Money, Prices and Inflation

Gaurav Bhattacharya

Gargi College

University of Delhi

April 6, 2020

Gaurav Bhattacharya (Gargi College, DU) BA (H) April 6, 2020 1 / 24 Overview

1 Classical vs. Keynesian money demand function

2 Relation between current prices and

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

Gaurav Bhattacharya (Gargi College, DU) BA (H) Macroeconomics April 6, 2020 2 / 24 Classical vs. Keynesian money demand function

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 d = kY ;(k > 0) (1) P

where P and Y 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 dV dP dY + = + (2) M V P Y

Gaurav Bhattacharya (Gargi College, DU) BA (H) Macroeconomics April 6, 2020 3 / 24 Classical vs. Keynesian money demand function

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 d = L(i, Y ); L < 0, L > 0 (3) P i Y

where i is the nominal interest rate.

Gaurav Bhattacharya (Gargi College, DU) BA (H) Macroeconomics April 6, 2020 4 / 24 Relation between current prices and money supply

How does money growth contribute to inflation? Recall the Fisher equation i = r + E(π) (4) where r is the real interest rate and E(π) denotes expected inflation rate. Using this in (3), we have

M d   = L r + E(π), Y (5) P

Money market equilibrium requires

M   = L r + E(π), Y (6) P

M where P denotes real money supply.

Gaurav Bhattacharya (Gargi College, DU) BA (H) Macroeconomics April 6, 2020 5 / 24 Relation between current prices and money supply

Equation (6) determines the equilibrium 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.

Gaurav Bhattacharya (Gargi College, DU) BA (H) Macroeconomics April 6, 2020 6 / 24 Relation between current prices and money supply

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)!)

Gaurav Bhattacharya (Gargi College, DU) BA (H) Macroeconomics April 6, 2020 7 / 24 Relation between current prices and money supply

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 mt − pt = −γ (pt+1 − pt ); γ > 0 (7)

where mt = ln Mt , pt = ln Pt and γ denotes the rate at which real money balances respond to a change in the price level. From (7), we get, 1 γ p = m + p (8) t 1 + γ t 1 + γ t+1

This equation states that the current price level pt is a weighted average of the current money supply mt and the next period’s price level pt+1.

Gaurav Bhattacharya (Gargi College, DU) BA (H) Macroeconomics April 6, 2020 8 / 24 Relation between current prices and money supply

A mathematical treatment: A dynamic model Therefore, the price level in the next period would be 1 γ p = m + p (9) t+1 1 + γ t+1 1 + γ t+2 Using (9) in (8),

1 γ γ2 p = m + m + p (10) t 1 + γ t (1 + γ)2 t+1 (1 + γ)2 t+2

Again, from (9), 1 γ p = m + p (11) t+2 1 + γ t+2 1 + γ t+3

Gaurav Bhattacharya (Gargi College, DU) BA (H) Macroeconomics April 6, 2020 9 / 24 Relation between current prices and money supply

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

1 γ γ2 γ3 p = m + m + m + p (12) t 1 + γ t (1 + γ)2 t+1 (1 + γ)3 t+2 (1 + γ)3 t+3

Substituting future price levels in the same manner, we get

1 γ γ2 γ3 p = m + m + m + m + ..... (13) t 1 + γ t (1 + γ)2 t+1 (1 + γ)3 t+2 (1 + γ)4 t+3 or,

1  γ γ2 γ3  p = m + m + m + m + ...... (14) t 1 + γ t (1 + γ) t+1 (1 + γ)2 t+2 (1 + γ)3 t+3

Gaurav Bhattacharya (Gargi College, DU) BA (H) Macroeconomics April 6, 2020 10 / 24 Relation between current prices and money supply

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

1 γ γ2 γ3 p = m + E (m ) + E (m ) + E (m ) + ..... t 1 + γ t (1 + γ)2 t t+1 (1 + γ)3 t t+2 (1 + γ)4 t t+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.

Gaurav Bhattacharya (Gargi College, DU) BA (H) Macroeconomics April 6, 2020 11 / 24 Costs of inflation: Anticipated inflation

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. These costs are called menu costs, because the higher the rate of inflation, the more often restaurants have to print new menus.

Gaurav Bhattacharya (Gargi College, DU) BA (H) Macroeconomics April 6, 2020 12 / 24 Costs of inflation: Anticipated inflation

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.

Gaurav Bhattacharya (Gargi College, DU) BA (H) Macroeconomics April 6, 2020 13 / 24 Costs of inflation: Anticipated inflation

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. Hence, individuals must compute the present discounted value.

Gaurav Bhattacharya (Gargi College, DU) BA (H) Macroeconomics April 6, 2020 14 / 24 Costs of inflation: Unanticipated inflation

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.

Gaurav Bhattacharya (Gargi College, DU) BA (H) Macroeconomics April 6, 2020 15 / 24 Is inflation healthy for a growing economy?

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 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 inflation.

Gaurav Bhattacharya (Gargi College, DU) BA (H) Macroeconomics April 6, 2020 16 / 24 Is inflation healthy for a growing economy?

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.

Gaurav Bhattacharya (Gargi College, DU) BA (H) Macroeconomics April 6, 2020 17 / 24 Is inflation healthy for a growing economy?

From the Phillip’s curve relation, we have

π = f (u); fu < 0 (17)

From the Okun’s law, we have

u = g(y); gy < 0 (18)

Using (18) in (17), we get

π = f (g(y)); πy = fu.gy > 0 (19)

where π, u and y denote inflation rate, unemployment rate and real GDP respectively. From (19), it is evident inflation rate and real GDP are positively related..

Gaurav Bhattacharya (Gargi College, DU) BA (H) Macroeconomics April 6, 2020 18 / 24 Hyperinflation and its causes

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.

Gaurav Bhattacharya (Gargi College, DU) BA (H) Macroeconomics April 6, 2020 19 / 24 Hyperinflation and its causes

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 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 hyperinflation is often a fiscal phenomenon as well.

Gaurav Bhattacharya (Gargi College, DU) BA (H) Macroeconomics April 6, 2020 20 / 24 Classical dichotomy and neutrality of money

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).

Gaurav Bhattacharya (Gargi College, DU) BA (H) Macroeconomics April 6, 2020 21 / 24 Classical dichotomy and neutrality of money

A four quadrant diagram can be used to explain this phenomenon (last slide). Recall the quantity theory equation. MV¯ = PY¯ (20) where velocity V and long run output Y are constant. ∗ When the price level rises from P to P1 due 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 from W to W 0 to the extent that  ∗ W the real wage rate remains unchanged at P (quadrant 2).

Gaurav Bhattacharya (Gargi College, DU) BA (H) Macroeconomics April 6, 2020 22 / 24 Classical dichotomy and neutrality of money

Labour market equilibrium in quadrant 3 remains unaffected: equilibrium employment is L∗. Now, L∗ goes to produce Y ∗ 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.

Gaurav Bhattacharya (Gargi College, DU) BA (H) Macroeconomics April 6, 2020 23 / 24 Classical dichotomy and neutrality of money

Gaurav Bhattacharya (Gargi College, DU) BA (H) Macroeconomics April 6, 2020 24 / 24