the problems are attached below.

e] Prim-ride a restriction on parameter values such that a steady state equilibrium pair {11:13] exists. Is it unique?. {No need for a lengthy discussion} f] What is the effect of a decrease in a. on the equilibrium in and 6"? Explain analytically and intuitively {but shortly}. 3;} Describe the Eeveridge curve EEC} of this economy by looking at the ows of workers in and out of the 1various states. What effect will the decrease in u {dismissed in the previous part} have on equilibrium unemployment? \fQuestion '3 [IE] points} This question is about the standard decentralized real business cycle model. You do not need to derive anything for this question and keep your answers clear and concise. a} Briey explain the mechanisms through which TFP shocks affect output, con- sumptiorn1 hours worked and investment in the standard REC model. How well does the model replicate the business cycle facts seen in the data? Hosr would adding habits in consumption affect the dynamics of consumption and investment? h] Suppose you want to solve the model using computational methods. Explain one approach, the advantages of this method and the steps you would need to take. Question 1 [If] points} lEonsider the standard deterministic growth model in discrete time. There is a large number of identical households {normalized to 1}. Each household wants to maximise life-tirne discounted utility Hosea) = Z'na + iln EH}, 1: r EL 3:13 that is, households preferences are characterized by \"habit persistmce\". Each household has an initial capital stock In. at time D, and one unit of productive time in each period1 that can be devoted to work. Final output is produced using capital and labor services, a = Fit-111m] = Hamil This technology is owned by rms whose number will be determined in equilibrium. Output can be consumed {q} or invested {it} We assume that households own the capital stock [so they make the investment decision} and rent out capital services to the rms. We also assume that the capital stock {1;} fully depreciates at the end of a given period, i.e_ I5 = 1. Finally, it is assumed that households own the rms, i.e. they are claimants to the rms' prots. a} In this economy1 why is it a good idea to describe the AD equilibrium capital stock allocation by solving the {easier} Social Planner's Problem? b] Fully characterize [i.e. nd a closed fonri solution for} the equilibrium allocation of the capital steel-[.1 c} What is the capital stock equal to as t } on? What is the ADE value of the rental rate of capital and the rental rate oflabor as t } oo'i' Question 2 [2!] points} lConsider the MortensenPissarides model in continuous time. Labor force is nonnal ized to l, but here there are N types of workers l[this will be the only dilterence in comparison to the baseline model seen in class}. A worker of type i enjoys a benet equal to 2:.- while unemployed, and Z1 {:2 cg 4: s: z\" _ The measure of workers of type i is given by in, with 211's.- = 1. Since matching is random1 the probability 1with which a rm matches with a certain type 1' depends only on the relative measure of type i workers in the aggregate pool of unemployed. The rest of the model is standrard. Unemployed workers and rms [with one va- cancy each search for each other. Let the measure of unemployed workers be denoted by u = Zi=1 11,-, where \"u,- is the measure of unemployed workers of type i. Also, let the measure of vacant nns be denoted by a, which will be detennined endogenously by free entry. H. CH5 and increasing {in both arguments] matching function1 m[u,tr], brings together unemployed workers and vacant rms. It will be useful to dene the market tightness as H E ufu. Once a match has been formed, the wage is determined through Nash bargaining, with ,3 E [I], 1] representing the worker's power. The output of all jobs is p :h I] per unit of time, Le, 13 does not depend on the workers type and p :h 3,, for all i. Also1 while a rm is searching for a worker it has to pay a search {or recruiting} cost, pc :=- I], per unit of time. All jobs are exogenously destroyed at rate J. 3.5 U [again1 independently of the worker's type}. All agents discount future at the rate r 2: [IL Throughout this question focus on steady state equilibria. a} Based only on your knowledge of the environment [i.e., without analyzing the model}1 explain whether the following statement is true or false: \"In this economy1 all workers will be paid the same wage, since they are equally productive". b] Write down the value function of a rm with an unlled vacancy {V} and the value function of a rm matched with a worker of typei {.12}. c} Write down the value function of a worker of type 1' while unemployed {U;} and while employed {WI-l d] IBombine the free entry condition [i.e., V = D} with the expressions for JI- provided earlier in order to derive the job creation {JD} curve for this eezinomy.g e} Using the same methodoly as in the lectures {adjusted to accommodate the differ ences in the new environemnt], derive the wage curve {WC} for this economy}1 f} Combine the JC curve and the WC curve determined in the previous parts in order to provide an equation that l[implicitly] determines the equilibrium 6'. g} Describe the equilibrium wage for a worker of type i Earl-III as a fucntion of the model's parameters and the equilibrium 5' [which was implicitly detennined in part f]