Question

Consider an economy described by the following equations:

C=100+0.9Yd,

I=600-30r,

TR= 50

G=300,

T=50+1/3Y,

Md=0.4Y-50r,

Ms=520.

P=2

Where C is consumption expenditure, I is investment expenditure, G is government expenditure, T is the tax, TR is transfer payments, Md is nominal money demand, MS is nominal money supply, r is interest rate, Yd is disposable income, P is price level and Y is income.

Derive the IS and LM equations and find the equilibrium income and interest rate.

What is the new level of income and interest rate if government spending increases by 100.

define crowding out effect.

(present your solutions graphically)

Answer 1

C=100+0.9Yd,

I=600-30r,

TR= 50

G=300,

T=50+1/3Y,

Md=0.4Y-50r,

Ms=520.

P=2

For IS equation:

Y= C+I+G

Y= 100+0.9Yd+600-30r+300

Y= 1000-30r+0.9(Y-T+TR)

Y= 1000-30r+0.9(Y+50-50-1/3 Y)

Y= 1000-30r+0.9(2/3 Y)

Y-1.8/3 Y = 1000-30r

0.4Y= 1000-30r

Y= (1000-30r)/0.4

Y= 2500-75r IS Equation

For LM equation:

Md=Ms/P

0.4Y-50r= 520/2

0.4Y= 260+50r

Y=650+125r LM Equation

Equilibrium:

IS=LM

2500-75r = 650+125r

1850= 200r

r = 1850/200= 9.25 Equilibrium interest rate

Put r = 9.25 in LM equation:

Y= 650+125(9.25)= 1806.25 Equilibrium income

If government spending increases by 100 then:

New G= G'= 400

For new IS equation:

Y= C+I+G

Y= 100+0.9Yd+600-30r+400

Y= 1100-30r+0.9(Y-T+TR)

Y= 1100-30r+0.9(Y+50-50-1/3 Y)

Y= 1100-30r+0.9(2/3 Y)

Y-1.8/3 Y = 1100-30r

0.4Y= 1100-30r

Y= (1100-30r)/0.4

Y= 2750-75r New IS Equation

For new equilibrium:

New IS = LM

2750-75r = 650+125r

2100= 200r

r' = 2100/200= 10.5 new Equilibrium interest rate

Put r = 9.25 in LM equation:

Y'= 650+125(10.5)= 1962.5 new Equilibrium income

Crowding out: It refers to the decrease in private investment due to rise in government spending that is if government spending increases it will cause interest rate to rise which cause private investment to decrease. In the above graph, movement from point A to E' is due to crowding out.