Suppose Jimmy’s value function is given by v(x) =sqrt( x) for gains (x 0) and v(

Question

Suppose Jimmy’s value function is given by v(x) =sqrt(x) for gains (x 0) and v(x) = 2sqrt(x) for losses (x < 0).Jimmy is facing the choice between option (A) a sure amount $10000 and option(B) a gamble which gives Jimmy $40000 with probability 0.25 and $0 with probability 0.75.

1) If Jimmy uses his current endowment ($0) as his reference point, what are the values of thetwo options? Which option would Jimmy prefer? Draw the graph of Jimmy’s value function, pointout the values corresponding to the two options on the graph.
2) If Jimmy uses the highest possible amount of money he can earn as his reference point, whatare the values of the two options? Which option would Jimmy prefer? Draw the graph of Jimmy’svalue function, point out the values corresponding to the two options on the graph

Explanation / Answer

a) ValueA = sqrt(10000)=100

ValueB = sqrt(40000)*0.25+ 0.75* 0 = 0.25*200=50

He would choose option 1 since value is greater

b) If the highest possible value is 40000 , V(o) = sqrt(40000)=200

a - Value = -2*sqrt(30000) = -346.41

b) Value = -2*0.25*sqrt(0) - 2*0.75 *sqrt(40000) = -300

In this case, he will choose option 2

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