Consider the economy of Hicksonia: The consumption function is given by C = 300
ID: 1126898 • Letter: C
Question
Consider the economy of Hicksonia:
The consumption function is given by C = 300 + 0 . 70( Y T )
The investment function is I = 300 30 r
Money demand is given by ( M/P )^d = Y 100 r.
The money supply M is 1200 and the price level P is 3. Government expenditure is 100 and taxes are 150.
a) Find the equilibrium interest rate r and the equilibrium level of income Y.
b) Suppose that government purchases are raised from 100 to 150. How much does the IS curve shift?
c) Suppose instead that the money supply is raised from 1200 to 1500. How much does the LM curve shift?
Explanation / Answer
Consider the economy of Hicksonia:
The consumption function is given by C = 300 + 0 . 70( Y T )
The investment function is I = 300 30 r
Money demand is given by ( M/P )^d = Y 100 r.
The money supply M is 1200 and the price level P is 3. Government expenditure is 100 and taxes are 150.
a) Find the equilibrium interest rate r and the equilibrium level of income Y.
Find equation of IS and LM and keep them equal to each other
Goods market
C + I + G = Y
300 + 0.70(Y 150) + 300 30r + 100 = Y
300 + 0.7Y – 105 + 400 – 30r = Y
595 – 30r = 0.3Y
Y = 1983.33 – 100r
Money market
Y – 100r = 1200/3
Y = 400 + 100r
Solve these equations to get i* = 7.92 and Y = 1192
b) Suppose that government purchases are raised from 100 to 150. How much does the IS curve shift?
New IS equation is
300 + 0.70(Y 150) + 300 30r + 150 = Y
300 + 0.7Y – 105 + 450 – 30r = Y
645 – 30r = 0.3Y
Y = 2150 – 100r
See that autonomous part is $166.7 more. This is the required shift in IS. This can be computed from MPC also where multiplier is 1/1 – MPC = 1/1 – 0.7 = 3.33. Hence an increase in G by 50 raises GDP by 50*3.333 = 166.66
c) Suppose instead that the money supply is raised from 1200 to 1500. How much does the LM curve shift?
New LM equation is
Y – 100r = 1500/3
Y = 500 + 100r
LM shifts by 100.