ISLM Model: Suppose that the following equations describe an economy. (C, I, G,

Question

ISLM Model:

Suppose that the following equations describe an economy.

(C, I, G, T, and Y are measured in billions of dollars, and r is measured as a percent; for example, r = 10 = 10%):

C = 100 + 0.75 (Y - T)

I = 800 - (50/3)r

G = 500

T = 600

(M/P)^d = L = 0.5Y - 50r

(M/P)^s = M/P = 1200

QUESTIONS:

#1: Derive the equation for the IS curve, where r is a function of Y which looks like the following expression: r = a + bY.

#2: Derive the equation for the LM curve, where r is a function of Y which looks like the following expression: r = a + bY

Explanation / Answer

1)

The consumption function is expressed as a linear function of disposable income. Investment function is also a linear function of the interest rate. Government spending is given exogenously. Together they form the general equation for the IS curve:

Y = C + I + G + NX

Y = 100 + 0.75(Y - 600) + 800 - (50/3)r + 500

Y = 950 + 0.75Y - (50/3)r

Y = 3800 - (200/3)r

This is the general equation for the IS curve, epressed as a function of Y.

2) Demand for real money balances is a function of interest rate and income. Money market is in equilibrium when money demand equals money supply. The general equation for the LM curve is therefore:

L = M/P

0.5Y - 50r = 1200

Y = 2400 + 100r.

This is the general equation for the LM,  epressed as a function of Y.

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