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Consider the Mortensen-Pissarides model in discrete time. The labor force is normalized at 1. Let u denote the unemployment rate. There is a large number of firms who can enter the market and search for a worker. Firms who engage in search have to pay a fixed cost k per period until they find a worker. If in any given period a measure v of vacant firms search for workers, then the total number of matches created in the economy is given by m(u, v) = uv u + v . Each vacant firm has one job opening. Within each match, the firm and the worker bargain (a la Nash) for the wage, w, with denoting the bargaining power of the worker. If they agree, they move on to production, which will deliver output equal to p per period. All agents discount future at rate (0, 1). At the end of every period (after production has taken place), existing matches get destroyed with probability . 1 So far this is just the standard model (in discrete time). We now make two assumptions that depart from the baseline model. First, the unemployment benefit, z, does not represent utility of leisure or value of home production, as we conveniently assumed in class. Here, z is a payment made by the government and, naturally, this payment needs to be funded somehow. We assume that the government raises these funds by imposing a lump-sum (flat) tax (per period) on every matched firm. Thus, the government chooses both z and , and must do so in a way so that the budget constraint is satisfied at any t. The second assumption concerns the duration of unemployment benefits. In particular, we will assume that workers are eligible for unemployment benefits only for one period.2 (This assumption would be quite realistic for the US, if we were to assume that a period of the model corresponds to 6 months.) a) Describe the Beveridge curve (BC) of this economy in steady state, i.e., express u as a function of the market tightness v/u. b) This model predicts that a certain level of unemployment will persist even in the steady state. What is perhaps a little more subtle is that workers who are currently 1 A worker who was part of a match that got hit by the destruction shock at the end of period t, will be unemployed for sure in t + 1 and will try to find a job again in (the beginning of) period t + 2. 2 Consider again the worker described in footnote 1, i.e., a worker who was part of a match that got hit by the destruction shock at the end of period t. This worker will be unemployed for sure in t + 1 and will receive z. Starting in period t + 2, she will try to find a new job. If she is successful, she will move (immediately) into production. If she is unsuccessful, she will remain unemployed for another period, and, importantly, during that period she will not be eligible for unemployment benefits. This process will continue until the worker finds employment. 2 in the pool of unemployment have been unemployed for different periods of time. This is especially relevant in our question, where unemployment benefit eligibility depends on the duration of unemployment. Describe the measure of workers who have been unemployed for i periods, i = {1, 2, 3, ...}. 3 Verify 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 firm (V ) and a firm that has filled its vacancy (J). d) Describe the value function of a typical worker in the various states. e) Exploiting the usual free entry argument, derive the job creation (JC) condition. f) Describe the wage curve (WC) in this economy. g) What is the relationship between and z, u so that the government's budget constraint is satisfied in every period? Use this condition in order to get rid of in the WC and JC expressions you derived earlier. h) Plot the JC curve in the (w, ) space. Does it have the standard shape? i) Plot the WC in the (w, ) space. Does it have the standard shape? j) Shortly discuss the existence and uniqueness of a steady state equilibrium.

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 (0,) such that U 0 (X ) = 1, and we define the first-best quantity traded in the KW market as q {q : u 0 (q ) = 1}. We will assume that there are two types of money, m1 and m2. 4 There are also two types of sellers. For reasons that we will leave out of the model, Type-1 sellers, with measure [0, 1], do not recognize m2, thus, they accept only the local currency m1. Type-2 sellers, with measure 1 , recognize and, hence, accept m2, as well as m1. 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 is the probability with which a buyer meets a type-1 seller, and 1 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 controlled by an individual authority, and evolves according to Mi,t+1 = (1 +i)Mi,t. New money (of both types) is introduced, or withdrawn if i

Section B Question 3 (a) Discuss the logit demand model. In particular, discuss the assumptions underlying the model and the data needed to estimate the model (b) The next few questions deal with Berry, Levinsohn and Pakes (Econometrica 1995) which estimates a model partially based on the logit demand model. Discuss the empirical setting of the model and the data. (c) Discuss the major differences between BLP and a "standard" logit demand model as well as any issues/weaknesses with the standard model that BLP seek to address. (d) Give a brief overview of BLP's estimation strategy. Given the nature of their data are there additional hurdles that the authors must overcome? Discuss their results. (e) Compare and contrast BLP with Goldberg (Econometrica 1995). What are the similarities between the two papers? What the key differences in the data and estimation strategies? In doing so discuss Glodberg's empirical model and how it relates to the logit demand model. Question 4 This question relates to "New Empirical Industrial Organization" studies that seek to estimate market power levels without marginal costs data. (a) Discuss the identification strategy of NEIO models. That is, what equation NEIO papers are estimating as well as the theoretical underpinnings of this key equation? (b) The NEIO model has been challenged on at least two fronts. Discuss two challenges to the validity of the NEIO model. Be as specific as you can. (c) Discuss Genesove and Mullin (Rand 1998). What is the empirical setting, what is the key feature of their data, what is the main research question and what are the key results