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Math Help - Variables help asap

  1. #1
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    Variables help asap

    Hey

    I was wondering if someone could help me do this question as its quite urgent and i dont know where to begin

    A simple income model is given by

    Y = C + I* + G*
    C = a + bY (a > 0 and 0 < b < 1)

    for some constants a and b and where I*, G* are exogenous variables.

    Show that the relationship between equilibrium C and G* is linear.
    Deduce the change in C if G* increases by 1 unit.

    Thanks
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  2. #2
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    If anyone could help i would be greatful
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  3. #3
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    Quote Originally Posted by tv4me View Post
    Hey

    I was wondering if someone could help me do this question as its quite urgent and i dont know where to begin

    A simple income model is given by

    Y = C + I* + G*
    C = a + bY (a > 0 and 0 < b < 1)
    So C= a+ b(C+ I*+ G*)= a+ bC+ bI*+ bG*
    C- bC= a+ bI*+ bG*
    C(1- b)= a+ bI*+ bG*

    C= \frac{a}{1- b}+ \frac{b}{1-b}I*+ \frac{b}{1- b}G*



    for some constants a and b and where I*, G* are exogenous variables.

    Show that the relationship between equilibrium C and G* is linear.
    Deduce the change in C if G* increases by 1 unit.

    Thanks[/QUOTE]
    To show that the relationship between C and G* is linear, what is the definition of "linear"?

    C_0= \frac{a}{1- b}+ \frac{b}{1-b}I*+ \frac{b}{1- b}G*<br />

    C_0= \frac{a}{1- b}+ \frac{b}{1-b}I*+ \frac{b}{1- b}G*<br />
    C_1= \frac{a}{1- b}+ \frac{b}{1-b}I*+ \frac{b}{1- b}(G*+1)<br />
= \frac{a}{1- b}+ \frac{b}{1-b}I*+ \frac{b}{1- b}G*+\frac{b}{1- b}

    What is C_1- C_0?
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