Answer to Question #252545 in Macroeconomics for Vickie

Question

Cd=360-200r+0.1Y
I'd=120-400r
G=120 find an equation for desired national saving ,Sd in term of output Y and the reason . what value of the real interest rate clear the goods market Y=550 and when Y=650 ? Use the goods market equilibrium condition to derive the IS curve graph

2) Discuss the reason Why the aggregate demand curve will thus slope downwards

3) Cd=200+0.5Y-500r
I'd= 200-500r
L=0.5Y-250(r+à ƒ ƒ ƒ  €)
à ƒ ƒ ƒ  €=0
G=150
M=4900
Y=100
Derive the equilibrium levels of the real interest rates r, desired consumption Cp,desired investment Io ,and the price level p, L is money demand equation and M is money supply equation

Answer 1

Goods market equilibrium is achieved where the aggregate demand in the goods market is equal to the aggregate production/Income in the economy .

For Closed Economy :

C + I + G = Y 

Here ,

Cd=360-200r+0.1Y (Consumption demand )

I'd=120-400r  (Investment demand )

G = 120 (Government Expenditure )

Savings = s0 + s1 (Y ) ,

Where s0 = Autonomous savings and s1 = Marginal Propensity to save 

MPS = 1 - MPC (Marginal Propensity to Consume )

MPC = dC/dY = 0.1

MPS = 1 - 0.1 = 0.9 

s1 = 0.9 

s0 = - 360 , because when income is zero consumer still consumes this much so the autonomous saving are negative .

Therefore ,

S = -360 + 0.9(Y)

 

Now ,

Putting the values into the identity of Good Market Equilibrium (C + I + G = Y ) :

360-200r+0.1Y + 120-400r + 120 = Y 

600 - 600r = 0.9Y 

Now , at  Y = 550 ,

600 - 600r = 0.9*550 

r = 105/600 = 0.175 = 17.5%  (Market Clearing Interest rates )

When Y = 650 :

600 - 600r = 0.9*650 

r = 15/600 = 0.025 = 2.5 % (Market Clearing Interest rates )