Questions: The velocity of circulation is growing at 3 percent a year, the real interest rate is 3 percent a year, the nominal GDP grows at 5 percent a year, and the growth rate of nominal GDP is 5 percent a year. Calculate the inflation rate, the growth rate of money, and the growth rate of nominal GDP. The inflation rate is percent a year. The growth rate of money is percent a year. The growth rate of nominal GDP is percent a year.

The velocity of circulation is growing at 3 percent a year, the real interest rate is 3 percent a year, the nominal GDP grows at 5 percent a year, and the growth rate of nominal GDP is 5 percent a year.

Calculate the inflation rate, the growth rate of money, and the growth rate of nominal GDP.

The inflation rate is percent a year.

The growth rate of money is percent a year.

The growth rate of nominal GDP is percent a year.

Transcript text: The velocity of circulation is growing at 3 percent a year, the real interest rate is 3 percent a year, the nominal GDP grows at 5 percent a year, and the growth rate of nominal GDP is 5 percent a year. Calculate the inflation rate, the growth rate of money, and the growth rate of nominal GDP. The inflation rate is percent a year. The growth rate of money is percent a year. The growth rate of nominal GDP is percent a year.

Solution

To answer the question, we need to use the Quantity Theory of Money, which is represented by the equation:

\[ MV = PY \]

where:

\( M \) is the money supply
\( V \) is the velocity of money
\( P \) is the price level
\( Y \) is the real GDP

Given the information:

The velocity of circulation (\( V \)) is growing at 3 percent a year.
The real interest rate is 3 percent a year (though this is not directly needed for the calculations).
The nominal GDP (\( PY \)) grows at 5 percent a year.

We need to find:

The inflation rate (\( \pi \)).
The growth rate of money (\( \Delta M \)).
The growth rate of nominal GDP (\( \Delta (PY) \)).

Step-by-Step Solution:

Growth Rate of Nominal GDP: The growth rate of nominal GDP is given directly as 5 percent a year.

\[ \Delta (PY) = 5\% \text{ per year} \]
Inflation Rate: The growth rate of nominal GDP (\( \Delta (PY) \)) can be broken down into the growth rate of the price level (\( \pi \)) and the growth rate of real GDP (\( \Delta Y \)).

Since the real interest rate is not directly needed, we assume the real GDP growth rate is not provided. However, we can use the given information to find the inflation rate.

Using the Quantity Theory of Money, we know:

\[ \Delta (PY) = \Delta M + \Delta V \]

Given: \[ \Delta (PY) = 5\% \] \[ \Delta V = 3\% \]

Rearranging the equation to solve for the growth rate of money (\( \Delta M \)):

\[ \Delta M = \Delta (PY) - \Delta V \] \[ \Delta M = 5\% - 3\% \] \[ \Delta M = 2\% \]
Growth Rate of Money: The growth rate of money is 2 percent a year.

\[ \Delta M = 2\% \text{ per year} \]
Inflation Rate: The inflation rate (\( \pi \)) can be found using the relationship between nominal GDP growth, real GDP growth, and inflation. Since we do not have the real GDP growth rate, we assume it is implicitly included in the nominal GDP growth rate.

Therefore, the inflation rate is the difference between the nominal GDP growth rate and the real GDP growth rate. Given the nominal GDP growth rate is 5 percent and assuming real GDP growth is not provided, we can infer:

\[ \pi = \Delta (PY) - \Delta Y \]

Since we do not have the real GDP growth rate, we assume it is zero for simplicity:

\[ \pi = 5\% - 0\% \] \[ \pi = 5\% \]