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 LM 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

(i)

In the defined economy, IS equilibrium is

Y = C + I

Y = 100 + 0.8Y + 150

(1 - 0.8)Y = 250

0.2Y = 250

Y = 250 / 0.2 = 1,250 [Solved for IS]

Also, LM equation is:

MD = MS

0.2Y - 4r = 200

(0.2 x 1,250) - 4r = 200 [Since in equilibrium Y is same for IS & LM curves]

250 - 4r = 200

4r = 50

r = 12.5% [Solved for LM]

(ii)

Equilibrium income, Y = 1,250

Equilibrium interest rate, r = 12.5%

Consumption, C = 100 + 0.8Y = 100 + (0.8 x 1,250) = 100 + 1,000 = 1,100

Investment, I = 150 (Autonomous)

(iii)

New LM equation is

MD = MS

0.2Y - 4r = 200 + 20 = 220

(0.2 x 1,250) - 4r = 220 [Since, if MS increases, IS remains unchanged & Y remains unchanged at 1,250]

250 - 4r = 220

4r = 30

r = 7.5%

So income, consumption and investment all remains unchanged if money supply increases. Only interest rate changes, which decreases from 12.5% to 7.5%.