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Math Help - 2 equations with 2 unknows Y & C

  1. #1
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    2 equations with 2 unknows Y & C

    Hi this is part of a matrix question. I am ok with matrix but am having trouble with getting the equations -

    Here it is -

    Y = C + I + G
    C =C* + yYD C*>0: 0<y<1 (The D is supposed to be a small D at the bottom of the Y
    I=I*
    G=G*
    YD = Y -T (Again the D is supposed to be a small D down below the line
    T = tY 0<t<1

    Reduce the model to 2 equations in 2 unknowns Y and C.

    thanks again - Helen
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  2. #2
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    Re: 2 equations with 2 unknows Y & C

    \text{We have the following system of equations:}

    \text{(1) } Y = C + I + G

    \text{(2) } C = C^{*} + yY_{d}

    \text{(3) } I = I^{*}

    \text{(4) } G = G^{*}

    \text{(5) } Y_{d} = Y - T

    \text{(6) } T = tY


    \text{From (3), (4)}\rightarrow \text{(1), we have:}

    \text{(7) } Y = C + I^{*} + G^{*}


    \text{From (6)}\rightarrow \text{(5), we have:}

    \text{(8) } Y_{d} = (1 - t)Y


    \text{From (8)}\rightarrow \text{(2), we have:}

    \text{(9) } C = C^{*} + y(1 - t)Y


    \text{Hence, from (7) and (9), we have the final system of equations in the unknowns } Y \text{ and } C \text{:}

    Y = C + I^{*} + G^{*}

    C = C^{*} + y(1 - t)Y
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