Consider the following IS-LM model: C = 200 + 0.25Y D = 150 + 0.25Y - 1000i G =

Question

Consider the following IS-LM model:

C = 200 + 0.25YD

= 150 + 0.25Y - 1000i

G = 250

T = 200

(M/P)d = 2Y - 8000i

M/P = 1600

a) Derive the IS relation. (Hint: you want an equation with Y on the left side and everything else on the right)

b) Derive the LM relation. (Hint: it will be convenient for later use to rewrite this equation with i on the left side and everything else on the right)

c) Solve the equilibrium for real output. (Hint: Substitute the expression for the interest rate given by the LM equation into the IS equation and solve for output)

d) Solvw h eequilibrium interest rate. (Hint: Substitute the value you've obtained for your Y in part (c) into either the IS or LM equations and solve for i . If your algebra is correct you should get the same answers in both eqautions.)

e) Solve for the equilibrium values of C and I, and verify the value you obtained for Y by adding C, I, and G

f) Now suppose that the money supply increases to M/P = 1840. Solve for Y, i, c and T, and describe in words the effects of an expansionary monetary policy.

g) Set M/P equal to its initial value of 1600. Now suppose that government spending increases to G = 400. Summarize the effects of an expansionary fiscal policy on Y, i, and C.

Explanation / Answer

(a) IS equation:

Y = C+I+G+NX

Y = 200+0.25(Y-T) + 150+0.25Y-1000i +250

Y = 200+0.25(Y-200) +150+0.25Y-1000i+250

Y = 550+0.5Y-1000i

Y = 1100-2000i

(b) LM equation:

2Y-8000i = 1600

Y = 800+4000i

(d+c) AT equilibrium IS is equal to LM

1100-2000i = 800+4000i

300=6000i

i=0.05

i=5%

If i =0.05, then Y = 800+4000x0.05 = $1000

(e) C = 200+0.25(1000-200) = 400

I = 150+0.25Y-1000i = 150+0.25x1000-1000x0.05 = $350

G = $250

Y = C+I+G = 1000

(f) 1840= 2Y-8000i

Y = 920+4000i

Equating this with IS equation

920+4000i=1100-2000i

6000i = 180

i = 3% = 0.03

Y = 920+4000x0.03

Y = $1040

Expansionary monetary policy increases GDP income and lowers interest rate.

(g) If G increases to 400 that ius it increases by 400-250 = $150, then IS will increase by 150

1250-2000i = 800+4000i

450 = 6000i

i = 0.075

i =7.5%

Y = 800+4000x0.075 =1100

WIth increase in government expenditure interets rate increases and so does the income.

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