MV = PY on an AD/AS diagram with vertical LRAS; the classical and monetarist case that money growth causes inflation, the Keynesian objections about velocity and output, the 2020–22 and 1970s evidence; benign and malign deflation and debt deflation.
Between February 2020 and February 2021 the annual growth of UK broad money rose from about 4% to a peak of around 15%, as the Bank of England bought £450bn of government bonds and the Treasury borrowed to pay the wages of furloughed workers. Deposits piled up because there was little to spend them on. From early 2021 the economy reopened, and consumer price inflation rose from under 1% to 11.1% in October 2022, the highest for forty years.
Monetarist economists had predicted it: a surge in money followed, with a lag of 18 to 27 months, by a surge in prices, as in 1971–75 when broad money grew 25% a year and inflation peaked near 25%. The Bank and most forecasters pointed instead to Russia’s invasion of Ukraine, gas prices and post-pandemic shortages, noting that money grew faster still after 2009 without inflation. Both sides can quote the same equation.
What is the quantity theory, when does it hold, and what happens when prices fall instead of rise?
Source: Bank of England, M4x statistics; ONS, consumer price inflation, October 2022; Institute of Economic Affairs and Janus Henderson commentaries on broad money, 2021–23.
The quantity theory of money starts from the Fisher equation: M × V = P × Y. M is the money supply, V the velocity of circulation (how many times each pound is spent in a year), P the price level and Y real output, so PY is nominal GDP. As an identity it is always true: total spending equals total sales. It becomes a theory of inflation with two assumptions: that V is stable, set by payment habits, and that Y is fixed at full employment in the long run. Then any growth in M must show up in P: inflation ≈ money growth + velocity growth − real output growth. Milton Friedman: “inflation is always and everywhere a monetary phenomenon.”
Keynesian objections. V is not stable: it falls when people hoard money, as in 2009–19 when QE tripled the monetary base and inflation stayed at 2%, and in 2020 when shops were shut. Y is not fixed: with spare capacity, more spending raises output before prices. And causation can run the other way: banks create money when borrowers demand loans, so money growth may follow a boom rather than lead it. Monetarists reply that the lags are long and variable but the relationship holds over decades and across countries, from the 1970s to Zimbabwe and Venezuela.
Deflation is a sustained fall in the general price level (not disinflation, a fall in the inflation rate). Benign deflation comes from supply: productivity and cheap imports lower prices while output rises. Malign deflation comes from collapsing demand: consumers delay purchases expecting lower prices, real debt burdens rise (debt deflation), real interest rates stay high even at zero nominal rates, and real wages rise so firms shed labour. Japan from the 1990s is the standing example; it is why the UK’s 2% target is symmetric and why central banks fear falling prices more than slightly rising ones.
In February 2021 the UK’s broad money supply was growing at about 15% a year, its fastest since the 1980s. In October 2022 inflation hit 11.1%.
During 2020 the Bank of England bought £450bn of gilts and the government borrowed to pay furloughed wages; bank deposits swelled while shops were shut. In 2010–19 money had grown about 4% a year and inflation averaged 2%.
Was the money growth the cause of the inflation?
MV = PY. If money grows faster than output and velocity does not fall, prices must rise. In 2020 velocity collapsed as people could not spend; when it recovered, the extra money met shortages and an energy shock. How much blame belongs to money is this lesson’s question.
The quantity equation on a diagram. Aggregate demand is every combination of P and Y with PY = MV: with M = 1,000 and V = 2, nominal spending is £2,000bn, so AD1 is the curve P = 2,000 ÷ Y. LRAS is vertical at full employment, Y = 400. The economy settles at E1 with P = 5. In the classical world, Y is set by capacity and V by habit; M decides P.
Check: The money supply is £1,000bn, velocity is 2 and real output is £400bn. The price level implied by MV = PY is:
P = MV ÷ Y = 2,000 ÷ 400 = 5. On the diagram, AD1 passes through (400, 5).
The classical result. Money grows 20%; nominal spending grows 20%; AD shifts to AD2. Output cannot rise above 400, so the price level rises from 5 to 6: exactly 20%. Money is neutral: it changes prices, not real things. In growth terms, inflation = money growth + velocity growth − output growth: 20 + 0 − 0 = 20%. With output growing 2%, 7% money growth gives 5% inflation.
Check: The money supply rises 20% to £1,200bn, velocity and full-employment output unchanged. In the long run the price level:
2,400 ÷ 400 = 6. With Y fixed and V stable, prices rise in proportion to money: the neutrality of money.
The Keynesian short run. With spare capacity or wages fixed by contracts, SRAS slopes up, and AD2 first meets it at Y = 436, P = 5.5: output +9%, prices +10%. If the economy had deep slack, almost all the effect would be output. Only as wages and expectations adjust does the economy slide up to E2. Monetarists accept this: money is not neutral in the short run, which is why the lags are long and variable.
