Solve the following questions;

Question 2 [1.5 points} |Consider a standard \"Lucas trees" ectrnomy. There 15 a. large number of identical ho'useholds {normalized to 1) who wish to maximise expected life-time utility, given by Eu: Eta-Eel t=ll There is onlyr one nonvstorable commodity that agents consume, call it coconuts. There are also innitely lived objects, that wecall trees, 1which yield coconuts. There is no production in this world. Agents can buy their shares at some price that they take as given. Let the Supply}I of shares of the trees be nonnalized to 1. The holder of one share of the tree in period t is a. claimant to the fruit d1. We assume that a" follows a. Markov prom. For any t, (it E D E {(11, ..., nip}. Let I\Uooeider the toilet-ring static version oi the Mortenseni'isserides model. Labor force is normalized to 1. There is a large number of firms who can enter the market and march for a worker. Firms who engage in search rst have to pay a. xed cost k. if a measure u of rms enters the marl-rat, a @ matching function mil, o] gives us the total measure of matches in the economy. Witlnn each match, the rm and worker bargain for the wage, in, with ,Ei' denoting the bargaining power of the werloer. If they agree, they can move on to production, which will deliver output equal to 3;. If they disagree both parties get nothing. nations that trip s: l - Also, throughout this question focus on a. specic: matching technology, such that the arrival rate of workers to rms {or simply the probability with which a rm nds a worker} is given by ath] = l 15'\