Chapter 5 - The Classical Theory of Inflation (Long Run): Its Causes, Effects and Social Costs

Question 1

What is the Quantity Theory of Money, and how is the velocity of money calculated?

Answer 1

The Quantity Theory of Money: A simple theory linking the inflation rate to the growth rate of the money supply is this identity:
V= T/M

V = transaction velocity of money
T = value of all transactions
M = money supply

Velocity of Money, V: Number of times that the total money should circulate to transact (buy/sell) the total produced output.
Using nominal GDP as a proxy for total transactions:
V= P×Y / M

V = income velocity of money
P = price of output (GDP deflator)
Y = quantity of output (real GDP)
P × Y = value of output (nominal GDP)

Example:
$Y = P×Y =$120B M=$10B ⇒ V=12

Question 2

What is the relationship between real money balances (M/P), the exogenous constant (k), and real income (Y) in the demand for money function? Describe the equilibrium condition for money demand and supply.

Answer 2

Real money balances (M/P) represent the purchasing power of the stock of money, equal to the number of units of output that one unit of money can buy. In the demand function (M/P)^d = kY, k is the exogenous constant indicating desired money holdings per dollar of income, and Y represents real income (output). With the supply of real balances, the supply function is (M/P)^s = M/P. Equilibrium occurs when M/P=kY, meaning money demand equals money supply.

Question 3

Explain the relationship between K and V in the demand for money and how technological progress can influence velocity.

Answer 3

M/P = k Y -> M(1/k) = PY
V = P * Y / M -> MV = PY -> V = 1/k
The Demand for Money and Quantity Equation explains how money circulates in the economy. The formula M/P=k Y shows that people hold a certain amount of money (M) based on the price level (P) and their income (Y), with k representing the fraction of income people want to hold as cash. Rearranging gives M V=P Ywhere V, the velocity of money, is 1/k and measures how often money “changes hands,” or is spent, within a given period. If k is large (meaning people hold more cash relative to income), money circulates slowly (low V). Conversely, if k is small, V is higher, indicating money circulates faster. Technological advances like ATMs and online banking can change V by influencing how people hold and use money.

Question 4

How is the Price Level, P, Determined?

Answer 4

To determine the price level P, we use the equation where M * Vbar= P * Y. M represents the money supply, V bar is the constant and exogenous velocity of money, P is the price level, and Y is the real GDP. In this model, Vbar is assumed to be constant, meaning the frequency of money circulation doesn’t change. Real GDP Y is determined by the economy’s resources, specifically the supplies of capital (K), labor (L), and technology, as expressed by Y=F(Kbar, Lbar). The money supply M influences nominal GDP and, thus, the price level, with the relationship P=Nominal GDP/ Real GDP​. In essence, this model suggests that the money supply helps establish the price level by balancing nominal GDP with real output.

Question 5

In the context of the Quantity Theory of Money, how does the classical view explain inflation? Write the equations involved and explain the components.

Answer 5

The Quantity Theory of Money equation is expressed as:
M * Vbar = P * Y
where M is the money supply, V is the velocity of money (assumed constant), P is the price level, and Y is real GDP. To analyze inflation, we rewrite this equation in terms of growth rates:
changeM/M + changeV / V = changeP / P + changeY/Y

Since velocity Vbar is constant, its growth rate changeV / V is zero:
chagneM/M = changeP / P + changeY/Y
Here:
changeP /P = pie, which represents the inflation rate.
changeY/Y is the growth rate of output (real GDP).
Rearranging to solve for inflation, we get:
pie = changeM/M - changeY/Y
This equation shows that the inflation rate is determined by the difference between the growth rate of the money supply M/M and the growth rate of output Y/Y.

Question 6

Write the relationship between money growth and inflation and explain the components of it:

Answer 6

pie = changeM/M - changeY/Y

• Where pie is the inflation rate
• changeM/M is the growth rate of money supply
• changeY/Y is the growth rate of output

Key Points:
Money growth in excess of the normal economic growth leads to inflation.

changeY/Y depends on growth in production factors and technological progress.

