Consider an IS-LM-AS model with equations
Y = C(Y ? tY) + I(r ?? ) +G
L(Y, r)
P
M =
P = P
where the nominal interest rate, r, the real GDP, Y, and the price level, P are endogenous; government spending on goods and services, G, tax rate, t, the nominal money supply, M, and the anticipated rate of inflation, are exogenous; and,
0dL/dY>0,
dL/dr<0,
dI/d(r-?)<0

1) Derive an expression for the slope of the IS curve : dr/dY lIS, and show what its sign is.
2) Derive an expression for the comparative static result dY/dt (the effect of the change in the tax rate on the equilibrium output), and show what its sign is.
3) Derive an expression for the comparative static result dY/d? (the effect of the change in the anticipated inflation rate on the equilibrium output), and show what its sign is. Briefly explain the intuition for its sign.