Suppose that your value function is v(x)=x/2 for gains and v(x)=2x for losses.

a/ What does your value function look like graphically?

b/ Your friend the Joker gives you two newly issued dollar coins on your birthday. In terms of value, how much did you just gain?

c/ Once you have a closer look at them, though, you realize that The Jokers coins are fake, and you feel like you just lost two dollars. In terms of value, how much did you just lose?

d/ At the end of the day, you have no more or no less money than you did at the beginning. In terms of value, though, what is the net gain or loss of the whole sequence of events?