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    GDP & Aggregate Demand - Multiplier

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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.

    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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    https://brainmass.com/economics/general-equilibrium/6180

    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.

    $2.49

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