Tonight at 7pm a professional basketball game featuring the Golden State Warriors and the Washington Wizards will be played at the Chase Center, an indoor arena in the Mission Bay neighborhood of San Francisco, California. Our teaching assistants Yang and Guangchu are making fair bets on the game. During office hours you learn that Yang thinks the Warriors will win and believes he is making a fair bet, assigning a probability of 5/6 or 83 % to the Warriors winning. Guangchu is betting on the Wizards and also believes he is making a fair bet, assigning a probability of 7/12 or 58% to the Wizards winning. You seek to bet a total of $N with Yang and Guangchu and capture a guaranteed, risk-free arbitrage profit. Now assume that N $240. Let z be the number of dollars bet with Yang. What is the exact range of x that guarantees that your profit is greater than or equal to zero, no matter who wins the game? O 40 < a< 140 O 40 < a < 240 00S< 140 O0S< 240 O0 << 40 O 80 < a < 160

Microeconomic Theory
12th Edition
ISBN:9781337517942
Author:NICHOLSON
Publisher:NICHOLSON
Chapter7: Uncertainty
Section: Chapter Questions
Problem 7.3P
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Tonight at 7pm a professional basketball game featuring the Golden State Warriors and
the Washington Wizards will be played at the Chase Center, an indoor arena in the
Mission Bay neighborhood of San Francisco, California. Our teaching assistants Yang
and Guangchu are making fair bets on the game. During office hours you learn that Yang
thinks the Warriors will win and believes he is making a fair bet, assigning a probability
of 5/6 or 83 % to the Warriors winning. Guangchu is betting on the Wizards and
also believes he is making a fair bet, assigning a probability of 7/12 or 58% to the
Wizards winning. You seek to bet a total of $N with Yang and Guangchu and capture
a guaranteed, risk-free arbitrage profit.
Now assume that N = $240. Let x be the number of dollars bet with Yang. What is
the exact range of x that guarantees that your profit is greater than or equal to zero, no
matter who wins the game?
O 40 < ¤ < 140
O 40 < ¤ < 24O
O0 < x< 140
O0 <r< 240
O0<I< 40
O 80 < ¤ < 160
Transcribed Image Text:Tonight at 7pm a professional basketball game featuring the Golden State Warriors and the Washington Wizards will be played at the Chase Center, an indoor arena in the Mission Bay neighborhood of San Francisco, California. Our teaching assistants Yang and Guangchu are making fair bets on the game. During office hours you learn that Yang thinks the Warriors will win and believes he is making a fair bet, assigning a probability of 5/6 or 83 % to the Warriors winning. Guangchu is betting on the Wizards and also believes he is making a fair bet, assigning a probability of 7/12 or 58% to the Wizards winning. You seek to bet a total of $N with Yang and Guangchu and capture a guaranteed, risk-free arbitrage profit. Now assume that N = $240. Let x be the number of dollars bet with Yang. What is the exact range of x that guarantees that your profit is greater than or equal to zero, no matter who wins the game? O 40 < ¤ < 140 O 40 < ¤ < 24O O0 < x< 140 O0 <r< 240 O0<I< 40 O 80 < ¤ < 160
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