Question

Based on the data bellow, answer questions A and B:

2006

Cash in Circulation: $800B

Bank reserves: $20B

Checkable Deposits: $600B

M1 Velocity: 10.2

Real GDP: $14,602B

2017

Cash in Circulation: $1,460B

Bank reserves: $2,317

Checkable Deposits: $1,985B

M1 Velocity: 5.6

Real GDP: $16,872B

a)  Calculate the average annual percentage growth M1, Velocity, and real GDP from 2006 to 2017.

b)  Calculate the annual inflation that that should be expected from 2006 to 2017.

Answer 1

M1 = cash in circulation + Checakbale deposit.

M1 in 2006 = $800B + $600B

M1 in 2006 = $1400B

M1 in 2017 = $1460B + $1985B

M1 in 2017 = $3445B

The number of years between 2017 and 2006 = 11 years.

Average annual percentage growth M1 = [(M1 in 2017 / M1 in 2006)^(1/11) ] - 1

Average annual percentage growth M1 = [($3445B / $1400B)^(1/11)] - 1

Average annual percentage growth M1 =0.085

Average annual percentage growth M1 =8.5%

Average annual percentage growth velocity = [(Velocity in 2017 / Velocity in 2006) ^ (1/11)] -1

Average annual percentage growth velocity = [(5.6 / 10.2) ^ (1/11)] - 1

Average annual percentage growth velocity =-0.053

Average annual percentage growth velocity = -5.30%

Average annual percentage growth real GDP = [(Real GDP in 2017 / Real GDP in 2006) ^ (1/11) ] - 1

Average annual percentage growth real GDP = [($16872B / $14602B)^(1 /11) ] - 1

Average annual percentage growth real GDP = 0.0132

Average annual percentage growth real GDP = 1.32%

Note: Average annual growth rate = [(Future value / Present value )^ (1 / number of years) ] - 1

(b) According to the quantity theory of money.

M * V = P * Y

where M is the M1 money supply.

V is the velocity

P is the price level

Y is the real GDP.

In terms of growth

% Change in M + % Change in V = % Change in P + % Change in Y

8.5 + (-5.30) = % change in P + 1.32

8.5 - 5.30 = % change in P + 1.32

3.2 = % change in P + 1.32

% change in P = 3.2 - 1.32

% change in P = 1.88

The annual inflation rate expected from 2006 to 2017 is 1.88%