# Monetary growth and inflation

### From Baripedia

The aim of this chapter is to identify the origins of inflation and to analyse the link between the supply of money and price increases.

The basic assumption of the classical model of economics is that prices are perfectly flexible. They adjust to balance markets => economy in the long run.

The quantitative theory of money is used to explain the long-run determinants (→ classic model) of the price level and the inflation rate. This theory establishes the links between the quantity of money and other macroeconomic variables.

In reality, there are many rigidities in the market that prevent prices from adjusting freely → rigidities in the short run.

The theory of economic fluctuations studies the behaviour of the economy when prices are rigid (unbalanced markets) => economy in the short term. These aspects are dealt with in the fourth and last part of the course.

# The Classical Theory of Inflation

## Inflation

Inflation occurs when the general price level rises. Inflation is a general phenomenon that concerns the value of the trade intermediary: when the general price level ↑, the value of money ↓.

The rate of inflation (= % change in the general price level) varies substantially over time and between countries. In the United States, for example, prices rose by an average of 2.4% per year in the 1960s, rising to a rate of change of 7.1% in the 1970s. At the same time, the inflation rate in the UK was 20%. Currently in Switzerland the inflation rate is around 0.2 - 0.3%.[11]

We talk about hyperinflation in the presence of episodes of extraordinarily high inflation. The best-known historical example of hyperinflation is that of Germany in the early 1920s, when the inflation rate averaged 500% per month. Many more recent examples followed (Zimbabwe and Argentina in the early 2000s).

## Money supply and demand and the equilibrium price level

In the long run the general price level (${\displaystyle P}$) adjusts to equalize the supply and demand for money, the inverse of the general price level (1/P) being the value of money (${\displaystyle M}$). (Reminder: ${\displaystyle P}$ = quantity of money needed to buy a typical consumer basket ⇒ ${\displaystyle {\frac {1}{P}}}$ = quantity of goods that can be bought with one unit of money).

The supply of money is controlled by the central bank. We then make the hypothesis that this control is perfect ⇒ exogenous (${\displaystyle M^{s}={\bar {M}}}$)

The demand for money is influenced by several determinants, the most important of which are the level of prices, output and the interest rate. Economic agents hold money for transactions (⇒ the higher the price level and output, the more money they demand) and as a store of liquid value (⇒ the higher the interest rate, The less money they ask for → opportunity cost of holding wealth in liquid form) ⇒ ${\displaystyle M^{d}=L(r_{-},P_{+},Y_{+})}$ or ${\displaystyle M^{d}=L(r_{-},{\frac {1}{P}}_{-},Y_{+})}$ , where, taking a long-term view, ${\displaystyle Y}$ is fixed at its full employment level.

## The Classical Theory of Inflation

The quantitative theory of money explains how the general price level is determined and why it can change.

The quantity of money that exists in the market determines its own value.

The main cause of inflation in the long run is money growth. Any change in the quantity of money in circulation results in an increase in the price level.

Adjustment mechanism: initial equilibrium → injection of money → excess supply of money → demand for goods and services ↑, but the supply remains unchanged (long-term view, ${\displaystyle Y}$ fixed) → the price level ↑ and consequently the demand for money also → new equilibrium.

The data show that, in general, during the decades of high money supply growth there was also high inflation and the decades of low money growth had low inflation (see chart).

## Empirical Evidence

Historical data on inflation and monetary growth in the United States

Source: Milton Friedman et Anna Schwartz; Note: monnaie mesurée par M2

## Currency neutrality

According to a number of economists (e.g. Hume or Friedman), variables in the real economy are not influenced in the long run by changes in the money supply.

Nominal variables are defined as variables measured in money units. Real variables are variables measured in physical units.

According to the classical dichotomy, real and nominal variables are influenced by different forces. In particular, changes in the money supply affect only the nominal variables and have no effect on the real variables. This is referred to as money neutrality (at best).

No impact of money on production decisions (which depend on factor productivity) or on consumption and savings (which are influenced by wages and the real interest rate). A change in money is equivalent to a simple change in the scale of measurement.

