PDF Money, Prices and Inflation - Gargi College

Gaurav Bhattacharya

Gargi College University of Delhi

April 6, 2020

1 Classical vs. Keynesian money demand function

2 Relation between current prices and money supply

3 Costs of inflation

Costs of anticipated inflation Costs of unanticipated inflation

4 Is inflation healthy for a growing economy?

5 Hyperinflation and its causes

6 Classical dichotomy and neutrality of money

Classics and money demand

In an economy, money is held by people for undertaking transactions.

Demand for real money balances depends on real income.

Individuals demand a fixed proportion of income as money.

The money demand function is given by

M

P ^d

=kY; (k >0) (1)

whereP andY are prices and real income.

From the money market equilibrium condition, the quantity theory equation follows, which shows that any change in money supply would only affect prices in the economy, output remaining unchanged.

Recall the expression derived from the quantity theory dM

M +dV V =dP

P +dY

Y (2)

Keynes and money demand

Keynes propounded the theory of speculative demand for money.

Apart from real income, real money demand is also determined by nominal interest rates (note that in the short run, prices are sticky, hence real interest rates roughly equal nominal interest rates).

Interest rate is the opportunity cost of holding money, hence, there exists an inverse relation between the two.

Draw an analogy with the quantity demanded for any product and its relation with the price (for money held, the price is the interest rate).

The money demand function is given as

M

P ^d

=L(i,Y);Li <0,LY >0 (3)

How does money growth contribute to inflation?

Recall the Fisher equation

i =r+E(π) (4)

wherer is the real interest rate andE(π) denotes expected inflation rate.

Using this in (3), we have

M

P d

=L

r+E(π),Y

(5) Money market equilibrium requires

M P =L

r+E(π),Y

(6) where ^M_P denotes real money supply.

Equation (6) determines the equilibrium price level for a given level of income and nominal interest rate; an improvement over the quantity theory which states that current money supply determines current price level.

However, (6) shows an additional channel which affects the current price level.

Growth in money supply affects the nominal interest rate which further depends on expected inflation, which in turn depends on growth in the money supply.

This cycle contributes to an inflationary spiral.

Suppose, the RBI announces that it will increase money supply in the future, keeping the current money supply unchanged.

This announcement causes people to expect higher money growth and hence higher inflation in future.

The increase in expected inflation raises the nominal interest rate through the Fisher effect.

Rise in nominal interest rates reduces the demand for real money balances today.

Since the current money supply is unchanged, equilibrium in the money market would be restored only through a rise in the current price level (check (6)!)

A mathematical treatment: A dynamic model with discrete time

As we know that real money balances are inversely related to changes in the price level, we can write

m_t−p_t =−γ(p_t+1−p_t);γ >0 (7) wherem_t =ln M_t,p_t=ln P_t andγ denotes the rate at which real money balances respond to a change in the price level.

From (7), we get,

p_t = 1

1 +γm_t+ γ

1 +γp_t+1 (8)

This equation states that the current price levelp_t is a weighted average of the current money supplymt and the next period’s price levelpt+1.

A mathematical treatment: A dynamic model Therefore, the price level in the next period would be

pt+1 = 1

1 +γmt+1+ γ

1 +γpt+2 (9)

Using (9) in (8),

pt = 1

1 +γmt+ γ

(1 +γ)²mt+1+ γ²

(1 +γ)²pt+2 (10) Again, from (9),

p_t+2 = 1

1 +γm_t+2+ γ

1 +γp_t+3 (11)

A mathematical treatment: A dynamic model Plugging in the result in (11) in (10)

pt = 1

1 +γmt+ γ

(1 +γ)²mt+1+ γ²

(1 +γ)³mt+2+ γ³

(1 +γ)³pt+3 (12) Substituting future price levels in the same manner, we get

p_t = 1

1 +γm_t+ γ

(1 +γ)²m_t+1+ γ²

(1 +γ)³m_t+2+ γ³

(1 +γ)⁴m_t+3+... (13) or,

pt= 1 1 +γ

mt+ γ

(1 +γ)mt+1+ γ²

(1 +γ)²mt+2+ γ³

(1 +γ)³mt+3+...

(14)

A mathematical treatment: A dynamic model

Since money balances would be determined through people’s expectations formed in the current period, we replace

mt =Et(ms);∀s>t (15) Substituting (15) in (14), we get

pt= 1

1 +γmt+ γ

(1 +γ)²Et(mt+1) + γ²

(1 +γ)³Et(mt+2) + γ³

(1 +γ)⁴Et(mt+3) +...

(16) (16) states that the current price level depends on the current money supply and expected future money supplies.

Because the price level depends on both current and expected future money, inflation depends on both current and expected future money growth.

Therefore, to end high inflation, both money growth and expected money growth must fall.

Shoeleather cost

A higher inflation rate raises the nominal interest rate which increases the opportunity cost of holding money.

People hold less of liquid money.

This compels them to visit banks more frequently to withdraw money: they might withdraw Rs. 5000 twice a week rather than Rs. 10000 once a week.

This inconvenience of reducing money holding is known as the shoeleather cost of inflation, because walking to the bank more often causes one’s shoes to wear out more quickly.

Menu cost

High inflation induces firms to change their posted prices more often.

Changing prices is sometimes costly: for example, it may require printing and distributing a new catalogue.

Volatility of relative prices of goods and services

Firms facing menu costs change prices infrequently; therefore, the higher the rate of inflation, the greater the variability in relative prices.

