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### Course: Macroeconomics>Unit 5

Lesson 3: Money growth and inflation

# Lesson summary: money growth and inflation

In this lesson summary review and remind yourself of the key terms and calculations related to money growth and inflation. Topics include the quantity theory of money, the velocity of money, and how increases in the money supply may lead to inflation.

## Lesson summary

The nobel prize winning economist Milton Friedman once said that “Inflation is always and everywhere a monetary phenomenon.” The evidence to back his claim was pretty clear: whenever countries experience very high inflation for a sustained period of time, those countries also experience a rapid increase in the rate of growth of their money supply.
At the same time, increases in the money supply in those countries isn’t associated with sustained increases in output that we would have predicted with monetary policy. It seems that in the short run, increases in the money supply lead to increases in output, but in the long run increases in the money supply just cause inflation.

## Key terms

Key termdefinition
Velocitythe number of times in a year that an “average” dollar gets spent on goods and services; for example, if the velocity of money is 2, then every dollar in an economy gets used twice in a year.
Money neutralitythe concept that money only impacts nominal variables, not real variables, in the long run; in other words, increasing the money supply might decrease the nominal interest rate, but it won’t have an impact on the real interest rate.
Monetarisma way of analyzing the impact of monetary and fiscal policy actions based on the equation of exchange
the equation of exchangea mathematical identity that describes the relationship between the money supply and nominal GDP
the quantity theory of moneya theoretical model that when the velocity of money is fixed and real output is limited to full employment output, any increase in the money supply causes an increase in the price level

## Key equations

### The equation of exchange

The equation of exchange states that the effective money supply is equal to nominal GDP:
$M×V=P×Y$
Where
Note that $P×Y$ is the same as nominal GDP.
The equation of exchange of money is actually just saying that all of the nominal GDP that is bought ($P×Y$) has to be bought with the effective amount of money available ($M×V$). Think of the quantity theory of money this way: “you need $\mathrm{}100$ to buy $\mathrm{}100$ worth of stuff.”
Equations (like the equation of exchange) become theories when we start describing attributes of the parts of the equation. For example, if we assume that the velocity of money never changes, then any increase in the money supply must also cause a change in one of the variables on the right-hand side of the equation.

### The quantity theory of money

$M×V=P×Y$
Where V, the velocity of money, is constant.
The quantity theory of money has these important implications:
• If output ($Y$) is increasing and velocity is constant, the money supply will have to increase to keep the price level from decreasing; and
• An increase in the money supply ($M$) without an increase in output ($Y$) causes the price level to change by the same change in the money supply. In other words, output doesn’t change, but when the money supply doubles, the price level also doubles.
For example, suppose we had a really simple economy that only produced mangoes. The velocity of money is 5 and there are 100 mangoes:
$M×5=P×Y$
What will the price be if there is $\mathrm{}20$ in the money supply?
$\begin{array}{rl}\mathrm{}20×5& =P×100\\ \\ \mathrm{}100& =P×\mathrm{}100\\ \\ \mathrm{}1& =P\end{array}$
So, according to this theory, each mango will cost $\mathrm{}1$. What if instead there is $\mathrm{}40$ in the money supply?
$\begin{array}{rl}\mathrm{}40×5& =P×100\\ \\ \mathrm{}200& =P×100\\ \\ P& =\mathrm{}2\end{array}$
When there was no accompanying increase in output, the price level doubled.

### A slightly different version of the quantity theory of money

$\mathrm{%}\mathrm{\Delta }M+\mathrm{%}\mathrm{\Delta }V=\mathrm{%}\mathrm{\Delta }P+\mathrm{%}\mathrm{\Delta }Y$
This form of the equation is just the first form after some complicated math (that is beyond the scope of the course) has been applied. These mathematical operations transformed each variable into their growth rates.
For example, suppose real GDP is growing at $5\mathrm{%}$, the velocity of money is constant, and the money supply is growing at $5\mathrm{%}$. Then this equation becomes:
$\begin{array}{rl}\mathrm{%}\mathrm{\Delta }M+\mathrm{%}\mathrm{\Delta }V& =\mathrm{%}\mathrm{\Delta }P+\mathrm{%}\mathrm{\Delta }Y\\ \\ 5\mathrm{%}+0\mathrm{%}& =\mathrm{%}\mathrm{\Delta }P+5\mathrm{%}\end{array}$
We conclude from this that the rate of change of the price level is $0\mathrm{%}$.
But, if the money supply is growing by $7\mathrm{%}$, the this equation becomes:
$\begin{array}{rl}\mathrm{%}\mathrm{\Delta }M+\mathrm{%}\mathrm{\Delta }V& =\mathrm{%}\mathrm{\Delta }P+\mathrm{%}\mathrm{\Delta }Y\\ \\ 7\mathrm{%}+0\mathrm{%}& =\mathrm{%}\mathrm{\Delta }P+5\mathrm{%}\end{array}$
If the money supply grows faster than the rate of growth of output, the only place for that increase in the money supply to go is the price level.

