(Differential Equations: Three exogenous variable cases)Consider the macroeco- nomic model

(1)Y=C+I+G,(2)C=F(Y,T,r),(3)I=f(Y,r)

whereFandfare continuously differentiable functions withFY>0, FT<0, Fr<0,fY>0, fr<0 and FY+fY<1.

i) (6 points) Differentiate the system and expressdY,dCanddIin terms of dT,dGanddr.

ii) (6 points) What happens toY,CandIwhen onlyGdecreases? What happens toY,CandIwhen onlyTdecreases?

iii) (6 points) Suppose that the government decreasesGandTby the same proportion. What is the effect onY?

if you answer I would be appreciated