Question

The table provides some data for the United States in the first decade following the Civil War. $$\begin{array}{lcc} & \text { 1869 } & \text { 1879 } \\ \text { Quantity of money } & \$ 1.3 \text { billion } & \$ 1.7 \text { billion } \\ \text { Real GDP (1929 dollars) } & \$ 7.4 \text { billion } & Z \\ \text { Price level }(1929=100) & X & 54 \\ \text { Velocity of circulation } & 4.50 & 4.61 \end{array}$$ a. Calculate the value of \(X\) in 1869 b. Calculate the value of \(Z\) in 1879 c. Are the data consistent with the quantity theory of money? Explain your answer.

Short answer

a. X is approximately 0.791. b. Z is approximately 0.145 billion. c. Yes, the data are consistent with the quantity theory of money.

Step-by-step solution

- Understand the Quantity Theory of Money

The quantity theory of money states that the money supply multiplied by the velocity of circulation equals the price level multiplied by real GDP, represented as: \( M \times V = P \times Y \), where \( M \) is the money supply, \( V \) is the velocity of circulation, \( P \) is the price level, and \( Y \) is the real GDP.

- Set Up the Equation for 1869

For 1869, the equation will be \( M_{1869} \times V_{1869} = P_{1869} \times Y_{1869} \). Plug in the given values: \( 1.3 \text{ billion} \times 4.50 = X \times 7.4 \text{ billion} \).

- Solve for \(X\) in 1869

Rearrange the equation to solve for \( X \): \( X = \frac{1.3 \text{ billion} \times 4.50}{7.4 \text{ billion}} \). Calculate \( X \): \( X = \frac{5.85}{7.4} \approx 0.791 \). The price level in 1869 is approximately 0.791 (1929=100).

- Set Up the Equation for 1879

For 1879, the equation is \( M_{1879} \times V_{1879} = P_{1879} \times Y_{1879} \). Plug in the given values: \( 1.7 \text{ billion} \times 4.61 = 54 \times Z \).

- Solve for \(Z\) in 1879

Rearrange the equation to solve for \( Z \): \( Z = \frac{1.7 \text{ billion} \times 4.61}{54} \). Calculate \( Z \): \( Z = \frac{7.837}{54} \approx 0.145 \). The real GDP in 1879 is approximately 0.145 billion (1929 dollars).

- Check Consistency with the Quantity Theory of Money

To check for consistency, compare the values: \( 1.3 \text{ billion} \times 4.50 \approx 5.85 \text{ billion} \), and \( 0.791 \times 7.4 \text{ billion} \approx 5.84 \text{ billion} \) for 1869; and \( 1.7 \text{ billion} \times 4.61 = 7.837 \text{ billion} \) and \( 54 \times 0.145 \text{ billion} = 7.83 \text{ billion} \) for 1879. Since the numbers match closely, they are consistent with the quantity theory of money.

Key concepts

money supply

The money supply is the total amount of money available in an economy at a particular point in time. It includes all the physical currency in circulation and various types of deposits held in banks. When we talk about the money supply within the context of the Quantity Theory of Money, we're referring to how changes in the amount of money influence other economic variables. For example, in the provided exercise, the money supply increased from \(1.3 billion in 1869 to \)1.7 billion in 1879. This can affect the price level and the real GDP when paired with changes in other factors like the velocity of circulation.

The money supply is controlled by a country's central bank. They use different tools to manage it, such as altering interest rates or buying and selling government bonds, to either stimulate the economy or control inflation. Understanding the money supply is vital because it's a key component in assessing economic health and making policy decisions.

velocity of circulation

The velocity of circulation refers to how frequently money changes hands within an economy over a specific period. In more mathematical terms, it's the number of times a single unit of currency is used in transactions within a given timeframe. It can be thought of as a measure of the economic activity facilitated by each unit of money.

In the formula from the Quantity Theory of Money, velocity is denoted as 'V'. For instance, in 1869 and 1879, the velocities were 4.50 and 4.61, respectively. This means, on average, each dollar was spent 4.50 times in 1869 and slightly more frequently, 4.61 times, in 1879.

Velocity can vary based on numerous factors, including consumer confidence, payment technologies, and economic conditions. For example, in times of economic recession, people tend to save more, thus reducing the velocity of circulation.

price level

The price level represents the average of current prices across the entire spectrum of goods and services produced in the economy. It provides a snapshot of the cost of living and inflation. In the Quantity Theory of Money equation, the price level is denoted by 'P'.

In our exercise example, the price level in 1869 was approximately 0.791, using the 1929 prices as a base of 100, and it increased to 54 by 1879. These values indicate how much the average prices have changed from one period to another.

Understanding the price level is crucial because it helps illustrate the relationship between money supply and inflation. If the money supply in an economy grows faster than the real output of goods and services, this results in an increase in the general price level, leading to inflation.

real GDP

Real GDP, which stands for Real Gross Domestic Product, measures the value of all goods and services produced in an economy, adjusted for inflation. It is an essential indicator of economic health since it accounts for the economy's actual growth, free from the distortions of price changes.

In the Quantity Theory of Money, 'Y' represents real GDP. The table provided indicates the real GDP for 1869 as \(7.4 billion, while for 1879, it's calculated to be approximately \)0.145 billion using the data provided. These figures are based on the constant 1929 dollar value to adjust for inflation.

Tracking real GDP allows economists to compare the economic output over different periods while removing the effects of inflation. It helps in understanding whether the economy is genuinely growing, stagnating, or declining, thus aiding policymakers in making informed decisions.