Resolve 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"