Inflation Simulator: Quantity Theory of Money & Purchasing Power Erosion

simulator intermediate ~10 min
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Inflation: 3% — money growth 5% minus real GDP growth 2%

With default parameters (5% money growth, 0% velocity change, 2% real GDP growth), inflation is approximately 3% per year. Over 10 years, the CPI rises from 100 to 134, and $100 loses about 26% of its purchasing power. This illustrates the Quantity Theory of Money: inflation equals money growth minus real output growth.

Formula

Quantity equation: M · V = P · Y
Inflation: π ≈ ΔM/M + ΔV/V - ΔY/Y
Fisher equation: i = r + π_e (nominal = real + expected inflation)
CPI growth: CPI(t) = CPI(0) · (1 + π)^t

The Quantity Theory of Money

The equation of exchange, MV = PY, is one of the oldest identities in economics. The money supply (M) times its velocity (V) — how fast money circulates — equals the price level (P) times real output (Y). In growth rate form, this becomes: inflation = money growth + velocity growth - real GDP growth. Milton Friedman's famous dictum, 'Inflation is always and everywhere a monetary phenomenon,' captures the essence: persistent inflation requires persistent money supply growth beyond what real economic growth absorbs.

Money Growth and Inflation

When central banks increase the money supply faster than the economy grows, the excess money chases the same amount of goods, driving prices up. The relationship is not instantaneous — Friedman estimated 'long and variable lags' of 12-24 months. But over decades, the correlation between money growth and inflation is remarkably tight across countries and eras. Hyperinflation episodes — Weimar Germany (1923), Zimbabwe (2008), Venezuela (2018) — all involved explosive money supply growth.

The Fisher Equation

Irving Fisher's 1930 insight connects inflation to interest rates: nominal rate = real rate + expected inflation. This is why savings accounts paying 2% actually lose money when inflation is 3% — the real return is -1%. It also explains central bank behavior: raising interest rates fights inflation by making borrowing more expensive, slowing money creation through the banking system.

Purchasing Power Erosion

The top chart shows the CPI rising over time while purchasing power declines — the two lines moving in opposite directions tell the same story from different perspectives. Even 'moderate' 3% inflation halves your purchasing power in 24 years. The shrinking $100 bill illustrates this viscerally: your cash is losing value every day. This is why financial literacy emphasizes investing over saving — your returns must exceed inflation to preserve real wealth.

Decomposing Inflation

The bottom section decomposes inflation into its components. Money growth pushes prices up. Velocity changes can amplify or dampen this effect. Real GDP growth absorbs some monetary expansion without inflation — a growing economy needs more money to facilitate more transactions. When money growth is 5% and real GDP grows at 2%, roughly 3% shows up as inflation. The policy implication: if you want price stability, money supply growth should approximately equal real GDP growth.

FAQ

What is the Quantity Theory of Money?

The Quantity Theory of Money, expressed as MV = PY (or the equation of exchange), states that the money supply (M) times its velocity of circulation (V) equals the price level (P) times real output (Y). In growth rate form: inflation ≈ money growth + velocity growth - real GDP growth. Milton Friedman famously summarized it: 'Inflation is always and everywhere a monetary phenomenon.'

What is the Fisher equation?

The Fisher equation, formulated by Irving Fisher in 1930, relates nominal interest rates, real interest rates, and expected inflation: nominal rate = real rate + expected inflation. This means lenders must charge higher interest rates during inflationary periods to maintain their real return, and it explains why central banks raise interest rates to combat inflation.

What is velocity of money?

Velocity measures how many times each dollar is spent per year. If velocity is 5, each dollar in the money supply changes hands 5 times annually. Velocity tends to be relatively stable in the short run but can change due to financial innovation, changes in payment technology, or shifts in saving behavior. During crises, velocity often drops sharply as people hoard cash.

How does inflation erode purchasing power?

If inflation is 3% per year, $100 today buys only $97 worth of goods next year in today's prices. Over 10 years, it buys only about $74 worth. Over 30 years, only about $41 worth. This 'silent tax' is why holding cash long-term destroys wealth, and why investment returns must be evaluated in real (inflation-adjusted) terms.

Sources

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