Question

In year \(1,\) the economy is at full employment and real GDP is \(\$ 400\) million, the GDP deflator is 200 (the price level is 2 ), and the velocity of circulation is \(20 .\) In year \(2,\) the quantity of money increases by 20 percent. If the quantity theory of money holds, calculate the quantity of money, the GDP deflator, real GDP, and the velocity of circulation in year 2.

Short answer

Year 2: Quantity of Money = \(4800 million, GDP Deflator = 240, Real GDP = \)400 million, Velocity = 20.

Step-by-step solution

- Calculate the Initial Quantity of Money (Year 1)

Use the formula from the Quantity Theory of Money: \[ MV = PY \]where: -\( M \) is the quantity of money-\( V \) is the velocity of circulation-\( P \) is the GDP deflator (price level)-\( Y \) is the real GDPGiven: \( V = 20 \), \( P = 200 \), \( Y = 400 \text{ million} \), Substitute the values in:\[ M \times 20 = 200 \times 400 \]\[ M = \frac{200 \times 400}{20} \]\[ M = 4000 \text{ million} \]

- Calculate the Quantity of Money in Year 2

The quantity of money increases by 20 percent. So,\[ M_{2} = M_{1} \times (1 + 0.2) \]Since \( M_{1} = 4000 \text{ million} \):\[ M_{2} = 4000 \times 1.2 \]\[ M_{2} = 4800 \text{ million} \]

- Calculate the GDP Deflator in Year 2

According to the Quantity Theory of Money, if \( V \) and \( Y \) remain constant, then the price level \( P \) will adjust proportionally to the change in \( M \). Therefore, \[ P_{2} = P_{1} \times (1 + 0.2) \]Given: \( P_{1} = 200 \)\[ P_{2} = 200 \times 1.2 \]\[ P_{2} = 240 \]

- Real GDP in Year 2

Given that the economy is at full employment and assuming that real GDP remains the same in Year 2:\[ Y_{2} = Y_{1} = 400 \text{ million} \]

- Velocity of Circulation in Year 2

If the Quantity Theory of Money holds and the real GDP and the GDP deflator adjust as calculated, the velocity of circulation remains constant because there is no change in \( Y \) and \( V \) with the increase in money supply.\[ V_{2} = V_{1} = 20 \]

Key concepts

GDP Deflator

The GDP Deflator is a measure of the price level of all goods and services included in a country's gross domestic product (GDP). It's an important indicator to understand the inflation rate and the health of the economy. The GDP deflator can be calculated using the formula: \[ \text{GDP Deflator} = \frac{\text{Nominal GDP}}{\text{Real GDP}} \times 100 \] This ratio compares the current prices with the base year prices. If the deflator increases, it indicates that the price level has risen in comparison to the base year.
In Year 1 from our example, the GDP deflator is 200, meaning prices have doubled compared to the base year. To calculate the GDP deflator for Year 2, if the price level adjusts with the same proportion as the money supply (as per the quantity theory of money), we use the following: \[ P_2 = P_1 \times (1 + 0.2) \] Since the GDP deflator in Year 1 \[ P_1 = 200 \] So, \[ P_2 = 200 \times 1.2 = 240 \] Hence, the deflator increased by 20%, reflecting the rise in the money supply.

Real GDP

Real GDP measures the value of economic output adjusted for price changes (inflation or deflation). It shows the true growth of the economy by using constant prices from a base year, giving us a more accurate depiction of economic health. In Year 1, as given in our problem, the real GDP is 400 million dollars. Assuming the economy is at full employment, the real GDP remains constant, reflecting the total economic output unaffected by inflation.
Thus for Year 2, even with a 20% increase in the money supply, since the real output is assumed unchanged, we get: \[ Y_2 = Y_1 = 400 \text{ million} \] Real GDP is crucial because it portrays actual growth and helps in comparing economic productivity over time without price level distortions.

Velocity of Circulation

The velocity of circulation (often just called 'velocity') is how frequently money is turned over in an economy over a certain period. It indicates the efficiency with which money is used to generate economic activity. According to the Quantity Theory of Money: \[ MV = PY \] where \( M \) is the money supply, \( V \) is the velocity, \( P \) is the price level (GDP deflator), and \( Y \) is the real GDP. In Year 1, the velocity of circulation \[ V = 20 \]
If \( V \) and \( Y \) are constant according to the theory and the economy is at full employment, \[ V_2 = V_1 = 20 \]
Thus, the velocity remains unchanged despite the 20% increase in the money supply. This constancy holds as long as there's no structural change in the economy's financial facilities or spending habits.

Money Supply

The Money Supply is the total amount of monetary assets available in an economy at a specific time. It comprises various forms of money including coins, currency, and balances held in checking and savings accounts. The Quantity Theory of Money, which states \[ MV = PY \] links money supply \( M \) directly to nominal GDP, holding the velocity \( V \) and real GDP \( Y \) constant.
In Year 1, the money supply is calculated as follows: \[ M = \frac{P \times Y}{V} = \frac{200 \times 400}{20} = 4000 \text{ million dollars} \] For Year 2, given that the money supply increases by 20%, we compute: \[ M_2 = 4000 \text{ million} \times 1.2 = 4800 \text{ million} \]
Understanding the money supply helps in analyzing inflationary trends, implementing monetary policies, and assessing the overall economic stability.