TACLKLE ALL THE QUESTIONS.
\fin the pool of unemployment have been unemployed for different periods of time. This is especially relevant in our question, where unemployment hent eligibility depends on the duration of unemployment. Describe the measure of worlsers 1Ivho have been unemployed for 1' periods, i = {1, 2, 3, ....}il 1|u'er'ir that your result is correct by adding up the various unemployment durations. [They should add up to the steady state u!} c} Describe the value function for a vacant rm {if} and a firm that has lled its vacancy {I}. d] Describe the value function of atypical mrker in the various states. e} Exploiting the usual free entry argument, derive the job creation [JG] condition. f] Describe the 1Ivage curve [WC] in this economy. g} What is the relationship between T and z,r.r so that the gmernnient's budget constraint is satisfied in every period? Use this condition in order to get rid of r in the WC and JG expressions you derived earlier. h] Flot the JC curve in the (or, IE] space Does it have the standard shape? i} Plot the WC in the {will} space. Does it have the stande shape? j] Shortly discum the existence and uniqueness of a steady state equilibrium. Question '2 [25 points} This question studies the co-existence of different currencies. Time is discrete with an innite horizon. Each period consists of two subperiods [n the day, trade is bilateral and anonymous as in Kiyotaki and Wright [1989] {call this the KW market}. At night trade takes plane in a Walrasian or centralised 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 buyersis 1:!qu +U{X} H, and for sellers it is a +UI{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 IBM. In the CM, all agents have access to a tedmology that turns one unit of work into a unit of good. The functions tr, U satisfy the usual assumptions; I will only spell out the most crucial ones: There exists X\" E {,oo] such that U'{X*} : 1, and we dene the rst-best quantity traded in the KW market as q" E {q : 1:11;\") 2 1}. We will assume that there are two types of money, In, and m.' There are also two typa of sellers. For reasons that we will leave out of the model, Type-l sellers, with measure or E W, 1], do not recognize mg, thus, they accept only the local currency m1. Type'2 sellers, withmeasurelo,recogniseand, hence,acceptm9,aswell as I'm. Hence1 local currency has a liquidity advantage over the foreign one, since it is recognised 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 l o is the probability with which she meets a type- selIH. In any type of meeting, buyers have all the The rest is standard. Goods are non storable. The supply of each money is con trolled by an individual authority, and evolves according to Mil\
