a)
To plot:Graphical representation of inflation rates.
a)
Answer to Problem 8NP
Explanation of Solution
Given Information:
Given the following information:
L = 0.2Y-500i
L = M/P
Y = 1000
r = 0.04
i = r + inflation(p)
Where,
i is the nominal interest rate
r is the real interest rate
M is the nominal money supply
L is the real money demand
Substitute the value of nominal interest rate into the equation of real money demand to get:
Since at equilibrium L = M/P, therefore,
Formula to calculate seignorage revenue is:
Substituting equation (1) in the above equation to get
Plotting the above equation for values of p = 0, 0.02, 0.04...0.3 in the form of a graph gives the following:
Table-1
Inflation | Revenue |
0 | 0 |
0.02 | 3.4 |
0.04 | 6.4 |
0.06 | 9 |
0.08 | 11.2 |
0.1 | 13 |
0.12 | 14.4 |
0.14 | 15.4 |
0.16 | 16 |
0.18 | 16.2 |
0.2 | 16 |
0.22 | 15.4 |
0.24 | 14.4 |
0.26 | 13 |
0.28 | 11.2 |
0.3 | 9 |
Introduction:
Inflation is the persistent increase in price level over a short period of time.
b)
Inflation rate that maximizes seignorage.
b)
Answer to Problem 8NP
Inflation rate that maximizes seignorage is 0.18.
Explanation of Solution
Given Information:
L = 0.2Y-500i
L = M/P
Y = 1000
r = 0.04
i = r + inflation(p)
Where,
i is the nominal interest rate
r is the real interest rate
M is the nominal money supply
L is the real money demand
Inflation | Revenue |
0 | 0 |
0.02 | 3.4 |
0.04 | 6.4 |
0.06 | 9 |
0.08 | 11.2 |
0.1 | 13 |
0.12 | 14.4 |
0.14 | 15.4 |
0.16 | 16 |
0.18 | 16.2 |
0.2 | 16 |
0.22 | 15.4 |
0.24 | 14.4 |
0.26 | 13 |
0.28 | 11.2 |
0.3 | 9 |
As it can be seen from the above table, value of seignorage revenue gets maximized at the inf1ation rate of 0.18.
Introduction:
Inflation is the persistent increase in price level over a short period of time.
c)
Maximum amount of seignorage revenue.
c)
Answer to Problem 8NP
The maximum amount of seignorage that is earned is 16.2 units.
Explanation of Solution
Given Information:
L = 0.2Y-500i
L = M/P
Y = 1000
r = 0.04
i = r + inflation(p)
Where,
i is the nominal interest rate
r is the real interest rate
M is the nominal money supply
L is the real money demand
Inflation | Revenue |
0 | 0 |
0.02 | 3.4 |
0.04 | 6.4 |
0.06 | 9 |
0.08 | 11.2 |
0.1 | 13 |
0.12 | 14.4 |
0.14 | 15.4 |
0.16 | 16 |
0.18 | 16.2 |
0.2 | 16 |
0.22 | 15.4 |
0.24 | 14.4 |
0.26 | 13 |
0.28 | 11.2 |
0.3 | 9 |
The maximum amount of seignorage that is earned is 16.2 units by referring to above table.
Introduction:
Total revenue is calculated by multiplying price into Quantity. It is the sale amount which is earned.
d)
Graphical representation of inflation rates, maximum value of inflation and revenue when Y = 1000 and r 0.08.
d)
Answer to Problem 8NP
Revenue of seignorage is maximized (at the value of 12.8) at inflation rate of 0.16.
Explanation of Solution
Given Information:
L = 0.2Y-500i
L = M/P
Y = 1000
r = 0.08
i = r + inflation(p)
Where,
i is the nominal interest rate
r is the real interest rate
M is the nominal money supply
L is the real money demand
At equilibrium L = M/P, therefore,
For Y = 1000 and r = 0.08 gives the result as:
Table-2
Inflation | New Revenue |
0 | 0 |
0.02 | 3 |
0.04 | 5.6 |
0.06 | 7.8 |
0.08 | 9.6 |
0.1 | 11 |
0.12 | 12 |
0.14 | 12.6 |
0.16 | 12.8 |
0.18 | 12.6 |
0.2 | 12 |
0.22 | 11 |
0.24 | 9.6 |
0.26 | 7.8 |
0.28 | 5.6 |
0.3 | 3 |
Revenue of seignorage is maximized (at the value of 12.8) at inflation rate of 0.16.
Introduction:
Inflation is the persistent increase in price level over a short period of time.
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