IS-LM

INTERACTIVE IS-LM MODEL (closed economy in the short run)

\(\overline{\mathbf{M}}\) (money supply) \(\overline{\mathbf{P}}\) (price level) \(\mathbf{s_{LY}}\) (sensitivity of demand to Y)

\(\mathbf{s_{Lr}}\) (sens. of demand to real interest rate) \(\overline{\mathbf{aD}}\) (autonomous demand)

\(\mathbf{mpc}\) (marginal propensity to consume) \(\overline{\mathbf{T}}\) (taxes)

\(\overline{\mathbf{aC}}\) (aut. consumption) \(\overline{\mathbf{aI}}\) (aut. investment)

\(\overline{\mathbf{G}}\) (government expenditure) \(\mathbf{s_{Ir}}\) (sens. of investment to real int. rate)

               Actual Expenditure \(= Y\)

               Planned Expenditure \(\,= \,mpc \, \cdot \, (\,Y\, -\, \overline{T}\,) \,+\, \overline{aC}\, -\,s_{Ir}\,*\,r \,+ \,\overline{aI}\, +\, \overline{G}\)

               Real Money Supply \(= \frac{{\overline{M}}}{{\overline{P}}}\)                                   Real Money Demand \(\,= \,s_{LY}\, \cdot\, Y\, - \,s_{Lr} \,\cdot\, r\, +\, \overline{aD}\)

                IS: \(\,r\, =\, \frac{{-Y \,+\, \text{mpc}\, \cdot\, (\,Y\, - \,\overline{T}\,)\, +\, \overline{aC}\, + \,\overline{aI}\, + \,\overline{G}}}{{s_{Ir}}}\)           LM: \(\, r \,= \,\frac{{s_{LY}\, \cdot \,Y\, +\, \overline{aD}\, -\, \frac{\overline{M}\,}{\overline{P}}}}{{s_{Lr}}} \)