© 1999-2020, Douglas A.Ruby (06-16-2020)

Changes in the money supply can have an impact on the overall price level. As Milton Friedman stated:

“Inflation is always and everywhere a monetary phenomenon in the sense that it is and can be produced only by a more rapid increase in the quantity of money than in output.”

A popular identity defined by Irving Fisher is the The quantity
equation commonly used to describe the relationship between the money stock **M** and aggregate expenditure:

MV = PY

An "identity" is an expression that is true by definition such as the following:

a triangle = a three sided geometric figure

There is no debate about this equality, its truth comes from the nature of the definitions used.

The variables on the right-hand side represent the price level (P) and Real GDP (Y). Taken together these two terms represent Nominal GDP or a measure of the total spending that takes place in an economy in a given time period.

On the left-hand side, M represents some measure of the money supply, perhaps M_{1}, and 'V'
represents the velocity of this monetary measure. Velocity represents the number of times
money changes hands in support of the total spending in an aggregate economy.

We might more accurately restate this identity as follows:

M_{1}V_{1}= PY^{R}

denoting the use of M_{1}, its corresponding velocity and Real GDP 'Y^{R}'. If we chose to
use M_{2} as our monetary measure then the expression would be:

M_{2}V_{2}= PY^{R}

The truth of the expression does not change. Even though, we find ourselves using a broader definition of money,
and corresponding velocity measure will be smaller. For example, in 2016, Nominal GDP (PY) was equal to
roughly $18.6 trillion. In that same year, M_{1} was measured at roughly $3.3 trillion allowing us to derive a
corresponding velocity of 5.6. or

$3.3 x (5.6) = $18.6

In that same year M_{2} was measured at $13.2 trillion with a corresponding velocity of 1.41

There is some debate about the stability of these velocity measures. If these values are little changed over time we are able to identify a proportional relationship between changes in the money supply and changes in the price level combined with changes in real GDP.

Year | NGDP | M_{1} |
M_{2} |
V_{1} |
V_{2} |

1970 | 1,075.89 | 209.1 | 601.5 | 5.15 | 1.79 |

1975 | 1,688.92 | 281.3 | 963.5 | 6.00 | 1.75 |

1980 | 2,862.51 | 395.7 | 1,540.2 | 7.23 | 1.86 |

1985 | 4,346.74 | 587.0 | 2,416.5 | 7.41 | 1.80 |

1990 | 5,979.58 | 810.6 | 3,222.2 | 7.38 | 1.86 |

1995 | 7,664.06 | 1,143.0 | 3,555.6 | 6.71 | 2.16 |

2000 | 10,284.78 | 1,103.7 | 4,780.0 | 9.32 | 2.15 |

2005 | 13,093.72 | 1,371.8 | 6,520.9 | 9.54 | 2.01 |

2010 | 14,964.38 | 1,742.2 | 8,613.2 | 8.59 | 1.74 |

2015 | 18,120.71 | 3,021.1 | 12,034.0 | 6.00 | 1.51 |

2019 | 21,427.7 | 3949.2 | 14826.0 | 5.42 | 1.45 |

When we examine the table above, there does seem to be some variation in the velocity for M_{1} -- fairly dramatic
differences when we consider that the velocity for 2005 is almost double that for 1970. However, if we consider the values for M_{2},
velocity here seems more stable ranging from 1.51 to 2.16.

Through logarithmic transformation and differentiation, the quantity equation can be transformed into the following:

%ΔM+ %ΔV = %ΔP + %ΔY^{R}

where each term represents growth in the money stock, growth in velocity, the rate of inflation, and the rate of Real economic growth respectively.

If we are able to assume that velocity is a numerical constant (its value determined by institutions and habits that see little change over time), then %ΔV = 0 and the quantity equation can be written as follows:

E[π] ~ π = %ΔP = %ΔM - %ΔY^{R}

Again, if we take a look at actual data...

Year | %ΔM_{1} |
%ΔM_{2} |
%ΔP | %ΔY^{R} |

1970 | ||||

1975 | 4.53 | 9.41 | 9.14 | -0.20 |

1980 | 6.20 | 8.03 | 13.50 | -0.20 |

1985 | 8.99 | 8.90 | 3.53 | 4.2 |

1990 | 3.63 | 5.51 | 5.42 | 1.90 |

1995 | -0.19 | 2.07 | 2.81 | 2.70 |

2000 | 0.13 | 6.05 | 3.37 | 4.10 |

2005 | 2.05 | 4.29 | 3.37 | 3.30 |

2010 | 6.39 | 2.50 | 1.64 | 2.50 |

2015 | 7.34 | 5.77 | 0.12 | 2.90 |

We observe that when growth rates in the money stock (M_{2}) exceed the
rate of real economic growth, inflation does take place.

If economic agents assume a real economic growth rate of 2.5 - 3.0%, than any growth in the money supply in excess of these values will provide fuel for inflationary expectations.

We should also note that if the money stock growing by a smaller amount as compared to the rate of economic growth then this will lead to deflationary pressures in the aggregate economy. And, of course, price stability implies that growth in the money stock should match the [expected] rate of growth in a particular economy.

- Inflationary Expectations
- Quantity Equation
- Real Economic Growth (rate)
- Rate of Inflation
- Velocity (of Money)