For example, suppose a firm issues a new catalogue every January. If there is no inflation, then the firm’s prices relative to the overall price level are constant over the year.

Yet if inflation is 1 percent per month, then from the beginning to the end of the year the firm’s relative prices fall by 12 percent.

Sales from this catalogue will tend to be low early in the year (when its prices are relatively high) and high later in the year (when its prices are relatively low).

Hence, when inflation induces variability in relative prices, it leads to microeconomic inefficiencies in the allocation of resources.

Burden on tax payers

Inflation can alter individuals’ tax liability.

Flawed treatment of capital gains: tax code measures income as the nominal rather than the real capital gain.

A positive capital gain, which might be entirely attributed to inflation is taxable.

Adverse impacts on consumption smoothing decisions

Inconvenience of living in a world with a changing price level.

Inflation complicates personal financial planning.

Households decide how much of their income to consume today and how much to save for retirement: the decision is affected by inflation.

Real value of savings will determine the retiree’s living standard, which depends on the future price level.

Adverse impact on deferred payments

Most loan agreements specify a nominal interest rate, which is based on the rate of inflation expected at the time of the agreement.

If inflation turns out differently from what was expected, the ex post real return that the debtor pays to the creditor differs from what both parties anticipated.

On one hand, if inflation turns out to be higher than expected, the debtor wins and the creditor loses because the debtor repays the loan with less valuable money.

On the other hand, if inflation turns out to be lower than expected, the creditor wins and the debtor loses because the repayment is worth more than the two parties anticipated.

Likewise, unanticipated inflation also hurts individuals on fixed pensions.

Pensions are deferred earnings: the worker is essentially providing the firm a loan, i.e., the worker provides labour services to the firm while young but does not get fully paid until old age.

For a growing economy, inflation is unavoidable.

Inflation is directly linked to output and unemployment through the Phillip’s curve and the Okun’s law.

Phillip’s curve

In 1958, economist A. W. Phillips observed a negative relationship between the unemployment rate and the rate of wage inflation in data for the United Kingdom.

The modern Phillips curve substitutes price inflation for wage inflation since price inflation and wage inflation are closely related (in periods when wages are rising quickly, prices are rising quickly as well).

Therefore there exists a trade-off between price inflation and unemployment, i.e., in order to reduce the rate of inflation policy-makers must temporarily raise unemployment, and to reduce unemployment they must accept higher

Okun’s Law

What relationship should we expect to find between unemployment and real GDP?

Because employed workers help to produce goods and services and unemployed workers do not, increases in the unemployment rate should be associated with decreases in real GDP.

This negative relationship between unemployment and real GDP is known as the Okun’s law.

In the 1970s, economist Arthur Okun studied the annual data for the United States and found that a decrease in unemployment of 1 percentage point is associated with additional growth in real GDP of approximately 2 percent.

From the Phillip’s curve relation, we have

π=f(u); f_u<0 (17)

From the Okun’s law, we have

u=g(y); g_y <0 (18) Using (18) in (17), we get

π=f(g(y));πy =fu.gy >0 (19) whereπ,u andy denote inflation rate, unemployment rate and real GDP

respectively.

From (19), it is evident inflation rate and real GDP are positively related..

Hyperinflation is often defined as inflation that exceeds 50 percent per month, which is just over 1 percent per day.

Compounded over many months, this rate of inflation leads to very large increases in the price level.

An inflation rate of 50 percent per month implies a more than 100-fold increase in the price level over a year, and a more than 2-million-fold increase over three years.

Therefore, all costs associated with anticipated inflation get aggravated.

Causes

Hyperinflations are due to excessive growth in the supply of money.

When the central bank prints money, the price level rises.

When it prints money rapidly enough, the result is hyperinflation [refer to equation (16)]

Most hyperinflations begin when the government has inadequate tax revenue to pay for its spending.

When it is unable to borrow through public debt, the government turns to seigniorage.

Rapid money creation leads to hyperinflation, which leads to a larger budget deficit due to a fall in real tax revenue, which leads to even more rapid money creation.

Hence, even if inflation is always a monetary phenomenon, the end of

Classical dichotomy refers to the theoretical separation of real and nominal variables in the classical model, which implies that nominal variables do not influence real variables.

Nominal variables are those which are expressed in currency units (eg., wages).

Real variables are not expressed in currency units. They are expressed in inflation-adjusted units. Eg., real wage, real GDP, real interest rate.

Due to this dichotomy, money supply (a nominal variable) has no impact on GDP in the long run (a real variable).

A four quadrant diagram can be used to explain this phenomenon (last slide).

Recall the quantity theory equation.

MV¯ =PY¯ (20)

where velocityV and long run outputY are constant.

When the price level rises fromP^∗ toP₁due to an increase in money supply (quadrant 1), the labour market adjusts easily due to flexible nominal wage rates.

The nominal wage curve shifts to the right fromW toW⁰ to the extent that the real wage rate remains unchanged at

W P

^∗

(quadrant 2).

Labour market equilibrium in quadrant 3 remains unaffected: equilibrium employment isL^∗.

Now,L^∗ goes to produceY^∗ via the production function in quadrant 4.

Therefore, any change in prices keeps the long run output unaffected.

This is due to the assumption of flexibility in nominal wages in the classical model.

The long run aggregate supply curve (LRAS) is vertical.

Hence, growth in money supply only causes inflation: monetary policy is ineffective in the long run.

Money is neutral in the classical model since it cannot influence GDP.