Money Growth and Inflation: Comprehensive Study Notes

Administrative Announcements and Course Expectations

Students should be aware of the upcoming schedule and regulations for Quiz 2. The quiz is scheduled to take place on April 15, which falls on a Wednesday, during the regular class time. The assessment will cover material from Chapters 29 and 30. The examination will be administered via the ExamSoft platform. Students will be provided with a formula sheet and a calculator directly within the ExamSoft software. While students are permitted to bring their own physical calculators, they are strictly limited to simple scientific, non-graphic models. The use of cell phones and smartwatches is strictly prohibited during the examination period. While scratch paper will be provided by the proctors, students are responsible for bringing their own writing utensils, specifically pens and/or pencils.

Fundamental Questions Regarding Money and Inflation

This study of money growth and inflation seeks to address several critical economic inquiries based on the Principles of Economics Middle East Edition by N. Gregory Mankiw and Mohamed H. Rashwan. Key objectives include understanding how the money supply influences inflation rates and nominal interest rates. Furthermore, it explores the relationship between the money supply and real variables, such as real Gross Domestic Product (GDP) and the real interest rate. The text also investigates the conceptualization of inflation as a form of taxation, alongside an exhaustive analysis of the various costs associated with inflation and their overall severity within an economy.

The Level of Prices and the Value of Money

In economic theory, the price level can be interpreted through two distinct lenses. First, it represents the price of a standard basket of goods and services. Second, it serves as a measure of the value of money itself. If we let $P$ represent the price level, defined as the amount of currency needed to purchase a basket of goods and services, then the reciprocal, $1/P$ , represents the value of $1 as measured in terms of those goods and services. For example, consider a basket containing cups of tea where $P$ is the price of a single cup. If the price of a cup of tea is P = $2, then the value of a dollar is exactly half a cup ( $1/2$ ). Should the price rise to P = $3, the value of that same dollar falls to one-third of a cup ( $1/3$ ). This demonstrates a fundamental economic principle: when the general price level rises, the value of money inevitably falls.

Money Supply, Money Demand, and Monetary Equilibrium

The money supply in this economic model is assumed to be a fixed amount set and precisely controlled by the central bank. Conversely, money demand refers to the quantity of wealth that individuals and businesses wish to hold in liquid form. This demand is heavily dependent on the price level ( $P$ ). An increase in the price level reduces the value of money, thereby necessitating more money to facilitate the purchase of the same volume of goods and services. Consequently, the quantity of money demanded shares a negative relationship with the value of money and a positive relationship with the price level $P$ , assuming all other factors remain constant. Monetary equilibrium is achieved when the supply of money provided by the central bank intersects with the demand for money from the public, which ultimately determines the equilibrium price level within the economy.

The Quantity Theory of Money and the Adjustment Process

The quantity theory of money asserts that the quantity of money available in an economy determines the price level, while the growth rate of that money supply determines the inflation rate. According to Milton Friedman, the 1976 Nobel laureate, an increase in the money supply creates an excess supply of money. To eliminate this excess, people will either spend the surplus on goods and services or loan it to others who will then spend it. This behavioral response leads to an increased demand for goods. Because the actual supply of goods does not increase in tandem with this monetary injection, prices must rise to clear the market. This logic underpins the assertion that inflation is primarily a monetary phenomenon.

The Classical Dichotomy and Monetary Neutrality

Economists differentiate between types of economic variables through the classical dichotomy, which is the theoretical separation of nominal and real variables. Nominal variables are those measured in monetary units (e.g., prices or wages in dollars), while real variables are measured in physical units (e.g., quantities of corn or the relative price of one good in terms of another). David Hume and other classical economists proposed the theory of monetary neutrality, suggesting that changes in the money supply affect nominal variables but leave real variables unaffected. For instance, if the central bank were to double the money supply, all nominal variables, including price levels, would double, but all real variables, such as relative prices or real GDP, would remain unchanged. Most modern economists believe this neutrality describes the economy accurately in the long run, though monetary changes can significantly impact real variables in the short run.

Case Study: The Babysitting Cooperative

To illustrate monetary principles, consider a cooperative of young couples who each have $2$ children. To facilitate babysitting, they create a system using coupons where $1$ coupon represents "1 kid per 1 hour" of sitting. Each couple is initially issued $10$ coupons. These coupons serve as a form of currency to manage unexpected needs for childcare. Problems arise if the supply of coupons does not match the needs of the participants. For example, if couples typically need $4$ hours of sitting per outing, the system may function, but if they require $6$ hours and lack enough coupons to feel secure (their "money demand"), the system may stall. While printing more coupons (increasing the money supply) might initially encourage more babysitting activity, excessive printing would likely lead to the devaluation of the coupons, requiring more coupons for the same hour of service, effectively illustrating inflation within a micro-model.

