David is holding a yard sale before he moves out of Chicago. Among other items, he's selling some used video games of his. Gebra'iel attends the yard sale and he considers buying a video game, although he cannot at all tell what the quality of the game is before he actually buys it.

Let the quality of video games, q, be distributed q U[0,2], UA = 3q, and UB = 4q.

(a) If David sets a price of p, what is Gebra'iel's updated belief on the expected quality of the video game?

(b) What is Gebra'iel's willingness to pay?

(c) Will trade take place in equilibrium? and if so, what quality of video games will be sold?