Consider an economy where GDP is given by

Z = (Y -T) - G - I(r),

C(Y -T)-C₀ -C₁ (Y -T)

I(r) = I₀ I₁ r

where Z is planned expenditure,

Y is GDP

T is taxes,

G is public consumption

I are investments

r is interest

C₀, C₁, I₀, I₁ > 0 are all parameter and C₁ < 1. T and G are exogenous variables. In this part of the task is r exogenous too.

How can I discharge the IS curve, i.e. discharge Y as a function of r, G, T ?