\(\frac{M}{P} = L(i, Y)\)

Fiscal multiplier

Using Cramer's rule, we can show the impact of government expenditures on output:
\((\frac{dy}{d \bar G} ) = ( \frac{L_i}{(1 - c_y)L_i + (c_r + I_r)L_y}) > 0\)

New Keynesian Model