Joel, who has reference-dependent preferences over beer and money, goes to Uni Bar with a friend, but is not planning on drinking any beer or spending any of his $50 in cash. Let his end-of-evening outcomes in pints of beer consumed and cash be c and c2, respectively, and let his reference point in pints of beer and cash be and 12, respectively. Then, Joel's utility is given by: v(6c - 6r) + v(cr); where u(x) = x for x 0 and v(x) = 3x for x < 0. (a) [10 points] Calculate Joel's buying price for a pint of beer by writing down his reference point and solving for the price PB such that he is indifferent between getting a pint for PB and not getting or paying anything. (b) [10 points] Suppose Joel gets a pint of beer as part of a promotion at Uni Bar, and incorporates its consumption into his reference point in beer. Calculate his selling price by writing down his reference point and solving for the price ps that makes him indifferent between keeping his pint and receiving nothing and giving up his pint and getting ps. (c) [10 points] Now suppose that after Joel gets his promo pint but before he decides whether to sell it, he notices that he lost $10 on the way to the pub. He does not yet incorporate this $10 loss into his reference point for cash. Calculate his selling price for the pint of beer. For the rest of this question, you do not need to make any calculations, just explain in words. Imagine that we are back at the start of the night. (d) [5 points] How would projection bias affect Joel's buying price for a pint of beer? Explain carefully in at most 3 sentences. (e) [5 points] Now suppose that instead of pints of beer, Uni Bar offers nice beer mugs for people to take home. Assuming that Joel has reference-dependent preferences over beer mugs as well, how would projection bias affect his buying price for a beer mug? Explain carefully in at most 3 sentences. (f) [5 points] How would projection bias affect Joel's selling price for a beer mug? Which is bigger, the impact of projection bias on the buying price, or on the selling price? Explain carefully in at most 4 sentences.