Normal economic growth requires a certain amount of money supply growth to facilitate the growth in transactions.

The quantity theory suggests a one-for-one relationship between changes in money growth and inflation.

Question 7

What does the quantity theory of money imply:

Answer 7

The quantity theory of money implies that countries with higher money growth rate should have higher inflation rates. The long-run trend in a country’s inflation rate should be similar to the long-run trend in the country’s money growth rate.

Question 8

Suppose the velocity of money is constant, and the money supply (M) is growing at 5% per year while the output (Y) is growing at 2% per year.

Calculate the inflation rate (π) using the formula.
If the growth rate of output (Y) falls by 1 percentage point per year, what will happen to π? What must the central bank do to keep π constant?

Answer 8

Inflation Calculation:
= 5%- 2% = 3%

If the central bank doesn’t do anything, the inflation rate (π) will increase by 1%.

To keep inflation constant, the central bank should reduce the growth rate of the money supply by 1 percentage point.

Question 9

What are the ways the government can finance its spending, and how does printing money lead to seigniorage and inflation?

Answer 9

The government can finance its spending in three ways:

It can raise revenue through all sorts of taxes
It can borrow from the public by selling government bonds
It can raise revenue by printing money.

The revenue raised by printing money is called seigniorage. The government has the exclusive right to print money, so the exclusive right to collect seigniorage.

When the government prints money to increase revenue through seigniorage, it causes the money supply to rise, leading to inflation and inflation tax.

This inflation acts as an inflation tax on people holding money, as the value of their money decreases with the new money introduced, making their old money less valuable.

Question 10

What is the difference between nominal and real interest rates, and what does the Fisher Effect state?

Answer 10

Answer:

Nominal interest rate (i): The rate of return on assets, measured in terms of current dollars. It is the interest rate that banks pay.

Real interest rate (r): The rate of return on assets, measured in terms of goods (reflects the increase in purchasing power).

Fisher Effect (Long Run): It states that the nominal interest rate (i) is equal to the real interest rate (r) plus the inflation rate (π):

i = r+ pie or r =i - pie

The real interest rate is the return on assets, adjusted for the inflation rate

Implication of Fisher Effect: An increase in the inflation rate (π) causes an equal increase in the nominal interest rate (i):
changei= changepie

Question 11

What is the Fisher Effect, and how does it relate the nominal interest rate (i), real interest rate (r), and inflation rate (π)? (write formula for nominal)

Answer 11

Answer:
The Fisher Effect states that the nominal interest rate (i) is equal to the real interest rate (r) plus the inflation rate (π):

i = r + pie
The real interest rate is determined by the long-run equilibrium in the loanable funds (or goods) market. S = I, Y = C+ I + G

Question 12

If the velocity of money is constant, the real interest rate is 4%, money supply grows at 5% per year, and real GDP grows at 2% per year, how do you calculate the inflation rate (π) and nominal interest rate (i)? What happens if the central bank increases the growth rate of the money supply by 2%?

Answer 12

Answer:
Calculate Inflation Rate π:
= changeM/M - changeY/Y = 5% - 2% = 3%
Calculate Nominal Interest Rate i:
i = r + pie = 4% + 3%
Effect of a 2% Increase in Money Supply Growth:
Nominal interest rate iii will increase by 2%, as Δi=Δπ=2%

Question 13

What is the difference between ex ante and ex post real interest rates?

Answer 13

Context:

When borrowers and lenders agree on a nominal interest rate, they do not know the actual inflation rate over the loan term.
They don’t know the actual real interest rate(return)
They have to come up with an expected inflation rate

Definitions:
Actual Inflation Rate (π): not known until after it has =
Expected Inflation Rate (πe): The inflation rate that the market anticipates based on current information.

Types of Real Interest Rates:
Ex Ante Real Interest Rate (re=i−πe): The real interest rate that lenders and borrowers expect at the time they agree on the loan terms.
Ex Post Real Interest Rate (r = i−π): The actual real interest rate that is realized after the inflation rate is known.

