Consider the following IS-LM model with a banking system:
Consumption:
C = 7 + 0.6YD
Investment:
I = 0.205Y − i
Government expenditure:
G = 10
Taxes:
T = 10
Money demand: Md / P = Y / i
Demand for reserves:
Rd =0.375Dd
Demand for deposits:
Dd = (1 −0.2)Md
Demand for currency:
CUd = 0.2Md
This says that consumers hold 20% (c = 0.2) oftheir money as currency and the required reserve ratio is 37.5%(θ = 0.375). Demand for central bank money(Hd) is the total amount of currency beingdemanded plus the total demand for reserves. Suppose the pricelevel is P = 1 and that the initial supply of central bankmoney is $100.
1.Solve for the money multiplier. Explain your work.
2.Solve for equilibrium output and the equilibrium interest rateat the initial supply of central bank money (ie. $100).
3.Suppose that the central bank sells $80 worth of bonds usingopen market operations. Solve for the new equilibrium output.
4.Solve for the the new equilibrium interest rate after the openmarket operations and use an IS-LM graph to explain whathappened.
