Question 1 Alice has a painting that she wants to sell. Bertie values the painting at $200. Alice tells Bertie that she is willing to sell the painting if he makes her a sufficiently attractive offer. Bertie doesn't know how much the painting is worth to Alice, but he thinks the painting's value to her is equally likely to be any amount between zero and $100. That is, the probability that Alice's value of the painting is less than or equal to 1: is 1} F (1)) = a 100 for any 0 S 'U S 100. (1) If Bertie wants to maximize his expected surplus, what should he bid for the painting. [Bertie is making a \"take it or leave it\" offer, which Alice is assumed to accept if and only if Bertil's offer is greater than the value of the painting to her.] (2) What is Alice's expected revenue from the auction? (3) What are the potential gains from trade? What are the actual gains from trade using this auction