Question 14

What does the more precise form of the Fisher effect reveal about the relationship between nominal interest rates, real interest rates, and expected inflation?

Answer 14

Answer: The Fisher effect in its precise form is given by r=i−πe, r = i - π^e, which shows that the nominal interest rate (i) is equal to the real interest rate (r) plus the expected inflation rate (πe). Empirically, nominal interest rates are strongly correlated with actual inflation rates because actual inflation is generally persistent, so higher actual inflation often leads to higher expected inflation.

Question 15

What factors influence the demand for money, and how is the money demand function represented? (consider fisher effect)

Answer 15

According to the quantity theory, demand for real money balances (M/P) depends on real income Y (for transactions).

The money demand is a function of nominal interest rate, because it represents the opportunity cost of holding money (forgone returns on assets like bonds).

Money demand depends negatively on i

Money Demand Function: (M/P)^d=L(i,Y) where i negatively affects demand, and Y positively affects it.

Incorporating Expected Inflation: Using Fisher’s effect, (M/P)^d=L(r+πe,Y) where r is the real interest rate, and πe is expected inflation.

Question 16

What determines the economy’s long-run equilibrium in terms of real money balances, interest rates, and GDP?

Answer 16

Demand for Real Money Balances: (M/P)^d = L( r + πe, Y)
r + πe = expected nominal interest rate

Y = real GDP (drives transactions).
Supply of Real Money Balances:
(M/P)^s = M/P

Equilibrium Condition: M/P = L( r + πe, Y)

Price Level (P) adjusts to balance money supply and demand.
Real Interest Rate (r): Determined by long-run loanable funds equilibrium (S = I) or Y=C+ I+ G
Real GDP (Y): Determined by capital (K), labor (L), and technology: Y=F(K,L)

Question 17

What is the impact of an expansionary monetary policy on the long-run equilibrium?

Answer 17

Increase in Money Supply (M↑): In the long run:
Real interest rate (r) and real GDP (Y) are fixed (classical view).
Expected inflation (πe is also assumed fixed.
Demand for Real Money Balances is fixed.
Supply of Real Money Balances (M/P​) must match demand, fixed
Result: The price level (P) must rise at the same rate as money supply (M) to maintain equilibrium: MP=L(r+πe,Y)

Question 18

What happens to the long-run equilibrium if the central bank announces a future increase in money supply?

Answer 18

Answer:

Future Money Supply Increase (Future M↑):
In the long run, real interest rate (r) and real GDP (Y) are fixed (classical view).

Announced future M↑ raises expected inflation (πe).

Effects:
Nominal interest rate (i) rises due to higher πe.
Holding money becomes costlier.

Demand for real money balances falls.

Supply of real money balances must also fall.

Result: Price level (P) rises today in response to the expected future increase in money supply.

Question 19

What is a common misperception about inflation and real wages?

Answer 19

Answer:

Common Misperception: Inflation reduces real wages.

Short Run: True when nominal wages are fixed by contracts, so inflation temporarily reduces purchasing power.

Long Run: False. Real wages are determined by labor supply and the marginal product of labor, not inflation or the price level.

Question 20

Why is inflation bad? List the costs of inflation.

Answer 20

Unexpected Inflation:
Arbitrary Redistribution of Purchasing Power:
Increased Uncertainty:

Expected Inflation:
Shoe Leather Cost:
Menu Cost:
Relative Price Distortions:
Unfair Tax Treatment
General Inconvenience

Question 21

Explain Shoe Leather Cost:

Answer 21

Shoe Leather Cost: The cost of time, effort, and inconvenience that people spend to offset the effects of inflation, such as holding less cash and having to make additional trips to the bank.

