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# Variables help watch

1. Hey

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

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. (Original post by hughes123)
Hey

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

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
By substituting Y into the second equation you get:

C=a+b(C+I*+G*)

C (1-b) = a+bI* + bG*.

C= (a+bI*+bG*)/(1-b)

The relationship is clearly linear, and if G* increases by one unit, C will increase by b/(1-b). You can see that as you can split the fraction C into three fractions, and the only one dependent on G* is bG*/(1-b). Hence if G* increases by one unit, then C increases by b/(1-b).

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Updated: July 22, 2009
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