please answer a, b, c, d, and e for thumbs up!! thank you!!

Q8. Lemons (25 points) A buyer wishes to purchase a good from a seller. The good is worth 0 to the buyer and 0.80 to the seller. The buyer makes a take-it-or-leave-it offer of price p to the buyer, and the seller either accepts or rejects. Rejection means the buyer gets nothing but pays nothing (0), and the seller keeps the good (0.80). Acceptance means the buyer pays p but gets the good (0 - p) and the seller loses the good but gets the money (p). a. First, suppose this is a dynamic game of complete information, i.e., 0 is common knowledge. Find the unique SPNE outcome-i.e., what p is offered, is it accepted or rejected. Hint: Use backward induction. Going forward, it is common knowledge that 0 is distributed as follows: 1 of the time 0 = 1, of the time 0 = 2, and of the time 0 = 3. Thus, the (unconditional) average" is 2. Importantly, the seller knows the true value of 0. b. What is the seller's decision rule (accept when circumstance), reject otherwise) for some p? Hint: No probability theory here, since the seller knows what's going on. c. Suppose the buyer offers p = 2. What type of seller accepts the offer, and what type rejects? What is the expected value of a conditional on acceptance? (Hint: Bayes Rule) d. What price does the buyer ultimately offer, and what kinds of goods ultimately get sold? e. Name one intervention that can alleviate this inefficiency