When inflation (π) rises:
The Inflation tax rises (as money loses its value faster).
Average money holding falls (people prefer to hold more bonds and less cash, noting that as inflation rises, nominal interest rate rises too).
Given that inflation cannot affect real income and expenditure (Neutrality of money), the necessary real money for spending remains the same.
The same spending but lower average money holdings means more frequent trips to the bank to withdraw smaller amounts of cash.

Question 22

What is the Menu Cost?

Answer 22

The costs of changing prices.
Cost of printing new menus and catalogues.

Cost of estimating new prices. The higher is inflation, the more frequently firms must change their prices and incur these costs.

Question 23

What is the Cost of Relative Price Distortion?

Answer 23

Firms facing menu costs change prices infrequently. For example, a firm issues a new catalogue each January.

As the general price level rises throughout the year, the firm’s relative price will fall.

Different firms change their prices at different times, leading to relative price distortions.
Microeconomic inefficiencies in the allocation of resources.

Question 24

What is General Inconvenience?

Answer 24

Continuous change of unit of measurement is inconvenient, like if a meter gets longer every year.

Inflation makes it harder to compare nominal values from different time periods.

This complicates long-range financial planning.

Question 25

What is the effect of unexpected inflation on Random Redistribution of Wealth?

Answer 25

Many long-term contracts are not indexed but are based on the expected inflation rate (πe).

If actual inflation (π) differs from πe, some people gain at the expense of others.

Example:
If π > πe : r < re (real interest rate falls below expected), wealth is transferred from lenders to borrowers.

If π<πe>re (real interest rate exceeds expected), wealth is transferred from borrowers to lenders.</πe>

Question 26

What is the effect of unexpected inflation on uncertainty?

Answer 26

When inflation is high, it’s more variable and unpredictable. π turns out different from πe more often, and the differences tend to be larger, though not systematically positive or negative.

Arbitrary redistributions of wealth are more likely.

This increases uncertainty, making risk-averse people worse off.

Question 27

What is one benefit of inflation?

Answer 27

Nominal wages are rarely reduced due to labor unions, even when equilibrium real wages should fall.
This prevents the labor market from clearing, creating real wage rigidities and more unemployment.

Inflation allows real wages to fall toward equilibrium without nominal wage cuts.
Moderate inflation improves the functioning of labor markets.

Question 28

What is hyperinflation and its effects?

Answer 28

Hyperinflation is an inflation rate greater than 50% per month.
All costs of moderate inflation become HUGE under hyperinflation.
Money stops functioning as a store of value and may lose other functions (unit of account, medium of exchange).
People may resort to barter or use a stable foreign currency (dollarization).
Caused by excessive money supply growth due to printing money too much and too fast.

Question 29

How does hyperinflation occur when the government uses seigniorage, and what is the solution?

Answer 29

When a government cannot raise taxes or sell bonds, it may finance spending by printing money (seigniorage).

However, the inflation that results reduces the real value of government revenue. In the next round, the government should increase its nominal spending.
This leads the government to print more money to cover spending, increasing the risk of hyperinflation.

Solution (theoretical): Stop printing money.
Solution (real world): Requires drastic and painful fiscal restraint.

Question 30

What are Nominal and Real Variables, and how do they differ?

Answer 30

Nominal Variables: Measure of variables in terms of dollars.

Nominal output (GDP): Dollar value of produced output.
Nominal wage: Dollar earned per hour of work.
Nominal interest rate: Dollar earned in the future by lending out one dollar today.
Price level: Number of dollars needed to buy a representative basket of goods.

Real Variables: Measure of variables in terms of physical units, quantities, and relative prices.

Real output (GDP): Quantity of produced output.
Real wage: Output earned per hour of work.
Real interest rate: Output earned in the future by lending out one unit of output (or not consuming) today.
Real money: Number of units of goods that one dollar can buy.

Question 31

What is the Neutrality of Money and the Classical Dichotomy?

Answer 31

Neutrality of Money: Money supply does not affect real variables in the long run. So, in the real world, money is approximately neutral in the long run.

Classical Dichotomy: The theoretical separation of real and nominal variables in the classical model, which implies nominal variables do not affect real variables.