# 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"

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#### 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.