Q6 (25 points) Joe's value function for monetary gains and losses x is as follows: v(x) = {2.5x if x0 x x (1) Graph v(x). Use one sentence to describe what feature of preferences does v(x) capture. (2) Suppose Joe must decide whether to accept a gamble in which he wins $200 with probability 0.5 and loses $100 with probability 0.5. Will he accept the gamble? (3) Now Joe is offered a second gamble, which simply repeats the gamble above twice. That is, a coin is flipped with heads leading to a gain of $200 and tails a loss of $100, and then the coin is immediately flipped again with heads leading to a gain of $200 and tails a loss of $100. What is the probability distribution of total gains and losses from this gamble? (4) Given the distribution of total gains and losses you have just computed, will Joe accept this second gamble? (5) Now suppose Joe has mental accounting. In other words, when presented with the second gamble, Joe would evaluate the first coin flip and the second coin flip as two distinct gambles. Now will he accept it? Briefly explain why