Using Aggregate Supply and Demand Models

P = 1.41 + .0001Y

where P = the average price level and Y = GNP

An investment function in which I = 400 - 40P

Government expenditures, G = 300

Lump sum taxes, T = 100

*Hint: you want an equation in which Y is a function of P.*

*
Ans: To find the aggregate demand curve solve for equilibrium Y (which will depend on the price level as follows:
Y = C + I + G
Y = 100 + .9(Y - 100) - 20P + 400 - 40P + 300
Y = 710 + .9Y - 60P
.1Y = 710 - 60P
Y = 7,100 - 600P, which is the equation for the aggregate demand curve.*

Y = 7100 - 600(1.41 + .0001Y)

Y = 7100 - 846 - .06Y

1.06Y = 6,254

Y = 6,254/1.06

Y = 5,900

To find the equilibrium price level, substitute 5,900 into the AS curve equation:

*
P = 1.41 + .0001(5,900)
P = 2.0*

C = 100 + .9(5,900 - 100) - 20(2.0)

C = 5,280

From the investment function:

I = 400 - 40(2.0)

I = 320

To check:

*
5,280 + 320 + 300 = 5,900*

Y = C + I + G

Y = 100 + .9(Y - 100) - 20P + 400 - 40P + 400

Y = 810 + .9Y - 60P

.1Y = 810 - 60P

Y = 8,100 - 600P

Because the intercept 8,100 is larger than it was before (7,100) we know the AD curve has shifted to the right by 1000.

To find the new level of GNP, we once again combine the aggregate demand and supply curves:

Y = 8,100 - 600(1.41 + .0001Y)

Y = 8,100 - 846 - .06Y

1.06Y = 72,254

Y = 7,254/1.06

Y = 6843.40

So, we see that the equilibrium level of GNP has risen from 5,900 to 6843.40

To find the new price level, substitute 6,843 into the AS curve:

P = 1.41 + .0001(6,843.40)

P = 2.094

So, we see that the government stimulus has raised the price level.

To solve for the components of GNP:

From the consumption function:

C = 100 + .9(6,843.40 - 100) - 20(2.094)

C = 6,127.18

So, we see consumption spending has increased from 5,280 to 6127.18.

From the investment function:

I = 400 - 40(2.094)

I = 316.24

So, we see investment expenditure has decreased from 320 to 316.24.

*
Therefore, we can see that yes, there has been a "crowding out" of investment. However, whereas the consumption function suggests that a rise in the price level will reduce consumer spending it has, in fact, increased. The negative influence of the rise in prices has been offset by the positive effect of the rise in income brought about by the increase in government expenditures.*

P = 1 + .00125Y

I = 200 - 30P

G = 200

T = 50

*Ans: To derive the aggregate demand function, we proceed as before:*

*
Y = C + I + G
Y = 50 + .8Yd - 10P + 200 - 30P + 200
Y = 50 + .8(Y - 50) - 10P + 200 - 30P + 200
Y = 410 + .8Y - 40P
.2Y = 410 - 40P
Y = 2,050 - 200P
which gives us the equation for the AD function.*

AD curve = Y = 2,050

AS curve = P = 1 + .00125Y,

then

subsituting AS into AD:

Y = 2,050 - 200(1 + .00125Y)

Y = 1,850 - .25Y

1.25Y = 1,850

Y = 1,480

which gives us the equilibrium level of GNP, and :

From the AS curve:

P = 1 + .00125(1,480)

P = 2.85 (br)
which gives us the equilibrium level of prices.

C = 1165.5

I = 200 - 30(2.85)

I = 114.5

So: 1116.5 + 114.5 + 200 = 1,480 = Y, which checks

Y = 50 + .8(Y - 50) - 10P + 200 - 30P + 200

becomes:

Y = 50 + .8(Y - 100) - 10P + 200 - 30P + 200

Y = 370 + .8Y - 40P
.2Y = 370 - 40P
Y = 1,850 - 200P
which is the new AD curve. Because the intercept has dropped we know the AD curve has been shifted to the left.

To find the effects on Y, we substitute as before and solve for Y:

Y = 1,850 - 200(1 + .00125Y)

Y = 1,650 - .25Y

1.25Y = 1,650

Y = 1,320

and we see that Y has dropped (as expected) due to an increase in taxes.

To find the effects on C and I we must find the effects on P, so we substitute the new Y into the AS curve:

P = 1 + .00125(1,320)_

P = 2.65(br)
which we see has dropped.

From the consumption function:

C = 50 + .8(1,320 -100) - 10(2.65)

C = 999.5

so we see C has dropped.

From the investment function:

I = 200 - 30(2.65)

I = 120.5

and we see I has risen.

*
The drop in consumption is from 1165.5 to 999.5, or 166.0. This drop is greater than the tax increase of 50, because the tax increase causes GNP and income to decrease which further drops consumption.*