Consider the following numerical version of the IS-LM model in a closed economy:
C=400+0.5Yd; I=700-4000r+0.1Y; G=200; TP=200; Yd=Y-TP
RLMD=0.5Y-7500r; RLMS =500; X=M
A) Find the equations for the IS curve and LM curve.
C) If government spending increased to 700, solve again for the equilibrium Y, r, C, and I.
A) IS curve:
Y = C + I + G + (X - M)
Y = (400 + 0.5Yd) + (700 - 4000r + 0.1Y) + 200 + 0
Y = 400 + 0.5(Y - TP) + 700 - 4000r + 0.1Y + 200
Y = 400 + 0.5Y - 0.5(-200) + 700 -4000r + 0.1Y + 200
Y = 0.5Y + 0.1Y + 400 - 100 + 700 + 200 - 4000r
Y - 0.5Y - 0.1Y = 1200 - 4000r
0.4Y = 1200 - 4000r
4000r = 1200 - 0.4Y
Solving for r gives us the equation of the IS curve:
r = 0.3 - ...
This solution shows how to find the equations of the IS and LM curves and how to use them to find equilibrium output (Y), interest rate (r), consumption (C), and investment (I). Then the equilibrium is recalculated if government spending (Q) increases.