Hi whitney !

Do you have the answers to these exercises ? Or at least half of them ?

Macro monetaria y financiera Tarea 3. March 31, 2017 Exercise 1 Consider an OLG economy where each generation lives for 3 periods. The preferences are given by: Ut [ct (t), ct (t + 1), ct (t + 2)] = ct (t) (ct (t + 1)) (ct (t + 2)) 2 Each individual receives an endowment h (t) = [th (t), th (t + 1), th (t + 2)]. Population grows at rate n. As we did in class, let us suppose that investment in capital cannot be observed. Moreover, let us assume that there exists a market for lending and borrowing l(t) at the one period rate of interest r(t) and moreover that it exists a market for private loan l2 (t) that pays after 2 periods an interest rate r2 (t). As a consequence, we have a term structure of interest rates. Let us conclude assuming that there exists a fixed supply of fiat money. 1. Write down the budget constraints for the first, the second and the third period. Assume the agent could buy money in the first period and sell it in the second period. 2. Write down the intertemporal budget constraint 3. Now suppose that physical capital pays a return of X > n2 after 2 periods. Based on the previous intertemporal budget constraint, which asset are young using for saving to each period? Explain it clearly. 4. Using all your previous results, solve the problem of the individual, i.e., maximize his utility function subject to the restrictions. Write the first order conditions and find consumption and saving of each individual in each period. Assume (t) = [t (t), 0, 0] 5. Find the market equilibrium conditions. 6. Use the equilibrium conditions and solve for a symmetric stationary equilibrium. Find the equilibrium interest rate r(t) and the return on money. 1 Exercise 2 Solve the previous exercise assuming that: X = 1.05, h (t) = [10, 0, 0], n = 1.03 y = 1. Exercise 3 Solve exercise 1 assuming that X = 1.05, h (t) = [10, 0, 0] y = 1. Moreover assume that the government raises real revenue using seignorage by setting the growth rate of money to = 1.02, with n = 1. 1. Compute the real return on money in the symmetric stationary equilibrium. 2. Find the Bailey curve. At what time of their life, agents will be paying the seignorage? 3. What is the maximum growth rate of money for which the government gets some real revenue from seignorage? And the growth rate of money for which the government gets the maximum revenue? Exercise 4 Suppose an economy with constant population where the individuals want to keep 5000 goods in their bank deposits in each period. The economy has an endowment of 10, 000 goods per period. There is a total stock of capital not intermediated of 1000 goods in each period. Bank deposits are the only form of money. Bank deposits are subject to a reserve requirement of 20%. The net real rate of return on capital is 10% per period. After complying with the reserve requirements, the bank invest the rest of its liabilities on capital. Individuals do not own capital. The monetary base is 2000 units of money per period. Compute: 1. The price of a good in terms of fiat money 2. The real return on bank deposits offered in a competitive industry of intermediation 3. The total stock of M1 4. The money multiplier 5. The stock of capital 6. The real GDP Exercise 5 Repeat the previous exercise assuming that the central bank can lend up to 10% of the reserves ( = 0.1). 2 Exercise 6: from Ch 7 in Champ, Freeman and Haslag (2011) Supose an OLG model where people live for 2-periods and receive and endowment in the first period of life. To invest in capital, there's a minimum level k > k . Assume k > the endowment of a single individual but less than the total endowment of a single generation. Capital pays a one-period gross real rate of return equal to x. The population growth rate is n = 1.10 each period. Assume there's fiat money M and is constant. 1. Is capital illiquid? In which sense? Is fiat money illiquid in this sense? 2. Describe an intermediary that will be likely to overcome the illiquidity of capital. 3. Suppose there is only one person in each generation who is able to run an intermediary. What is the minimum rate of return that person must offer to attract depositors? For what values of x can this individual make a profit? 4. What rate of return will be offered on deposits if the bank industry is competitive? Exercise 7 Discus the differences between ILF and FMC models of banks (max 2 pages) 3