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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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.