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 t 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 + #) Me. 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?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