Velocity and the Quantity Equation

The velocity of money refers to the rate at which currency changes hands as it travels through the economy. The calculation involves the following notation: $P \times Y$ represents nominal GDP, where $P$ is the price level and $Y$ is real GDP. If $M$ represents the money supply and $V$ represents velocity, the velocity formula is written as:

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

By rearranging this formula, we arrive at the quantity equation, which relates the quantity of money to the dollar value of the economy's output of goods and services:

$M \times V = P \times Y$

The Five Steps of the Quantity Theory

The quantity theory of money can be summarized in five logical steps. First, the velocity of money ( $V$ ) is observed to be relatively stable over time. Second, because velocity is stable, any change in the money supply ( $M$ ) causes nominal GDP ( $P \times Y$ ) to change by a nearly identical percentage. Third, a change in the money supply does not affect real output ( $Y$ ) because money is neutral in the long run; output is determined by technology and the supply of factors of production. Fourth, as a result, any change in the money supply and nominal GDP is reflected directly in the price level ( $P$ ). Fifth, and finally, a rapid growth in the money supply leads to a rapid rate of inflation.

Exceptions and Quantitative Easing

Recent historical data provides an exception to the strict quantity theory. Starting in 2008, the Federal Reserve injected trillions of dollars into the U.S. economy via depository institutions. Between 2008 and 2014, the money supply grew at an annual rate of approximately $6\%$ , yet the average inflation rate remained low at roughly $2\%$ . This occurred because banks chose to keep the majority of these injections as excess reserves with the Federal Reserve to earn Interest on Reserve Balances (IORB). Because these reserves did not transition into loans or increased economic activity, the velocity of money ( $V$ ) decreased significantly. Consequently, the price level ( $P$ ) rose at a much slower rate than the money supply ( $M$ ).

Active Learning 1: Computing Nominal GDP and Velocity

Consider an economy that produces only one good: corn. The economy possesses enough land, labor, and capital to produce a real GDP of $Y = 800$ tonnes of corn. In the year 2020, the money supply is M = $2,000 and the price level is P = $5 per tonne. To find the nominal GDP for 2020, we calculate:

\text{Nominal GDP} = P \times Y = $5 \times 800 = $4,000

To find the velocity ( $V$ ) for 2020, assuming it remains constant, we use the formula:

V = \frac{P \times Y}{M} = \frac{$4,000}{$2,000} = 2

Active Learning 2: Impacts of Changes in Money Supply and Technology

Building on the previous example where $Y = 800$ , $V = 2$ , and M = $2,000, let us assume the central bank increases the money supply by $5\%$ , raising it to M = $2,100 for the year 2021.

Part A: If real GDP ( $Y$ ) remains at $800$ and velocity is constant, the new nominal GDP is:

\text{Nominal GDP} = M \times V = $2,100 \times 2 = $4,200

The new price level ( $P$ ) is:

P = \frac{\text{Nominal GDP}}{Y} = \frac{$4,200}{800} = $5.25

The inflation rate is calculated as:

\text{Inflation Rate} = \frac{$5.25 - $5.00}{$5.00} = 5\%

This confirms that when real output is constant, the inflation rate matches the money supply growth rate.

Part B: If technological progress allows real GDP to increase to $Y = 824$ (a $3\%$ increase) in 2021 while M = $2,100, the new price level is:

P = \frac{M \times V}{Y} = \frac{$2,100 \times 2}{824} = \frac{$4,200}{824} \approx $5.10

The resulting inflation rate is:

\text{Inflation Rate} = \frac{$5.10 - $5.00}{$5.00} = 2\%

The Inflation Tax and Hyperinflation

When a government faces inadequate tax revenue and possesses limited borrowing capacity, it may resort to printing money to fund its expenditures. This practice is the root cause of almost all hyperinflations. The revenue raised by the government through the creation of money is known as the inflation tax. This is not a formal tax but rather a levy on everyone who holds money, as the printing of new currency reduces the purchasing power of existing currency. Hyperinflation is defined as an inflation rate exceeding $50\%$ per month. A historic example occurred in Germany in 1923, following World War I. Allied reparations totaled $132\,b$ marks, leading to a fiscal collapse. As production plummeted and money was printed excessively, the prices of daily items doubled every $3.7$ days, resulting in an inflation rate of $20.9\%$ per day. During this time, German currency became so worthless that children used stacks of banknotes as toys or building blocks.

