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Question 2 (20 points) This question studies the co-existence of different currencies. Time is discrete with an infinite horizon. Each period consists of two subperiods. In the day, trade is bilateral and anonymous as in Kiyotaki and Wright (1989) (call this the KW market). At night trade takes place in a Walrasian or centralized market (call this the CM). There are two types of agents, buyers and sellers, and the measure of both is normalized to 1. The per period utility for buyers is u(q) + U(X) - H, and for sellers it is -q + U(X) - H, where q is the quantity of the day good produced by the seller and consumed by the buyer, X is consumption of the night good (the numeraire), and H is hours worked in the CM. In the CM, all agents have access to a technology that turns one unit of work into a unit of good. The functions u, U satisfy the usual assumptions; I will only spell out the most crucial ones: There exists X" E (0, co) such that U'(X*) = 1, and we define the first-best quantity traded in the KW market as q' = {q : u'(q") = 1}. We will assume that there are two types of money, m, and my. There are also two types of sellers. For reasons that we will leave out of the model, Type-1 sellers, with measure o E (0, 1), do not recognize me, thus, they accept only the local currency m1. Type-2 sellers, with measure 1 - o, recognize and, hence, accept my, as well as mi. Hence, local currency has a liquidity advantage over the foreign one, since it is recognized by all sellers. All buyers meet a seller in the KW market, so that o is the probability with which a buyer meets a type-1 seller, and 1 - o is the probability with which she meets a type-2 seller. In any type of meeting, buyers have all the bargaining power. The rest is standard. Goods are non storable. The supply of each money is con- trolled by an individual authority, and evolves according to Mitti = (1 + p;)Mis. New money (of both types) is introduced, or withdrawn if ;