Question

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

Consumption: C = 10 + 0.5YD

Investment: I = 0.4Y − 100i

Government expenditure: G = 5

Taxes: T = 10

Money demand: Md /P = Y /i

In periods of financial turmoil, banks often choose to hold excess reserves above and beyond what they are required to hold by law. We shall denote the proportion of deposits held as excess reserves as ρ and the required reserve ratio as θ. Suppose that consumers hold 37.5% of their money as currency (c = 0.375) and the required reserve ratio is 20% (θ = 0.2). The banking system is then described by:

Demand for reserves: R d = 0.2Dd + ρDd

Demand for deposits: Dd = (1 − 0.375)Md

Demand for currency: CUd = 0.375Md

Demand for central bank money (Hd ) is the total amount of currency being demanded plus the total demand for reserves. Suppose the price level is P = 1.

2. Solve for equilibrium output and the equilibrium interest rate when H = 500.

Answer 1

Y: C+I+G z 10t0 SYDT 0.44-100i+SY - 10+015 (y-7)+0.94-1001+5 MOWE money Solving fon Y, Y=100-1000i Now money demand and money supply equation Yi 2 500 (trice = 1) (100-1080i)/: - 1195 solving for i, i: 0.04 Now if we substract i=0.04 in the equation Y = 100-1080i Y2100 - 100(0:04) = 60

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