## The quantitative equation

The equation expressing the link between transactions and the money supply is called the quantitative money equation:

${\displaystyle M\times V=P\times Y}$

where ${\displaystyle P}$ = price level, ${\displaystyle Y}$ = quantity of output (real terms), ${\displaystyle M}$ = quantity of money and ${\displaystyle V}$ = speed of circulation of money.

The right-hand side of the quantitative equation measures the value of transactions = number of units of money exchanged in a year. Aggregate output replaces transactions: the more an economy produces, the more goods and services are exchanged. (NB: the number of transactions in a year is not exactly equal to GDP, but the two variables are strictly linked).

The member on the left measures the money used in transactions, ${\displaystyle V}$ being the speed of circulation of money = the number of times per unit of time that a unit of money is used to settle a transaction.

## Money creation and the rate of inflation

Based on the quantitative equation of money, an increase in the quantity of money in the economy should be reflected either in a ↑ of the general price level, in a ↑ of the output, or in a ↓ of the speed of money (%∆M + %∆V = %∆P + %∆Y).

But:

1. In principle, the speed of money is relatively stable over time (empirical evidence).
2. The quantity of output is not affected by the quantity of money in the long term (Y is fixed at its full employment level).

Conclusion: when the central bank injects money into the economic system, the result, in the long run, is a proportional increase in the rate of inflation.

## The inflation tax

The government can finance its expenses by collecting taxes, issuing bonds, printing money.

When the government covers its expenses by printing money (or, better still, by asking the Central Bank to do so), it is said to be collecting an inflation tax: when prices rise (following the issue of the new currency), the real value of banknotes in circulation decreases => inflation is a tax levied on the holding of money (a tax on liquid assets that lose purchasing power as prices rise).

It is also known as seigniorage, the revenue acquired by issuing money.

The volume of income derived from the issue of money varies considerably from one country to another. In hyperinflationary countries, seigniorage is often the main source of government revenue.

Note also that in the presence of economic growth, the Central Bank can derive income from seigniorage without creating inflation.

See Wall Street Journal - "How Gangsters Are Saving Euro Zone".

## The Fisher Effect

We have already had occasion to see that investment decisions are made on the basis of the real interest rate, which is approximated* by:

${\displaystyle r\approx i-\pi ^{e}}$

(real interest rate ≈ nominal interest rate - expected inflation rate)

The Fisher equation shows that the real interest rate and the inflation rate jointly determine the nominal interest rate :

${\displaystyle i\approx r+\pi ^{e}}$

The real interest rate is the result of the equilibrium of savings and investment → here, exogenous. Consequently, any change in the inflation rate is reflected in a proportional increase in the nominal interest rate (Fisher effect).

• The real interest rate, ${\displaystyle r}$, when the nominal lending rate is ${\displaystyle i}$ and the expected inflation rate is ${\displaystyle \pi ^{e}}$, is given by the following formula:
${\displaystyle 1+r={\frac {1+i}{1+\pi ^{e}}}}$,

When inflation rates are low, the real rate is approximately equal to the difference between the nominal rate and the inflation rate. Why is this? ${\displaystyle Ln(1+x)\approx x}$

## The nominal interest rate and the cross-countries inflation rate

Diagramme de dispersion du taux d’intérêt nominal de court terme et du taux d’inflation moyen dans 77 pays au cours des années 90. Source: Mankiw, 2003

# The social costs of inflation

## The cost of inflation

The 'cost in shoes' (cost of wear): inflation causes individuals to reduce their holdings of money → frequent visits to banks to withdraw money and reduce cash → time and energy sacrificed to change one's own position and alter asset holding choices.

The 'menu cost' (display cost): costs due to the continuous adjustment of prices → time and resources taken away from other productive activities to update catalogues, websites, make new proposals to its customers or examine proposals from its suppliers, etc.

After all, according to some, the costs of anticipated inflation are not too high.

