1 We have an IS-LM Model:
C = 200 + 0.25(Y-T)
I = 150 + 0.25Y – 1000i
G = 250
T = 200
Derive IS curve both mathematically and graphically
Determine the slope of IS curve (di/dY)
Identify the shift variables of the IS curve
Derive aggregate demand curve both graphically and mathematically
Find equilibrium level of output and the interest rate
Derive the following multipliers
Determine the impact of simultaneous increase in government expenditure and money supply (such that ) on equilibrium output and the interest rate.
IS curve is:
Y = C + I + G = 200 + 0.25(Y - 200) + 150 + 0.25Y – 1000i + 250,
0.5Y = 550 - 1000i,
Y = 1100 - 2000i or i = 0.55 - 0.001Y.
The slope is -0.001.
The shift variables of the IS curve are: C, I, G, T, i.
AD = Y = 550 - 1000i.
We need to know additional data about the LM curve to find equilibrium level of output and the interest rate.
The expenditure multiplier is:
A simultaneous increase in government expenditure and money supply will increase AD, as a result the equilibrium output will increase and the interest rate will decrease.