In: Economics
Tyler lives in Anchorage and has loss averse preferences. In particular, Tyler values a gain of amount x as u(x) = x^1/2 and values a loss of −x as u(−x) = −2x^1/2
(a) What is the maximum amount of money that Tyler would pay for a lottery that pays $1000 with probability 1/2 and $0 with probability 1/2 ?
(b) What is the maximum amount of money that Tyler would pay to avoid playing a lottery that loses $1000 with probability 1/2 and loses $0 with probability 1/2 ?
(c) What is the maximum amount of money that Tyler would pay to avoid playing a lottery that loses $1000 with probability 1/2 and gains $1000 with probability 1/2 ?
Given that tyler amounts gain of x as x^0.5 and loss of -x as -2x
1) through this lottery the expected gain = 1000 expected loss = 0
but tyler's expected gain = 1000^0.5 = 31.623
tyler's expected loss = -2*0 = 0
The maximum amount he could pay = expected value from the lottery = 1/2(expected gain + expected loss of tyler's) = 0.5(31.623-0) = 15.81
2)
through this lottery the expected loss = 1000 expected loss = 0
tyler's expected loss = -2*0 -2*1000 = -2000
The maximum amount he could pay = expected value from the lottery = 1/2(expected gain + expected loss of tyler's) = 0.5(-2000) = -1000
Therefore, tyler would pay max of 1000 to avoid playing lottery.
3)
through this lottery the expected gain = 1000 expected loss = 1000
but tyler's expected gain = 1000^0.5 = 31.623
tyler's expected loss = -2*1000 = -2000
The maximum amount he could pay = expected value from the lottery = 1/2(expected gain + expected loss of tyler's) = 0.5(31.623-2000) = -984.18
Therefore, he would pay the max amount of -984.18$ to avoid
playing lottery
Thank you....