Question 4 (5/50 points) 5 Consider again a "Lucas trees" economy as in Question 3. There are only two differences. First, the fruit process is deterministic: the tree yields d units of the fruit in each period with certainty. The second difference is the following: except from claims to the tree, there is another asset called fiat money. This is an intrinsically useless object (for example pieces of paper) that gives no fruit or utility to agents. What is special about money is that its supply is not exogenous, like the real asset. The supply of money in period { is given by M, and it is controlled by a monetary authority. This authority chooses the growth rate of money supply, /, so that Miti = (1 + /)M. As in the case of claims to the tree, agents can purchase any amount of the new asset (fiat money) in a perfectly competitive market. a) What is the competitive equilibrium price of one share of the Lucas tree? b) If u = 0 (fixed supply of money), what is the equilibrium price of fiat money? Why? c) What is the range of monetary policies (i.e. of values of /), that induce agents to hold fiat money?g) Let U be the present-dicounted value of the income stream of an unem- ployed worker, and W the analogous expression for an employed worker. Write down the Bellman equations that U and W satisfy. Explain intuitively. h) Consider a typical match of a vacant firm and an unemployed worker. Write down the Bargaining game solved by these two parties. After solving the bargaining problem, one can show that the equilibrium wage satisfies w = z + 8(p + pc# - z). Take this result as given. i) Explain the intuition behind the wage curve given above. Also, graph this relationship in the w,0 space. j) Which objects should a steady state equilibrium of the model define? Use your asnwers to parts (d), (f), and (i) in order to claim that the equilibrium is unique. You can do so either graphically or algebraically.Question 2 (17.5/50 points) Consider the Mortensen-Pissarides model in continuous time. Labor force is normalized to 1. Unemployed workers, with measure u