The Fisher Effect and Real Interest Rates

Recall that the real interest rate is determined by the supply and demand for loanable funds, while the inflation rate is determined by the growth of the money supply. According to the Fisher effect, named after Irving Fisher, the nominal interest rate adjusts one-for-one with changes in the inflation rate in the long run. The relationship is expressed as:

$\text{Nominal interest rate} = \text{Real interest rate} + \text{Inflation rate}$

Because of monetary neutrality, a change in the money growth rate affects the inflation rate but does not influence the real interest rate. Consequently, if the inflation rate rises by one percentage point, the nominal interest rate will also rise by one percentage point. Historical data from the United States over the last half-century demonstrates that short-term interest rates and the Consumer Price Index (CPI) move closely together, notably peaking in the double digits around 1980.

The Costs of Inflation and the Inflation Fallacy

A common misconception known as the inflation fallacy suggests that inflation directly erodes real incomes. However, inflation describes a general rise in the prices of both what people buy and what they sell, including their labor. In the long run, real incomes are determined by real variables (productivity) rather than the rate of inflation, illustrating the principle of monetary neutrality. Despite this, inflation imposes several real costs on society:

Shoe-leather costs: The resources and time wasted when individuals try to minimize their money holdings due to high inflation, such as making frequent trips to the bank to move money into interest-bearing accounts.
Menu costs: The physical and administrative costs incurred by firms to update and change their listed prices.
Relative-price variability: Since firms do not update prices simultaneously, relative prices can fluctuate, distorting market signals and leading to a misallocation of resources.
Tax distortions: Inflation causes nominal income to grow faster than real income. Since many taxes are based on nominal values, people may pay higher taxes even if their real purchasing power has not increased.
Confusion and Inconvenience: Inflation changes the numerical "yardstick" used for economic measurement, making it difficult to compare financial transactions over time.
Arbitrary redistributions of wealth: Unexpected inflation transfers wealth from creditors to debtors, as the money repaid in the future is worth less than expected. Conversely, lower-than-expected inflation transfers wealth from debtors to creditors. High inflation tends to be volatile, making these redistributions frequent and unpredictable.

Active Learning 3: Tax Distortions and Real Interest Rates

To see how inflation distorts taxes, consider a deposit of $1,000 in a bank for one year with a tax rate of $25\%$ .

Case 1: Inflation is $0\%$ and the nominal interest rate is $10\%$ .

Interest income is $100 .
Tax paid is 0.25 \times $100 = $25 .
After-tax nominal interest rate is $7.5\%$ .
After-tax real interest rate is $7.5\% - 0\% = 7.5\%$ .

Case 2: Inflation is $10\%$ and the nominal interest rate is $20\%$ .

Interest income is $200 .
Tax paid is 0.25 \times $200 = $50 .
After-tax nominal interest rate is $0.75 \times 20\% = 15\%$ .
After-tax real interest rate is $15\% - 10\% = 5\%$ .

Although the pre-tax real interest rate was $10\%$ in both cases, the presence of inflation in Case 2 increased the tax burden and reduced the after-tax real return by $2.5\%$ compared to Case 1.

The Problem of Deflation

While high inflation is detrimental, deflation (a falling price level) can be arguably worse. Deflation induces its own menu costs and relative-price variability. It is rarely predictable and results in a redistribution of wealth toward creditors. Because debtors are often less financially secure, this can lead to widespread loan defaults and economic instability. Often, deflation is a symptom of much deeper, systemic economic problems.

Questions & Discussion

Q: How does the money supply affect real variables like real GDP? According to the principle of monetary neutrality, the money supply does not affect real variables like real GDP or real interest rates in the long run. These are instead determined by technology and factors of production.

Q: What is the most likely impact of printing excess coupons in the babysitting cooperative? If coupons are printed excessively to the point that they outstrip the demand for babysitting services, the "price" of babysitting in terms of coupons will rise. This mirrors how an increase in the national money supply leads to price inflation.

Q: Why did inflation stay low during the 2008-2014 period of Quantitative Easing? Inflation remained lower than the money growth rate because the velocity of money dropped. Banks held excess reserves with the Fed rather than lending them out, preventing the monetary injection from stimulating broader economic price increases.