## Key Takeaways:

### The impact of changes in the money supply will depend on whether the economy is at full employment or not

Previously, we learned that a central bank can influence output by increasing the money supply. At first glance, it might seem like the quantity theory of money contradicts this, because when the money supply increases only the price level change.
The important assumption that drives this result is that output ($Y$) is fixed. This might be true in the long-run, but not in the short-run. In the short-run, an increase in the money supply decreases the nominal interest rate, which increases investment and real output. However, according to the self-correcting mechanism, the accompanying inflation will eventually lead to a decrease in short-run aggregate supply ($SRAS$). The decrease in $SRAS$ returns the economy to full employment and a new, permanently higher price level.
The impact of a change in the money supply on real output ultimately depends on the shape of the aggregate supply curve. If the aggregate supply curve is vertical (as it is assumed to be in the long run) then an increase in the money supply will only impact inflation. If the aggregate supply curve is relatively flat, then there might be large increases in output that result from an increase in the money supply and relatively little impact on the price level.

### The growth of the money supply determines the growth of the price level in the long run

The quantity theory of money treats money as neutral. That doesn’t mean that changes in the money supply have no impact. Rather, “neutral” means that changes in the money supply have no impact on one variable in particular: real output. In the long run, real output will depend on resources and technology, not the money supply.
This means that changes in the price level (and therefore the rate of inflation) depend primarily on changes in the money supply.

## Key misperceptions

Some people assume that money neutrality means monetary policy is pointless. In fact, Milton Friedman, the father of monetarism, believed that the lack of monetary policy contributed to the severity of the Great Depression. Rather, money neutrality states that monetary policy has limits to its appropriate uses. The money supply should grow enough to support any increase in the natural rate of output (in other words, support economic growth), and during severe downturns. However, the money supply shouldn’t be used to attempt to smooth out the business cycle

## Questions for review

1. What assumption turns the equation of exchange into the quantity theory of money?
2. If the velocity of money is constant and output is constant, what happens to the price level if the money supply doubles?
3. If the money supply is $\mathrm{}100$ and nominal GDP is $\mathrm{}500$, what is the velocity of money?

## Want to join the conversation?

• in key misperceptions it is given that "money supply should never be used to flat out the business cycle".What does it mean by it.Does it is not contradict to the objective of monetary policies(expansionary and contraction)?
• What does this statement mean- If the aggregate supply curve is relatively flat, then there might be large increases in output that result from an increase in the money supply and relatively little impact on the price level.
• Can anyone explain how the additive form of the formula is the same as the original. For example, if we use M+V=P+Y => 7% + 0% = 5% +2%. Then in the original formula this is MV = PY => (1.07)M*V =(1.05)P*(1.02)Y => 1.07 = 1.071? Thanks!
• Doesn't the increase in investment from the lower nominal interest rate also result in more capital stock being bought? Couldn't this cause long-run economic growth?
• does money supply affect nominal interest rate
(1 vote)
• Yes, it affects them. The increase in the quantity of money decided by the central bank, in particular QE or quantitative easing, which is an action of the central bank's unconventional monetary policy.
The central bank goes to the financial markets to inject money it "prints" itself, by buying financial securities (bonds/shares from households).
households, with the money provided by the central bank via the sale by households of their financial securities, will then buy financial securities again, thereby increasing demand for financial securities
via the interplay of supply and demand, the price of financial securities will rise(1), bringing in more income for companies, which will then invest more.
(however, in real life, besides QE the central bank has no control over the quantity of money in the economy, which is endogenous to money demand).

(1) imagine a bond worth €100, where each year, it gives you €5 (i.e. 5% interest), and in 3 years, the €100 is fully repaid.
let's imagine that in the same year as the issue, the market interest rate is now 2% (following QE action), so the price of the bond for resale on the market will be €108.65! well, the intuition is that a new €100 bond would only give you €2 a year, and since you own one that gives you €5, yours is worth more :O
if the interest rate rises to 8%, imagining that the CB is selling financial securities, then you'll have to sell it for only 92.27€.
(1 vote)
• If the demand for money increases, what happens to velocity?
(1 vote)
• M x V = P x Y
Because of this you can't answer this question without knowing more. However, I can say that the velocity of money is usually constant, so when the demand for money increase, either output (Y) or price level (P) need to increase as well. (Usually its price level). You could also look at it as higher demand for more money ---> less spending/investments---->therefore lower velocity.
(1 vote)