Q. Simultaneous determination of Y in the IS-LM model?

Simultaneous determination of Y and R in the IS-LM model

 By combining IS curve and LM curve, we can graphically explain what interest rate and what level of GDP which will satisfy both equations: Y_D(Y, R) = Y and M_D(Y, R) = M_S. For all points on IS-curve, we have equilibrium in the goods market and for all points on LM-curve, we have equilibrium in the money market. There is just one point where both markets are in equilibrium, Y* and R*.

Figure: IS-LM model

According to IS-LM model, economy will move to Y* and R*. Argument is as below. 

1. Imagine that R > R*. It's the not possible to be on both IS and LM-curve. 

2. Assume that we are on IS-curve but to the left of LM curve. The interest rate is higher than equilibrium interest rate and R will fall. 

3. Suppose that we are on LM-curve but to right of the IS-curve. Y is then higher than equilibrium value and Y will fall. We will then move away from LM-curve and interest rates will fall. 

4. If we are neither on IS- nor on LM-curve then Y will fall as long as we are to right of the IS-curve and R will fall as long as we are to left of the LM-curve.