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Consider the following IS-LM model with a banking system: Consumption: C = 7 + 0.6YD Investment: I = 0.205Y...

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Economics

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.

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