I should consider a following modification of IS-LM model:
IS curve is standard: Y = C(Y-T) + I(r) + G
In LM curve the demand for money depends now on after tax income: M/P = L(r, Y-T)
Price level is fixed in the short run
I need to solve for tax multiplier.
What I have done is that I took the full differential of two equations and got the following:
dY = C'(Y-T)dY - C'(Y - T) + I'dr + dG
1/pdM - M/p^2 * dP = Lr * dr + Ly * dy - Lt dT
Lr, Ly, Lt are partial derivatives
Next the book gives a hint to use Cramer's rule to solve for tax multiplier, but I am not sure how I can do it. Because to me it seems that I have 2 equations and 3 unknown variables