s ≡ Δ(MV) ≈ ΔM + ΔV
4.00%Macro Classroom Lab
MV-Fisher-Solow Interactive (5 min)
A quick clickthrough linking nominal spending growth, inflation, growth, expectations, and interest rates.
Step 1: MV sets nominal spending growth (s)
AD is nominal spending growth (s): in growth form, s ≡ Δ(MV) ≈ ΔM + ΔV.
Low+4.00High
Low+0.00High
Identity: s = π + g
4.00% = — + —AD is nominal spending growth (s).
Step 2: Solow speed limit splits s into g and π
Set potential (Solow) growth (g*), then apply this year's spending growth.
Slow3.00%Fast
Nominal spending growth (s)
4.00%Real GDP growth (g)
—Inflation rate (π)
—Long run: growth returns to g*; inflation absorbs the remainder.
Step 3: Expectations and Fisher equation
Update expected inflation (π^e), then read the nominal rate from Fisher.
Actual inflation (π)
—Expected inflation (π^e)
2.00%Nominal interest rate (i)
4.00%i = r* + π^e = 2.00% + 2.00% = 4.00%
Teacher controls (optional)
Low2.00%High
Higher expected inflation raises nominal interest rates.
Step 4: Mini-challenge
Target: keep inflation near 2% and growth near g*.
Low+4.00High
Attempt spending growth (s)
4.00%Ending growth (g)
—Ending inflation (π)
—Updated expected inflation (π^e)
—Nominal interest (i)
—Score |π-2| + |g-g*|
—Set ΔM, optionally draw a ΔV shock, then run an attempt.
Teacher notes
- Equation of exchange (growth form): s ≡ Δ(MV) ≈ ΔM + ΔV. Interpretation: AD is nominal spending growth (s).
- Nominal spending identity: s = π + g. Interpretation: inflation plus real growth must add up to spending growth.
- Solow potential growth: in the long run, g → g*. Interpretation: growth returns to the economy's speed limit.
- Fisher equation: i = r* + π^e. Interpretation: nominal rates rise when expected inflation rises.