Consider the wine seller model we covered in class. Wine offered for sale is characterized by two parameters q, t where q is quality and t is price Buyers are parametrized by their taste for quality 8:utility of bottle (q. t) to buyer type 8, in dollar terms, is eq_t. Utility is zero if wine is not purchased. There are two type of buyers: 8 and 0, where >. Population proportions of types are and = 1 # The seller may produce wine of any quality q> 0 Cost of producing a bottle of quality g is C(q). We assume cost function is increasing in quality and convex: C, >0, C> 0 C (0) = 0, C (c) = Consider the following game between one buyer and one seller: First, the buyer proposes terms of trade (g, t) Then, the seller either accept the offer (that is, produces bottle of quality 9 and sells it at price t) or declines (no trade). a.Characterize the equilibrium analytically orffand graphically. What is the seller's profit in equilibrium? b. Which type, or y, ends up consuming higher quality wine? Which type, or 8. ends up with greater utility? Now, consider the game with opposite timing: First, seller picks a (q, t) offer. Then, buyer either accepts 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 , how does it compare to equilibrium quality in (a)? What is producer's profit? Consumer's utility? Now, assume buyers are of two types, and where > - Population proportions of types are and = 1_ Information is asymmetric: buyer's type is unobservable to the seller. As in (e), the seller is a monopolist and sets prices which buyers can decline but cannot bargain with. d. The sellers offers two types of wine (9. t) and (9, t). Write the profit maximization condition and all constraints. e. Prove that in equilibrium, -type buyer is indifferent between (9.tz) and no trade. f. Prove that in equilibrium, -type buyer is indifferent between ( tz) and (x, t).