Teacher tip: Ask students to place 2020 on the diagram. Money rose sharply but velocity collapsed, so MV barely moved: AD did not shift. In 2021–22 velocity recovered while supply was constrained: AD shifted right into a steep SRAS, and prices did most of the adjusting. The equation organises both halves of the story.
Check: In the short run, with an upward-sloping SRAS, the same 20% rise in money supply:
With spare capacity or sticky wages, extra spending draws out output as well as prices. The split depends on the slope of SRAS.
The velocity problem. In 2009–19 the monetary base tripled but broad money grew about 4% a year and prices 2%: velocity fell, and MV tracked nominal GDP. In 2020–21 broad money itself jumped 15%, V collapsed, then recovered. The equation held throughout; what failed was the assumption that V is stable. That is the Keynesian point, and it is why central banks target inflation and interest rates, not money, since 1990.
Check: Between 2009 and 2019 the Bank of England created £445bn of reserves through QE and broad money grew about 4% a year, yet inflation averaged 2%. The quantity theory’s defenders explain this by:
Base money is not broad money: the credit multiplier collapsed after 2008, so reserves piled up while deposits grew slowly. V fell and MV stayed in line with nominal GDP.
Deflation is the equation run backwards: if MV falls while Y holds, P falls. Benign deflation from productivity, as in the late nineteenth century, comes with rising output. Malign deflation from collapsing demand brings debt deflation: debts fixed in pounds grow in real terms, real interest rates stay positive at the zero floor, and buyers wait for lower prices. Japan after 1990 is the warning; a 2% target keeps a buffer above zero.
Check: Prices fall 5% in a year while nominal debts and nominal interest rates are unchanged. The main danger is:
Falling prices raise the real burden of fixed nominal debts and the real cost of borrowing; households postpone purchases; firms cut jobs as real wages rise. Japan spent two decades here.
E2 is placed at output 480 with the price level unchanged. In the long run output cannot exceed full-employment output of 400: LRAS is vertical, so the extra spending raises the price level to 6. Output up 20% is the short-run Keynesian hope, not the long-run result.
Evaluate the view that inflation is always and everywhere a monetary phenomenon.
Friedman’s claim rests on the quantity equation MV = PY. If the velocity of circulation is stable and real output is fixed by capacity in the long run, any growth of the money supply beyond the growth of output must raise the price level: on an AD/AS diagram with a vertical long-run aggregate supply, a 20% rise in M shifts aggregate demand out and raises P by 20% with output unchanged. Inflation then equals money growth plus velocity growth minus real growth, and the only sustained cause of rising prices is money growing faster than the economy.
The evidence for the view is strong at the extremes and over long periods. Every hyperinflation has been a monetary expansion; UK broad money grew about 25% a year in 1971–73 and inflation peaked near 25% in 1975; broad money growth rose from 4% to about 15% in the year to February 2021 and consumer price inflation reached 11.1% in October 2022, roughly on the two-year lag monetarists expect. Across countries and decades, no economy has had persistent high inflation without fast money growth.
**However,** the two assumptions fail over the horizons that matter for policy. Velocity is not stable: between 2009 and 2019 the Bank of England created £445bn of reserves and broad money still grew only about 4% a year while inflation averaged 2%, because banks and households held the money; in 2020 velocity collapsed as shops closed, then recovered. Output is not fixed in the short run: with spare capacity, extra spending raises output before prices, as the upward-sloping short-run aggregate supply shows. Causation can run from prices to money, since banks create deposits when borrowers demand loans. And the 2022 inflation coincided with a doubling of gas prices after Russia’s invasion of Ukraine, a supply shock that would have raised prices with or without the earlier money growth; the monetarist reply is that without accommodating money the shock would have cut output rather than raised the price level permanently.
On balance the view is right in the long run and about the extremes, and unhelpful as a guide to the next two years. Sustained inflation requires money growth to sustain it, and no inflation target can be met if money is allowed to grow without limit; but velocity and output move too much, and supply shocks matter too much, for money growth alone to explain or predict inflation at the horizons central banks work on. That is why they watch money but target inflation, and why the 2020–22 episode has revived the quantity theory without reinstating it.
Money and inflation figures: Bank of England, M4 excluding intermediate OFCs (M4x), annual growth peaking at about 15% in February 2021; ONS, CPI annual inflation 11.1% in October 2022; M4 growth averaged about 4% a year in 2010–19 while CPI averaged about 2%. The numbers on the diagram are invented. Diagrams drawn with Rough.js and perfect-freehand, both MIT licensed.