Consider a closed economy with household sector and firm sec

Consider a closed economy with household sector and firm sector, money demand is MD=0.2Y-4r, money supply is 200, consumption function is 100+0.8Y, investment function is 1=150. Solve for IS and I.M equations Find out the amount of income, interest rate, consumption and investment in equilibrium If money supply increases by 20, but money demand remain unchanged, how will income, consumption and investment change

Solution

1.) Closed economy,which has two sectors,household and firm sector.

Money demand (M^D)=0.2Y-4r, Money supply(m^s)=200,Consumption function(C)=100+0.8Y

Investment(I)=150

In goods market,equilibrium condition is Y(income)=TE(total expenditure)

TE=C+I+G

G which is govt expenditure is not given here.

So TE=C+I

Y=TE

Y=C+I

Y=100+0.8Y+150

0.2Y=250

Y=1250 ;this is IS equation which is independent of interest rate

Money market is in equilibrium when M^D=M^s

0.2Y-4r=200

r = (0.2Y-200)/4;which is LM equation

2.)Equilibrium condition implies simultaneous equilibrium in both gooda and money market.

that is Y=TE and M^D=M^S

IS equation implies Y=1250

LM equation;

r =(0.2Y-200)/4

Put Y=1250 from IS equation

r = [0.2(1250)-200]/4

r = 12.5

Investment is constant at 150

C= 100+0.8Y

C=100+0.8(1250)

C=1100

3.) If M^S increases by 20,and M^D does not change;

M^S=200+20=220

For LM Equation

New M^S=Old M^D

220=0.2Y-4r

r = (0.2Y-220)/4

But According to IS curve Y= 1250 (constant)

r = [0.2(1250)-220]/4

r =[250-220]/4=30/4=7.5

r = 7.5 (new)

C=100+0.8Y=100+0.8(1250)=1100

Also investment remains same at 150