighted coin. The coin has a 70% chance of landing heads and a 30% chance of landing tails. If the coin lands heads, you receive $1000; if lands tails, you lose $2000. Your initial level of wealth is $3000 and your utility of wealth function can be modeled using the function U(wealth) = In(wealth). a) What is the utility of your expected wealth following this game? b) At what wealth level will you be indifferent between playing and not playing this game?
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