Monopolistie Wine Seller Consider the wine seller model we oovered in class. Wine o'ered ior sale is characterized by two parameters (q,t) where q is quality and t is price.Buyers are parametrized by their taste for quality Baltility of bottle [(1, t} to buyer type B, in dollar terms, is 3:} 15. Utility is zero if wine is not purchased. There are two type of buyers: 9;, and 33, where 33 > 91. Population proportions of types are \"EH andaLzlwH. The seller may produce wine of any quality 1; > 0 Cost of producing a bottle of quality (1 is C(q}. We assume cost function is increasing in quality and convex: C" > 0, C\" > U, (3'93) = lll, C'(eo} = 00. Consider the following game between one buyer and one seller: First, the buyer proposes terms of trade (q, t) Then, the seller either aceept the offer (that is, produces bottle of quality q and sells it at priec t) or declines (no trade). a.Cha.raeteri2.e the equilibrium analytically or/and graphically. What is the seller's prot in equilibrilun? b. Which type, 9;, or 6'3, ends up consuming higher quality wine? Which type, 9;, or 93, ends up with greater utility? Now, consider the game with opposite timing: First, seller picks a (q, 1:) offer. Then, buyer either aeeepts it or declines. c. Characterize equilibrium as sharply as you can. What is the quality of wine in equilibrium? For a given type of buyer .9, how does it compare to equilibrium quality in (a)? What is produeer's prot? Consumer's utility? On which type is the producer's prot greater in equilibrium? Now, assume buyers are of two types, 9\" and 91,, where I?\" > 31; Population proportions of types are 11'\" and 7T1. = 1 1r\". Information is asymmetric: buyer's type is Imobservable to the seller. As in (e), the seller is a. monopolist and sets priocs which buyers can decline but cannot bargain with. d. The sellers offers two types of wine (qL,tL] and [qH,tH). Write the prot maximization condition and all constraints. e. Prove that in equilibrium, {BLtype buyer is indiEferent between (in, Q) and no trade. f. Prove that in equilibrium, Histype buyer is indifferent between (qL, i5} and [qH,tH]