Question

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 ?

Answer 1

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