Question

onsider the following IS-LM model with a banking system:

Consumption:

C = 7 + 0.6Y_D

Investment:

I = 0.205Y − i

Government expenditure:

G = 10

Taxes:

T = 10

Money demand: Md/P=Y/i

Demand for reserves:

R^d = 0.375D^d

Demand for deposits:

D^d = (1 − 0.2)M^d

Demand for currency:

CU^d = 0.2M^d

This says that consumers hold 20% (c = 0.2) of their money as currency and the required reserve ratio is 37.5% (θ = 0.375). Demand for central bank money (H^d) is the total amount of currency being demanded plus the total demand for reserves. Suppose the price level is P = 1 and that the initial supply of central bank money is $100.

1.Solve for the money multiplier. Explain your work.

2.Solve for equilibrium output and the equilibrium interest rate at the initial supply of central bank money (ie. $100).

3.Suppose that the central bank sells $80 worth of bonds using open market operations. Solve for the new equilibrium output.

4.Solve for the the new equilibrium interest rate after the open market operations and use an IS-LM graph to explain what happened.

Answer 1

Answer:

Anbwe 1) The Money Multiplier is given as rata cu to cute na Money supply B = Movey base Cu = currency Da Disposit R> Reseauve Ma cuto oleur cute plur - (17 ) Now, od=0.8md cud = 0.2nd Rd = 0.375X0.8m 8.8 and do 01345 KD 8 + . Ara 0.375 l 6.62 08 0.375 +

2) given as The demand for money is met sy . Assuring, pol The initial money supply is 100. i Hd = 100 ox, =100 oxy 100...211 cove The goods Market eaubriun is is given ay Y C+I+ -7+0.640 + 0.205 Y - +10 = 7+06(y-7)+ogost-it10 17+0.6(Y-lo) +0.QOSY- = 1+0.895 Y- Ox, 0.195711- ve 56.1 - S.13 is curve At equilibrium is = LM 1001 - 56.41 - 5:13; of 105:13; = 56.41

.::.O.Su FYSU 3) The money multiplier is change in money supply for lund change in sucreasing base Transter, on our AMS MRAB swing poi na AB 0 11 Assuring AB 38 . SES AMS 2 * $o 160 New money supply would be MS 2100+160 tonnousus The noney talked equilibrium MS ard ox, 2602 Y2601 А та Зоом тока епохv? At situ Haneous equilibrun 2601 - 56.41-5:13; ox, 265-13: 56:41

riy-55.32 u) interest rate decreases to og The new from 0:59. As the SURRY of Money the li crve shift to the regled Bean L19 curve gives the money a naked east brun, the rise in supply of money deny interest rate at each output people fundit. Profitable to consure and rest and less lucreases expenditure. This increases the equilibriur out Puto 1. LOWASA) XT) torio Output Intent decrease tron into outrot increases from Yo tori