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Question 3 (30 points) Suppose an economy where 2,000 young agents are born in every period t. Each young individ- ual is endowed with 80 units of the consumption good. The young do not hold any at money; instead, they hold deposits to nance consumption later in life. In fact, each young individual deposits 50 units of the consumption good with banks. They do not invest in capital. Deposits at banks are subject to a reserve requirement of 15 percent. After meeting the re- serve requirement, banks invest the remainder of all deposits into capital. The net real rate of return on capital is 3 percent per period. The monetary base controlled by the Central Bank is constant and equal to 5,000 units of at money. There is no central bank lending. (a) (5 points) Find the equation describing the money market clearing, that is, the equality of total supply and demand for at money. Use it to calculate the exact price level in units of at money. (b) (5 points) Calculate the total nominal money stock (M 1),;. How large is the money multiplier? (c) (5 points) How large is total output (GDH) in this economy, assuming that capital needs two periods to produce output and then fully disintegrates? (Hint: There is no uninter- med'iated capital in this economy.) Now assume that the Central Bank allows private banks to obtain 25% of the reserve require- ment through Central Bank lending. The Central Bank charges an net real interest rate of 2% on those loans. ((1) (5 points) Set up the money market equilibrium taking into account Central Bank lend- ing. Derive the new price level. How have prices changed now that Central Bank lending is available? (e) (5 points) Calculate the gross real rate of return on deposits that competitive banks will offer. (f) (5 points) What would happen to the value of at money if Central Bank lending was unlimited but all rates of return remained unchanged (including the interest rate that the central bank charges, w = 1.02)