The attachments are provided below. help me to tackle them the question is complete
{f} (s) (11} 'What is the relationship between T and 2,11 so that the government's budget constraint is satised at all times? Use this condition in order to get rid of T in the \"TC- In the baseline model, it 1was easy to characterize the equilibrium values of {ux}? since equations .10 and \"'0 contained exclusively these two variables. To do this here, we need a little more work, since at least one of these equations also contains the third endogenous variable, namely, a. lCan you get rid of a and replace it with a term that contains 3 {and other parameters}? Hint: \"rhich equilibrium condition gives you a as a function of 6"? Plot the JC and \"EC curves in the w, 3 space. Do they have the standard shape? Use your graph to discuss existence and uniqueness of equilibrium- 'What is the intuition behind your ndings? Assume that the government increases 2;. 'What is the effect of this policy change on equilibrium unemployment? 5. {10} lConsider a standard growth model in discrete time. Throughout this question you can focus on the Social Plannerls problem [vs the more complicated model with competitive markets]. At t = I} there is a large number of identical agents normalized to 1. The population grows at rate in. per period, i.e., Ni = {1 + RF. The representative agent's preferences are described by 15! t c 10" Hansen) = 25* 1:0 The initial capital stock in this economy is K9, and each agent can devote one unit of productive time {in each period} to work. Final output is produced using capital and labor, and production is characterized by the socalled laboraugmenting technology: Y: = Hrs. Mu + g}, where F is a CR3 production function. ICapital depreciates at rate 5 E (D, 1}. The Social Planner wishes to maximize percapita lifetime discounted utility. {a} Describe the resource constraint of the Planner's problem. Hint: It will be useful express all the variables into I'growthadjusted percapita variables\Question 1 (20 points} Consider the standard MortensenPissarides model in continuous time. Labor force is normalized to 1. Unemployed workers with measure a search for jobs, and rms with measure 1: search for uneranOyed workers. The matching technology is given by the function m{n, c), which is increasing in both arguments and exhibits constant returns to scale. It is convenient to define the market tightness d E sin. A large measure of rms decide whether to enter the labor market with exactly one vacancy. When a rm meets an unemployed worker a. job is formed. The output of a job is 30 per unit of time. However, while the vacancy is unlled, rms have to pay a search or recruiting cost equal to pc per unit of time. Upon a suecemil match, the worker's wage is negotiated through Nash bargaining. Let )9 represent the worker's bargaining power. The destruction rate of existing jobs is exogenous and given by the Poison rate A. Once a. shock arrives, the rm closes the job down. Subsequently, the worker goes back to the pool of unemployment, and the firm exits the labor market. So far this is just the model we described in class. What is new here is that unemployed workers are not {necessarily} eligible for unemployment benets for the whole duration of their unemployment spell. More precisely, a worker who just lost her job starts receiving a benet a per unit of time right away, but she will stop being eligible for this benet at a. Poisson rate 5. Thus, at any point in time, there are two types of unemployed workers: those who are still eligible for s, and those whose unemployment benet eligibility has expired. This, of course, will be important for the negotiation process between a rm and an unemployed worker.1 Throughout this question focus on steady state equilibria and let the discount rate of agents be given by 1-. Also, amume that 6 2 A, which will simplify some of the derivations later on. a) Draw a gure that describes the ows in and out of the various states a worker may be in. Denote these states by E, for employed, U, for unemployed with benets, and U\c) Describe the value functions for a worker in the various states. d) Describe the value functions for a firm in the various states. e) Exploiting the free entry of firms into the labor market, describe the Job Creation (JC) condition for this economy." f) Solve the bargaining problem between a firm and an unemployed worker in state U and Un and derive the analogue of the Wage Curve (WC) for this economy. g) Using your findings in part (f) show that, for any given d, we have w > Wn. What is the economic meaning of this result? h) Without going into detail, provide a strategy to solve for the steady state equi- librium. More precisely, explain how you would combine the various equilibrium con- ditions derived so far in order to characterize the five cquilibrium variables.Questiom 2 {20 points] Consider an economy that consists of twp islands, i = {1,2}. Each island has a large population of innitely-lived, identical agents, normalized to the unit. There is a unique consumption good, say, coconuts, which is not storable across periods. Although within each island agents have identical preferences over consumption, across islands there is a diiference: Agents in island 2 are more patient. More precisely, the lifetime utility for the typical agent in island 17 is given by Ur ({diul = :55 laid), rue whcrc; E (ill, 1), for all i, and g 2: ,3]. Due to weather conditions in this economy, island 1 has a production of e :- units of coconuts in even periods and zero otherwise, and island 2 has a production of e units of coconuts in odd periods and sero othenrise. Agents cannot do anything to boost this production, but they can trade coconuts, so that the consumption of the typical agent in island i, in period t, is not necessarily equal to the production of coconuts on that island in that period [which may very well be zero}. Assume that shipping coconuts across islands is costless. a.) Describe the Arrow-Debreu equilibrium {ADE} allocations in this economy. You can use any method you like, but I stroneg recommend that you exploit Negishi's method. b) Describe the ADE prices in this economy. c] Plot the equilibrium allocation for the typical agent in island 1', Le, {5}, LE\