## The cost of anticipated inflation

Relative price distortion:

Distortion of relative prices: not all prices of goods and services are affected in the same way (adjustment delays, contracts...) → distortion of relative prices → distortions in consumer decisions: markets are no longer able to allocate resources according to their best use.

Distortion in taxes:

1. in the presence of inflation, capital gains (profits from the sale of an asset at a price higher than the purchase price) are exaggerated (generalised increase in all prices, including asset prices) → with a progressive taxation system, this results in disproportionate taxation of capital gains;
2. nominal interest on savings is treated for taxation purposes as income, even if part of this interest is in fact a simple compensation for inflation → savings are less attractive.

Uncertainty and confusion:

in the presence of unanticipated inflation it becomes difficult to compare real income, actual costs and profits at different times → uncertainty, which is never a good thing (e.g. difficult wage setting → purchasing power not guaranteed).

Arbitrary redistribution of wealth:

being most loans specified in terms of the unit of measurement of money, unexpected inflation redistributes wealth among individuals, especially between creditors and debtors, in an arbitrary way (an increase in inflation reduces the real value of a loan).

The costs of unanticipated inflation are generally considered to be greater than those due to anticipated inflation. See The Economist, 11.03.2010.

## Winners and losers

LOSERS:

• Savers (lenders), whose purchasing power declines over time;
• Employees and annuitants, whose remuneration is fixed in nominal terms and is *indexed irregularly;
• Tax payers, whose wages increase to maintain purchasing power, which may cause them to change tax class (cold progression), and who are taxed on nominal returns.

WINNERS :

• Debtors (borrowers), who must repay a debt set in terms of
• nominal;
• Owners, who are in debt and who are also seeing their property prices go up.

## Caveat emptor Advantage of controlled inflation

An economist will readily acknowledge that, in the long run, monetary policy primarily affects inflation.

However, he or she will add that if price and wage rigidities exist, in the presence of nominal or real shocks, it is output and employment that will adjust.

In particular, in a world with downward nominal wage rigidity, the inflation target should not be set too low if relative prices - and especially real wages - are to adjust to shocks. A little inflation can thus put oil in the wheels of the economy.

« To be concrete, are the net costs of inflation much higher at, say, 4 percent than at 2 percent, the current target range? Is it more difficult to anchor expectations at 4 percent than at 2 percent? »

— Blanchard, Dell’Ariccia & Mauro (2010) Rethinking Macroeconomic Policy

## Hyperinflation

Although a number of economists believe that moderate inflation is not a major problem for the community, none of them doubt the penalty imposed by hyperinflation.

Hyperinflation = inflation in excess of 50% per month (1% per day; the price ↑ more than 100 times a year!). Historically, all cases of hyperinflation have occurred in conjunction with excessive growth in the money supply.

Originally → budgetary problems: The state does not have enough revenue to pay its expenses and starts issuing money, thus causing rapid growth of the money supply and, as a consequence, a rise in prices → negative spiral: real tax revenues decrease with inflation (usually taxes are collected after the public expenditure has been made), the state has to issue more money, which aggravates inflation and, consequently, the public deficit...

Solution: ↓ expenditure and ↑ revenue. The end of hyperinflation is usually a budgetary issue. This is why the independence of central banks is nowadays supported.

# Summary

The general price level adjusts to balance the demand for and supply of money.

When the central bank increases the supply of money increases the price level. A persistent increase in the money supply causes continuous inflation.

According to the principle of money neutrality, the quantity of money in circulation does not influence the real variables in the economy.

The government pays to cover its expenses by printing money. This can result in a tax on inflation and in situations of hyperinflation.

According to the Fisher effect, when the expected rate of inflation increases, the nominal interest rate increases by the same proportion and the real interest rate remains unchanged.

Economists have isolated six costs of inflation: the cost in shoes, the cost in menus, uncertainty and confusion, distortion of relative prices, distortion of taxes, arbitrary redistribution of wealth. Nevertheless, a little inflation can put oil in the economy.