Chud Econ 304 Hw5
ECON 304 HOMEWORK # 5 due: June 14 in class 1. Numerical exercise # 6, Chapter 7, page 273, Abel & Bernanke a. We know that ηy = 2/3 and ηi = −0.1.
∆Y /Y = 0.045 = 4.5% ∆i/i = 0 πe = 0
Hence, if the central bank wants zero inflation over the next year, it should choose a growth rate of nominal money supply such that: ∆M ∆Y = ηy = 2/3 ∗ 0.045 = 0.03 = 3% M Y b. Velocity is defined as: V = Nominal GDP PY = Nominal Money Stock M
Hence: ∆P ∆Y ∆M ∆V = + − V P Y M If the central bank follows the policy that achieves zero inflation, we have: ∆P ∆Y ∆M ∆V = + − = 0 + 0.045 − 0.03 = 0.015 = 1.5% V P Y M Velocity increases by 1.5% 2. Suppose that an economy has a constant nominal money supply (M ), a constant level of real output, (Y = 500), and a constant real interest rate (r = 0.05). Suppose that the income elasticity of money demand is ηy = 0.6 and the interest elasticity of demand ηi = −0.2 a. Suppose that Y increases to 525, r remains constant at 0.05 and there is no change in the expected rate of inflation. What is the percentage change in the equilibrium price level? 1
We know that from the equilibrium condition for the asset market: π= We have that: ∆M/M = 0 ∆r/r = 0 ∆π e /π e = 0 π = ∆P/P = −ηy 525 − 500 ∆Y = −.6 ∗ = −0.03 = −3% Y 500 ∆M ∆Y ∆r + π e − ηy − ηi M Y r + πe
b. Suppose that r increases to 0.055 and Y remains at 500. Assuming that π e = 0, what is the percentage change in the equilibrium price level? Using the same formula as in part (a): ∆M/M = 0 ∆Y /Y = 0 ∆π e /π e = 0 π = ∆P/P = −ηi 0.055 − 0.05 ∆r + π e = −(−0.2) ∗ = 0.02 = 2% r + πe 0.05
3. Numerical exercise # 3, Chapter 6, page 242, Abel & Bernanke
Year 1 a. 2 3 4 This production function CAN y=
K
N
Y = K 0.3 N 0.7
K/N 0.2 0.25 0.2 0.25
Y /N 0.617 0.659 0.617 0.659
200 1,000 617.03 250 1,000 659.75 250 1,250 771.29 300 1,200 791.70 be written in per-worker terms:
Y K 0.3 N 0.7 = = K 0.3 N 0.7−1 = K 0.3 N −0.3 = N N
K N
0.3
= k 0.3
2
Year b. 1
∆Y /Y = 0.045 = 4.5% ∆i/i = 0 πe = 0
Hence, if the central bank wants zero inflation over the next year, it should choose a growth rate of nominal money supply such that: ∆M ∆Y = ηy = 2/3 ∗ 0.045 = 0.03 = 3% M Y b. Velocity is defined as: V = Nominal GDP PY = Nominal Money Stock M
Hence: ∆P ∆Y ∆M ∆V = + − V P Y M If the central bank follows the policy that achieves zero inflation, we have: ∆P ∆Y ∆M ∆V = + − = 0 + 0.045 − 0.03 = 0.015 = 1.5% V P Y M Velocity increases by 1.5% 2. Suppose that an economy has a constant nominal money supply (M ), a constant level of real output, (Y = 500), and a constant real interest rate (r = 0.05). Suppose that the income elasticity of money demand is ηy = 0.6 and the interest elasticity of demand ηi = −0.2 a. Suppose that Y increases to 525, r remains constant at 0.05 and there is no change in the expected rate of inflation. What is the percentage change in the equilibrium price level? 1
We know that from the equilibrium condition for the asset market: π= We have that: ∆M/M = 0 ∆r/r = 0 ∆π e /π e = 0 π = ∆P/P = −ηy 525 − 500 ∆Y = −.6 ∗ = −0.03 = −3% Y 500 ∆M ∆Y ∆r + π e − ηy − ηi M Y r + πe
b. Suppose that r increases to 0.055 and Y remains at 500. Assuming that π e = 0, what is the percentage change in the equilibrium price level? Using the same formula as in part (a): ∆M/M = 0 ∆Y /Y = 0 ∆π e /π e = 0 π = ∆P/P = −ηi 0.055 − 0.05 ∆r + π e = −(−0.2) ∗ = 0.02 = 2% r + πe 0.05
3. Numerical exercise # 3, Chapter 6, page 242, Abel & Bernanke
Year 1 a. 2 3 4 This production function CAN y=
K
N
Y = K 0.3 N 0.7
K/N 0.2 0.25 0.2 0.25
Y /N 0.617 0.659 0.617 0.659
200 1,000 617.03 250 1,000 659.75 250 1,250 771.29 300 1,200 791.70 be written in per-worker terms:
Y K 0.3 N 0.7 = = K 0.3 N 0.7−1 = K 0.3 N −0.3 = N N
K N
0.3
= k 0.3
2
Year b. 1