The Fed uses many tools to influence economic conditions but their three most common include: 1. Open-Market Operations (OMOs) - the purchase and sale of U.S. government securities. 2. Reserve Requirements (RR): affects how much money banks can create by making loans. 3. The Discount Rate - The interest rate on loans the Fed makes to banks.

Here are annual values for M2 and for nominal GDP (all figures are in billions of dollars) for the mid-1990s.

 Year          M2        Nominal GDP

1993     3,482.0         $6,657.4

1994     3,498.1         $7,072.2

1995     3,642.1         $7,397.7

1996.    3,820.5         $7,816.9

1997     4,034.1         $8,304.3

1. Compute the velocity for each year.

According to the equation of exchange in the textbook, the relationship between money supply, velocity, and nominal GDP can express like the equation below:

 Suppose that the M=money supply=M2, V=velocity, then

MV = nominal GDP

V = (nominal GDP)/M 

So, the velocity each year on the list will be:

Year.                   Velocity

1993                    6,657.4/3,482.0 = 1.912

1994.                  7,072.2/3,498.1 = 2.022

1995                   7,397.7/3,642.1 = 2.031

1996                   7,816.9/3,820.5 = 2.046

1997                   8,304.3/4,034.1 = 2.059

2. Compute the fraction of nominal GDP that was being held as money.

According to the textbook, the equation of exchange can express the demand for money as a percentage, given by 1/V, of nominal GDP. With a velocity of V, for example, people wish to hold a quantity of money equal to 1/V of nominal GDP.

So, the velocity each year on the list will be:

Year.                   Being Held

1993                    (6,657.4)*(1/1.912)=3481.90

1994.                   (7,072.2)*(1/2.022)=3497.63

1995                    (7,397.7)*(1/2.031)=3642.39

1996                    (7,816.9)*(1/2.046)=3820.58

1997                    (8,304.3)*(1/2.059)=4033.17

3. What is your conclusion about the stability of velocity in this five-year period?

In this case, during the five-year period, the stability of velocity might due to the stability of the interest rate. People do not like to hold something that expected to lose their value. The interest rate will affect the extra money that people can earn from deposit it more. The reason for the stability of velocity is likely to be a stability of interest rate policy.

Another reason for this case is possibly the expectation of stability. The expectation of deflation or inflation will affect the money people want to hold, they can turn their money back really fast these days. 

Here are annual values for M2 and for nominal GDP (all figures are in billions of dollars) for the mid-2000s.

Year.        M2                Nominal GDP

2003        6,055.5                $10,960.8

2004        6,400.7                $11,685.9

2005        6,659.7                $12,421.9

2006        7,012.3                $13,178.4

2007        7,404.3                $13,807.5

1. Compute the velocity for each year.

Suppose that the M=money supply=M2, V=velocity, then

MV = nominal GDP

V = (nominal GDP)/M 

So, the velocity each year on the list will be:

Year.                           Velocity

2003                            10,960.8/6,055.5 = 1.810

2004.                           11,685.9/6,400.7 = 1.826

2005                            12,421.9/6,659.7 = 1.865

2006                            13,178.4/7,012.3 = 1.879

2007                            13,807.5/7,404.3 = 1.864

2. Compute the fraction of nominal GDP that was being held as money.

Year.                      Being Held

2003                       (10,960.8)*(1/1.810)=6055.69

2004.                      (11,685.9)*(1/1.826)=6399.73

2005                       (12,421.9)*(1/1.865)=6660.54

2006                       (13,178.4)*(1/1.879)=7013.51

2007                       (13,807.5)*(1/1.864)=7407.45

3. What is your conclusion about the stability of velocity in this five-year period?

In this five-year period, people hold more and more money. And in the short run, it is not reasonable to assume that velocity and output are constants. Due to the expectations of the interest rate, people adjust their holding to react to the condition. In this case, people are likely to expect that there are some reasons for them to increase their holdings.

Suppose the velocity of money is constant and potential output grows by 3% per year. By what percentage should the money supply grow in order to achieve the following inflation rate targets?

Suppose that :

%ΔM = the percentage rates of change in the money supply

%ΔP = the percentage rates of change in the price level

%ΔYp = the percentage rates of change in the real GDP(potential output)

%ΔM ≌ %ΔP + %ΔYp

%ΔP ≌ %ΔM - %ΔYp

If the velocity of money is constant and potential output grows by 3% per year

1. 0% 

If the rate of inflation, %ΔP = 0% is our target, then

%0 ≌ %ΔM - 3%

%ΔM = 3%

The money supply should grow 3%, in order to achieve the inflation rate targets 0%

2. 1% 

If the rate of inflation, %ΔP = 1% is our target, then

%1 ≌ %ΔM - 1%

%ΔM = 2%

The money supply should grow 2%, in order to achieve the inflation rate targets 1%

3. 2%

If the rate of inflation, %ΔP = 2% is our target, then

%2 ≌ %ΔM - 2%

%ΔM = 4%

The money supply should grow 4%, in order to achieve the inflation rate targets 2%