I need help with f, g, and h only please. Thanks!

Abigail is holding a yard sale before she moves out of Nashville. Among other items, she is selling some used video games. Bing Yang attends the yard sale and is considering buying a video game, although he has no way to tell the quality of the game before purchasing.

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

(a) If Abigail sets a price of p, what is Bing Yang's updated belief on the expected quality of the video game?

(b) What is Bing Yang's willingness to pay?

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

Now, suppose that Bing Yang leaves and Catherine, who has utility function UC = 8q, visits the yard sale and is considering buying the used video games.

(d) What is Catherine's willingness to pay? (e) Will trade take place in equilibrium? If so, what quality of video games will be sold?

Next, suppose that Demetrius is holding a separate yard sale and selling used video games with quality, q, distributed q U[1,3]. Suppose that UD = 3q. Begin by assuming Bing Yang visits Demetrius's yard sale.

(f) If Demetrius sets a price of p, what is Bing Yang's updated belief on the expected quality of the video game?

(g) What is Bing Yang's willingness to pay?

(h) Will trade take place in equilibrium? If so, what quality of video games will be sold?