Question

Suppose desired consumption and desired investment are Cd = 300 + 0.75(Y − T) − 300r T = 100 + 0.2Y Id = 200 − 200r G is the level of government purchases and G=600 Money demand is Md P = 0.5Y − 500(r + πe ) where the expected rate of inflation, πe , is 0.05. The nominal supply of money M = 133,200. Suppose the full employment output is 2500 and the price level in the short run is 120.

4) Find the equation for the aggregate demand curve by using the IS and LM curve. [Hint: Use the form of the LM curve for an unspecified value of P. This aggregate demand function is measured by the solution of (1) and (2).]

Answer 1

 

Cd= 300+0.75(Y-T)-300r

Id=200-200r

T=100+0.2Y

G=600

Real money demand Md/P= 0.5Y-500(r+πe)

Expected rate of inflation πe=0.05

Nominal money supply Ms=133200

Full employment output Yf=2500

Short run price Ps=120

To obtain the IS curve, consider the goods market equilibrium condition.

Y= Cd+Id+G

=300+0.75(Y-T)-300r+200-200r+600

Substitute the value of T in the above equation

Y= 300+0.75(Y-(100+0.2Y))-300r+200-200r+600

Y= 300+ 0.75Y- 75- 0.15Y-300r+200-200r+600

Y-0.75Y+0.15Y= 1025-500r

r=2.05- 0.0008Y -----------------------------------(1)

Equation (1) represents the IS curve

To obtain the LM curve,consider the money market equilibrium condition.

Md/P= Ms/P

0.5Y-500(r+πe)= 133200/P

( deriving LM for an unspecified value of P)

Substitute the value of πe in the above equation.

0.5Y-500(r+0.05)= 133200/P

0.5Y- 500r -25=133200/P

500r= 0.5Y-25-133200/P

r= 0.001Y-0.05-266.4/P -----------------------------(2)

Equation (2) represents the LM curve.

Aggregate demand curve represents the relationship between aggregate price level and national income.

We obtain the AD curve using IS and LM curve equation.

Solving equation (1) and (2)

IS: r=2.05-0.0008Y

LM: r= 0.001Y-0.05-266.4/P

2.05-0.0008Y= 0.001Y-0.05-266.4/P

0.0018Y=2.10+266.4/P

Y= 1166.6+ 148000/P --------------------------(3)

Equation (3) represents the AD curve.

Given,price in the short run is 120.

Thus, P= Ps

Substitute P=Ps= 120 in equation (3)

Y= 1166.6+ 148000/120

Y=2400

Substitute Y=2400 in IS or LM curve equation.

r= 2.05-0.0008(2400)

r= 0.13

In the short run, Y=2400, P= 120, r=0.13

Given, the full employment output Yf=2500

Y= Yf=2500

Substitute in equation (3)

2500= 1166.6+ 148000/P

P= 111

Substitute Yf= 2500 in IS or LM curve equation to get the value of r.

r= 2.05- 0.0008(2500)

r=0.05

Thus, in the long run, Y= 2500, P= 111, r= 0.05