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aggregate demand and supply curve

Endogenous Variables
Income Y
Consumption C
Investment I
Net Exports X
Interest rates R
Government Purchases G
Money Supply M

Predetermined Variable
PriceLevel P

Algebra Name Numerical Example

Y=C+I+G+X Income Identity
C= a+b(1- t) Y Consumption function C = 220 + 0.63Y
I= E - dR Investment function I= 1,000 - 2000R
X =g - mY - Nr Net export function X= 525 - 0.1Y - 500R
M = (Ky - Hr) P Money demand M =(0.1583Y - 1,000R)P

Q1
Set the price level equal 1
Use the algebraic form of the aggregate demand curve to find the level of GDP that occurs when the money supply is 900billion and government spending is 1.2 billion
Use the IS curve and the LM curve to find the interest rate that occurs in this situation. Explain why you get the same answer in each case
Use the consumption function to find the level of consumption, the investment function to find the level of investment, and the net export function to find the level of investment, and the net export function to find the level of exports for this situation.
Show that the sum of your answers for consumption, investment, government spending, and net exports equals GDP
Repeat all the previous calculations if government spending increased to 1300 billion . How much investment is crowded out as a result of the increase in government spending? How much are net exports crowded out

2
For savings and the budget deficits , the problem pertains to the numerical example in the box on the macro relationships and uses the answers to problem 1

Set the government spending at 1.2 billion and the money supply at 900 billion. Calculate the government saving (the budget surplus) Calculate the level of private saving, and show that private saving plus government saving plus rest of world saving equals investment.
Now repeat the calculations for a level of government spending equal to 1.3 billion. Does private saving + government saving plus rest of the world having still equal investment? How does each element in the identity change?
Explain why private saving increases as a result of government spending. In light of these calculations , evaluate the statement " Government budget deficits absorb private saving that would otherwise be used for investment purposes
3
The following relationships describe the imaginary economy of Nineland

Y = C+I (Income identity)
C = 90+ 0.9Y (Consumption)
I= 900 - 900R (Investment)
M=(0.9Y - 900R)P(Money demand)
Y is output, C is consumption, I is investment, R is the interest rate, M is the money supply , and P is the price level . There are no taxes, government spending, or foreign trade in Nineland
The Year is 1999 in Nineland. The price level is 1. The money supply is 900 in 1999
A) Sketch the IS curve and the LM curve for the year 1999 on a diagram and show the point where the interest rate and output are determined. Show what happens in diagram if the money supply is increased above 900 in 1999
B) Sketch the aggregate demand curve. Show what happens in the diagram if the money supply is decreased below 900 in 1999
C) Derive an algebraic expression for the aggregate demand curve in which P is on the left -hand side and Y is on the right -hand side.
D) What are the values of output and the interest rate in 1999 when the money supply is 900?

Solution Preview

We have,
Y=C+I+G+X
C=220+0.63Y
I=1,000-2000R
X=525-0.1Y-500R
M=(0.1583Y-1,000R)P
P=1
Putting the values in the equation for Y, we get:
Y=220+0.63Y+1,000-2,000R+1,200+525-0.1Y-500R
Or,
Y=2,945+0.53Y-2,500R
Or,
0.47Y=2,945-2,500R
Y=(2,945-2,500R)/0.47
Also,
M=900=0.1583Y-1000R
Or,
0.1583Y-1000R=900-----(I)
Putting the value of Y in Equation I, we get
0.1583*((2,945-2,500R)/0.47)-1000R=900
Or,
0.1583/0.47*2945-0.1583/0.47*2,500R-1000R=900
Or,
992-842.02R-1000R=900
Or,
1842.02R=92
Or,
R=5%
Putting the value of R in Y we get:
Y=(2,945-2,500*6.8%)/0.47=6,000

We have,
LM equation as:
M=900=(0.1583Y-1,000R)*1
Or,
R=1/1,000*(0.1583Y-900)
Putting the value of Y we get,
R=1/1000*(0.1583*6,000-900)=5%
Therefore,
IS=LM=5%

Using the equations and the value of Y and R above we ...

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