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GDP & Aggregate Demand - Multiplier

Solve the following Problem:

C = 10 + 0.8(Yd),

Yd = Y - T,

T = 10,

I = 20, and

G = 30

Where C is the consumption, Yd is the disposable income, T is the tax, I is the investment and G is government spending.

1- Find mathematically and illustrate graphically the Aggregate Demand (AD) function.

2- Find the value of the multiplier.

3- Find mathematically and illustrate graphically the equilibrium level of income; i.e.
"Y=AD". 4- Derive mathematically and illustrate graphically the saving function.

5- Find mathematically and illustrate graphically the equilibrium level of income by using different way; i.e. "S+T=I+G".

6- How much will income in this economy increase if,

i- G is increased by
20 . ii- T is decreased by 20.

iii- G is increased by 20 and T is increased also by 20 in the same time.

* Derive and Calculate the multiplier of each case and illustrate graphically what will happen to the equilibrium income in each case.

7- Explain mathematically the idea of the multiplier.
II- Derive graphically IS curve.

III- Explain the following statement by using the tools of analysis that you have learned in the class:

"IS curve shows all the combinations of the interest rate and the income for which the goods market is in equilibrium"

Solution Preview

Please see the attached file.

Solve the following Problem:

C = 10 + 0.8(Yd),

Yd = Y - T,

T = 10,

I = 20, and

G = 30

Where C is the consumption, Yd is the disposable income, T is the tax, I is the investment and G is government spending.

No mention has been made of exports and imports. We therefore assume it is a closed economy.

1- Find mathematically and illustrate graphically the Aggregate Demand (AD) function.

AD=C+I+G Aggregate demand=AD
AD=10 + 0.8(Yd)+I+G AD curve
AD=10 + 0.8(Y - T)+I+G

Output=Income= Y

2- Find the value of the multiplier.

Multiplier= ΔY/ΔI

Multiplier= 1/ (1-0.8)= 5 Derivation of formula in 7 below

Value of the multiplier = 5
For unit increase in I , Y increases by 5 units

3- Find mathematically and illustrate graphically the equilibrium level of income; i.e.
"Y=AD".

AD=C+I+G T = 10
AD=10 + 0.8(Yd)+I+G I = 20
Since Y=AD G = 30
AD=Y=10 + 0.8(Y - T)+I+G
Y-0.8 Y=10 + 0.8( - T)+I+G
0.2 Y=10 - 0.8 T +I+G
Y=1/0.2* (10 - 0.8 T +I+G)
Y=5* (10 - 0.8 T +I+G)= 260

AD=Y
Aggregate demand=AD AD curve

Equilibrium Y Output=Income for equilibrium

4- Derive mathematically and illustrate graphically the saving function.

Y=C+I+G
S=Y-C-G
or S=I
But this is total ...

Solution Summary

The answers to a set of 7 problems on national income identity calculate and deriving aggregate demand (AD), multiplier, equilibrium level of income, IS curve etc.

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