Suppose in a small open economy, the money demand is given as: (MP)^d = Y 2000 ·
ID: 1116912 • Letter: S
Question
Suppose in a small open economy, the money demand is given as:
(MP)^d = Y 2000 ·r
The investment demand, consumption, and net export demand function are given as:
I(r) = 100 1000 × r
C = 0.5 × (YT)
NX(e) = 100 10 × e
Both of government spending, G, and lump-sum tax, T, are equal to 100, the real money supply (MP)^s is 100 and the world level real interest rate r*= 0.05.
1. Derive the IS curve.
2. Derive the LM curve.
3. Calculate the output and exchange rate in equilibrium.
4. If G increase to 200, calculate the output and exchange rate in short-run equilibrium?
5. If (MP)^s decrease to 50, calculate the output and exchange rate in short-run equilibrium.
Explanation / Answer
(1)
In goods market equilibrium, Y = C + I + G + NX
Y = 0.5 x (Y - 100) + 100 - 1,000r + 100 + 100 - 10e
Y = 0.5Y - 50 + 300 - (1,000 x 0.05) - 10e
(1 - 0.5)Y = 250 - 50 - 10e
0.5Y = 200 - 10e
Y = 400 - 20e [IS equation]
(2)
In money market equilibrium,
Y - 2,000r = 100
Y = 100 + 2,000r
Y = 100 + (2,000 x 0.05) = 100 + 100
Y = 200 [LM Equation]
(3)
In general equilibrium, IS equals LM:
400 - 20e = 200
20e = 200
e = 10
Y = 200
(4) When G rises to 200, Increase in G = 200 - 100 = 100
From IS equation,
0.5Y = 200 - 10e + 100
0.5Y = 300 - 10e
Y = 600 - 20e [New IS equation]
Equating new IS equation with LM,
600 - 20e = 200
20e = 400
e = 20
Y = 200
(5)
New LM equation is:
Y - 2,000r = 50
Y - (2,000 x 0.05) = 50
Y - 100 = 50
Y = 150
Equating with (Original) IS curve,
400 - 20e = 150
20e = 250
e = 12.5
Y = 150