Question

3. Suppose that in 2005 in Monetaria the money supply is 10,000 and the nominal GDP is 20,000.

A) Find the velocity of circulation V for 2005.

B) In 2018 the money supply was 18,850. The real GDP for 2018 was 29,370 in 2005 dollars. Find the average growth rate of the money supply and the average growth rate of real GDP. (Hint: what is the relationship between real and nominal GDP for the base year?)

C) Assuming that the velocity of circulation has stayed constant from 2005 to 2018, what was the inflation rate between those years?

D) Suppose that the real interest rate in Monetaria has been stable at 4% (0.04 as a fraction.) What was the nominal interest rate over that time frame?

Answer 1

A). For the Year 2005 we have been asked to find Velocity of circulation, we have following information:

Money Supply = 10,000

Nominal GDP = 20,000

We have Fisher's Quantity of Equation as:

MV = PT, M= Money Supply, V = Velocity of circulation, P = Price Level, T = Real GDP,

PT can be collectively read as Nominal GDP so PT = 20,000.

So, M V = P T

or, 10,000 * V = 20,000

or, V = 2.

Hence, the veloity of circulation is 2.

B). For the Year 2005,

Money Supply for 2005 = 10,000. Now for since 2005 is Base Year so, we have Real GDP = Nominal GDP,

So Real GDP for 2005 = Nominal GDP for 2005 = 20,000.

For the Year 2018,

Money Supply for 2018 = 18,850, Real GDP = 29,370.

Now we will cacluate growth rates:

Growth Rate of Money Supply = ( Money Supply for 2018 - Money Supply for 2005 ) / Money Supply for 2005

= ( 18,850 - 10,000 ) / 10,000  

= 8,850 / 10,000

= 0.885

= 88.5 %

Growth Rate of Real GDP = ( Real GDP for 2018 - Real GDP for 2005) / Real GDP for 2005

= ( 29,370 - 20,000 ) / 20,000

= 9,370 / 20,000

= 0.4685

= 46.85%

C). Given Constant Velocity of Circulation which means that there is no growth in velocity of Circulation.

Fisher Quantity theory of money equation in growth terms:

ΔM + ΔV = ΔP + ΔT

We have ,

ΔM = Growth in Money Supply=  88.5 % ; ΔT = Real GDP Growth = 46.85% as obtained in answers to Previous question.

So putting these values in the growth equation of Fisher Quantity theory of money:

ΔM + ΔV = ΔP + ΔT

or, 88.5% + 0 = ΔP + 46.85%

or, ΔP = 88.5% - 46.85% = 41.65 %

Hence, the Inflation Rate between 2005 to 2018 has been 41.65 %.

D). In the question it is given that Real Interest Rate has been 4% from 2005 to 2018.

Inflation Rates for 2005 to 2018 has been found in the answer to previos question as 41.65 %.

We have to find Nominal Interest Rate for the above mentioned period.

As per the Fisher Effect Equation we have:

Nominal Interest Rate = Real Interest Rate + Inflation Rate

Putting these values in the equation we have:

Nominal Interest Rate = 4% + 41.65 % = 45.65 %.

Hence, Nominal Interest for the time frame has been  45.65 %.