Question

Suppose that the velocity of circulation of money is constant and real GDP is growing at 3 percent a year. a. To achieve an inflation target of 2 percent a year, at what rate would the central bank grow the quantity of money? b. At what growth rate of the quantity of money would deflation be created?

Short answer

To achieve 2% inflation, grow the money supply at 5% per year. For deflation, grow the money at 1% per year.

Step-by-step solution

Understand the Quantity Theory of Money

The Quantity Theory of Money is given by the equation: \[ MV = PY \]where \( M \) is the money supply, \( V \) is the velocity of money, \( P \) is the price level, and \( Y \) is the real GDP. Assuming velocity of money (\( V \)) is constant, we can establish the relationship between the growth rates of these variables.

Express the Growth Rates

We know the relationship between the growth rates can be expressed as: \[ g_M + g_V = g_P + g_Y \]where \( g_M \) is the growth rate of money supply, \( g_V \) is the growth rate of velocity (which is 0 since it's constant), \( g_P \) is the growth rate of the price level (inflation rate), and \( g_Y \) is the growth rate of real GDP.

Calculate the Required Growth Rate for Inflation Target

To achieve an inflation target of 2 percent (\( g_P = 0.02 \)) and given that real GDP is growing at 3 percent (\( g_Y = 0.03 \)), we substitute these values into the formula: \[ g_M + 0 = 0.02 + 0.03 \]Solving this equation, we find: \[ g_M = 0.05 \]So, the central bank must grow the quantity of money at a rate of 5 percent.

Determine the Growth Rate for Deflation

Deflation occurs when the price level decreases (\( g_P < 0 \)). To find the rate creating deflation, set \( g_P \) as a negative value. Suppose a deflation rate of 2 percent (\( g_P = -0.02 \)) then: \[ g_M + 0 = -0.02 + 0.03 \]Solving this yields: \[ g_M = 0.01 \]Therefore, a growth rate of money supply at 1 percent would create a deflation of 2 percent.

Key concepts

Velocity of Money

The velocity of money refers to the frequency at which a unit of currency circulates through the economy over a given period of time. It's essentially a measure of how quickly money changes hands. In the formula for the Quantity Theory of Money, it is represented by the variable \(V\). A higher velocity means money is being used more often to purchase goods and services.
When the velocity of money is constant, as assumed in this exercise, it simplifies our calculations because we don't need to account for any changes in how quickly money is being spent. This allows us to focus solely on changes in the money supply and how they affect the price level and real GDP.
In essence, the velocity of money helps us understand the efficiency of the money supply in promoting economic activity.

Real GDP Growth

Real GDP growth measures the economic growth rate, taking into account the value of all goods and services produced, adjusted for inflation or deflation.
In this exercise, we are given that real GDP is growing at 3 percent per year. This means the economy's output is increasing by 3 percent annually. When the economy grows, more goods and services are produced, which can influence the price levels in the economy.
Understanding real GDP growth is crucial because it helps policymakers make informed decisions about monetary policy. If the economy is growing steadily, measures like adjusting the money supply can be fine-tuned to achieve specific targets like controlled inflation, promoting economic stability.

Inflation Target

An inflation target is a goal set by a central bank to achieve a specific rate of inflation over a certain time period. In the given exercise, the central bank aims for an inflation target of 2 percent per year.
To achieve this inflation target, the central bank needs to manage the growth rate of the money supply. Using the Quantity Theory of Money equation and the given real GDP growth, we can calculate the required growth rate in the money supply to achieve the desired inflation rate.
This is essential for maintaining stable prices and fostering a predictable economic environment. Predictable inflation rates help businesses and consumers make well-informed financial decisions.

Deflation

Deflation refers to a decrease in the general price level of goods and services. It is the opposite of inflation and can lead to negative economic consequences.
In the context of the exercise, deflation is considered when the inflation rate is set to a negative value. For example, a deflation rate of 2 percent corresponds to a decrease in prices by 2 percent annually.
Deflation can result from a decrease in money supply or slower economic activity. If deflation occurs, it could lead to reduced consumer spending, as people might delay purchases in anticipation of lower prices in the future. This can further slow down economic growth.
Therefore, understanding how changes in the money supply can lead to deflation is crucial for economic policy and maintaining a healthy economy.