GOVT. SPENDING AND TAXATION
Any govt. Spending will shift the investment demand curve and thus change the autonomous spending portion. But taxation will affect net disposable income and thus will absorb the effect of govt. spending to some extent. So govt. Spending and taxation will change income by the amount of govt. Spending only. This will result in a shift in IS curve as a result of changes in autonomous spending and a movement along the LM curve for change in income & interest rate.
Here, IS–LM equilibrium is at r=3 and Y=120, where total investment, I=20; given MPS=0.5. Now, an increase of govt. spending of $20 will shift the Investment demand curve by $20. Also it will move the IS-LM equilibrium from Y=120 & r=3% to Y=160 & r=3%. Here, the total effect on Y due to $20 increase in investment is $40. Now if govt. imposes $20 as tax, it will decrease net disposable income by $20 at each level, reducing S by $10 and I by $10. So, savings curve will shift from S1 to S2 and this $10 decrease in I makes the net change in I+G only $10 and makes rise in income only $20. Now the sum of savings and taxes, curve S2+T, shows the portion of income that is not spend for consumption.
Here I and S1 provides IS1 curve, the commodity market equilibrium without any govt. Spending and tax. Curve I+G and S2 leads to IS2 curve, commodity market equilibrium when govt. Spending is introduced. Finally, curve I+G and S2+T leads to IS3 curve, the equilibrium of commodity market when both govt. Spending and tax is introduced. Hence the new equilibrium position is indicated by the intersection of IS3 and LM curve, where Y=140 and r=3.50%. So adding G of $20 and an equal amount of T raises the equilibrium income level of Y by the size of the govt. spending.