Hi tutors. Please help me with this MACRO-ECON work.
Own work needed please.
1.
4. Find the equilibrium expressions for output Y, consumption Of, labor _, and the real wage We = p. They should be (non-linear) functions only of At- 5. After linearizing the model around its steady state, you can find the following expressions for the (lin- earized) Euler equation and money demand: C+ = E.C+1 - (Re - Exit+1 ) (1) mi = noct - naRt (2) where no, 78 > 0 (they are composite coefficients depending on model parameters), and, as in class, a "hat" denotes the percentage deviation of the variable from its steady state. Ex: C, = In . Fromnow on, let's suppose that At = 1 at all times, so that there is no more uncertainty in the model. This implies that you can drop the expectation operator from the Euler equation 1. Consider two alternative monetary policies: - the central bank controls nominal money growth: M. = Me,, for & 2 1 (Money Growth Rule, MGR) - the central bank directly controls the interest rate R. (Interest Rate Rule, IRR) Under the MGR, as seen in class, we have that mi = mi_-it. Under the IRR, assume that R = 4, it, where with the coefficient of > 1. Answer to the followings. a) Suppose the central banks adopts the MGR. Find the equilibrium inflation rate x, of the model. HINT: this is basically what we have done in class. First you have to solve for the equilibrium value of my, then recall that me = In #, and then use the definition of me = b) Now, suppose the central banks sets the interest rate Re (entering the Euler equation (1)) according to Re = 0_*+. In this case, we assume that the steady state inflation is a > 1. You can think of this also as a choice of the central bank (that is what the Fed actually does). Find the equilibrium inflation rate , and the equilibrium growth rate of nominal money, namely N. HINT: as for a), you will have to solve a difference equation. However, this time the difference equation will be in terms of a, not m. You have to find the unique stable solution of such difference equation.Problem Consider a model where money enters the utility function because of the transaction services it provides to households. The economy is populated by a continuum of identical infinitely-lived households. The representative households wants to maximize his lifetime utility: U = E. > gu ( C+, It, P. M+ 1=0 where 8 e (0, 1) is the discount factor, C, is consumption, L, is labor, Me is nominal holdings of money (cash), and Pe is the price level in the economy. Foor simplicity, assume utility takes the following form: Ll+x 2 ( Ct , Lt) P. = In C+ + yln p. where v > 0, x >0,720 1+x Notice that y indexes the importance of real money holdings for transactions, while w indexes the disutility from working. Utility is then increasing in consumption C+ and real cash-, but decreasing in labor Ly. The household's budget constraint in every period t is: P.C+ + M+ + B+ = R+-1B+-1 + Mi-1 + W.L+ + It where B, is a government bond which delivers a riskless gross return R, (hence Re-1B,-1 are payments in t from a bond purchased in t -1, including both the principal and the interests). The term It stands for transfers received by the central bank. As in class, we are going to denote gross inflation in period t as The firm's problem is the following. It chooses labor L, to maximize profits At = PYt - WL, subject to It = A.Ly, where a e (0, 1) under flexible prices and perfect competition. Answer to the followings.To start with, consider an economy with no production. There are two consumers in the economy. Consumer 1 has an initial endowment of (130, 190) and has an MRS for these two goods of 2y1/x1. Consumer 2 has an initial endowment of (70, 60) and has an MRS for these two goods of y2/x2. As with the last HW, decimal answers are possible. + + 1. Show that P = px/py =1 is not a competitive equilibrium price but P = 2 is. (3 points)+ 2. Draw an edgeworth box including the initial endowment, the CE allocation, the budget constraint, and the IC for both consumers through the CE allocation. Explain why we know the contract curve is not linear. (4 points)+ 3. Suppose that person 2 is considered more important and should, therefore, have a bigger allocation of the goods. So now the initial endowment of person 2 is (96, 225). Show that the new competitive equilibrium allocation ends up with person 1 having (80, 62.5) and person 2 having (120, 187.5) and show that the new equilibrium price is no longer 2. (Note: a picture is not required for credit here, but may be helpful in giving you insight on how to solve the problem) (3 points) + 4. Now there is a change so (200, 250) is just one of many options along a PPF that has a MRT of 5x/2y. Show that now, the outcome in (1) is PE but the outcome in (3) is not. (2 points)+ 5. If (176, 275) is also on the same PPF as in #4, find the PE allocation of the goods between the individuals. (Note: This becomes a bit tedious with the algebra since you have to solve 4 equations and 4 unknowns. Just do some substituting. Be careful that when you combine to eliminate an equation, you must also eliminate an unknown. Also, all answers are exact to 2 decimal places)(3 points) +
