Question

If the money supply is growing at a rate of 6 percent per year, real GDP is growing at a rate of 3 percent per year, and velocity is constant, what will the inflation rate be? If velocity is increasing 1 percent per year instead of remaining constant, what will the inflation rate be?

Short answer

When the velocity is constant, the inflation rate will be 3%. If the velocity is increasing 1% per year instead of remaining constant, the inflation rate will be 4%.

Step-by-step solution

Understand the Quantity Theory of Money

The equation MV = PQ, also known as the Quantity Theory of Money, describes the relationship between Money supply (M), Velocity of money (V), Price level (P), and Quantity of output (Q) or Real GDP. The growth rate of each side of the equation should be equal. So, if V remains constant, the growth rate of M plus the growth rate of V (which is zero) is equal to the growth rate of P plus the growth rate of Q.

Calculate the Inflation Rate with Constant Velocity

Given M's growth rate is 6% and Q's growth rate is 3%, and assuming V's growth rate is zero because velocity is constant, the inflation rate can be found by subtracting Q's growth rate from M's growth rate. So, the inflation rate P is 6% - 3% = 3%.

Calculate the Inflation Rate with Increasing Velocity

Now if V is increasing 1% per year instead of remaining constant, the inflation rate P is found by adding the growth rates of M and V and then subtracting Q's growth rate. So, the inflation rate P in this case is 6% + 1% - 3% = 4%.

Key concepts

Quantity Theory of Money

Understanding the Quantity Theory of Money is crucial when it comes to determining the inflation rate in an economy. This theory posits a direct relationship between the amount of money in an economy and the level of prices of goods and services.

The core equation representing this theory is known as the Equation of Exchange, which is expressed as:
\[\begin{equation} MV = PQ \ \end{equation}\]
Here,

• \textbf{M} stands for the Money supply,
• \textbf{V} represents the Velocity of money,
• \textbf{P} indicates the Price level,
• and \textbf{Q} is the Quantity of output or Real GDP.

When we talk about the growth rates in this equation and assuming V is constant, the growth in the money supply (\textbf{M}) plus the growth rate of the velocity of money (\textbf{V}, which is zero if constant) should equal the inflation rate (\textbf{P}) plus the rate of real GDP growth (\textbf{Q}). Simplifying this relationship helps us understand the dynamics behind inflation and its connection with the other variables in an economy.

Velocity of Money

The Velocity of Money is a measure of how frequently money is exchanged in an economy. To put it simply, it reflects the rate at which money moves around from one transaction to another within a specific period.

When the velocity is constant, as in our exercise example, it doesn't directly affect the inflation rate because it's not changing over time. However, If V increases, meaning money is changing hands more quickly, this can lead to higher overall spending, potentially contributing to a higher inflation rate if not matched by a corresponding increase in goods and services.

In our exercise, when V grows by 1%, even if the money supply growth remains at 6%, this accelerated movement of money through the economy influences the inflation. This is because the overall spending is higher than before, resulting in increased demand for goods and services which tends to push prices up, hence increasing the inflation rate.

Real GDP Growth

Real GDP Growth is the measure of how much an economy has grown over a certain period, adjusted for inflation. It is an essential indicator of economic health, showing whether the economy is expanding or contracting.

When Real GDP is growing, as stated in our exercise at a rate of 3% per year, this typically signals that more goods and services are being produced and consumed. However, for inflation calculations, this growth rate serves as a counterbalance to the growth rate of the money supply. In our example, if we increase money supply without a proportional increase in goods and services, there would be more money chasing fewer goods, leading to price increases, or inflation. However, when Real GDP grows, it can absorb some of the increased money supply, thereby mitigating inflationary pressures.

Therefore, understanding the interplay between money supply, velocity, and real GDP growth allows us to predict changes in inflation, pending other external factors remain constant. Knowing this helps in creating stable economic policies and making informed financial decisions.