# Math Help - Variables help asap

1. ## 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

2. If anyone could help i would be greatful

3. Originally Posted by tv4me
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*
$

$C_0= \frac{a}{1- b}+ \frac{b}{1-b}I*+ \frac{b}{1- b}G*
$

$C_1= \frac{a}{1- b}+ \frac{b}{1-b}I*+ \frac{b}{1- b}(G*+1)
$
$= \frac{a}{1- b}+ \frac{b}{1-b}I*+ \frac{b}{1- b}G*+\frac{b}{1- b}$

What is $C_1- C_0$?