Question

The answers are filled in but I have no idea how to work, can you walk be through steps to solve please, trying to work out similar problem. Thank you

Real money demand in an all currency economy with fixed real output and real interest rate and constant money growth and inflation rates is L 0.25Y 520i, where Y is real income and i is the nominal interest rate. In equilibrium, real money demand, L, equals real money supply, M/P. Suppose that Yis 600 and the real interest rate, r, is 0.07 a. What inflation rate maximizes seignorage? 0.11 (Round to two decimal places.) [Hint: Use calculus to maximize seignorage, or generate a table to calculate seignorage revenue for every.02 rates of inflation between 0.00 and 0.30.] What is the maximum amount of seignorage revenue? 6.20 (Round to two decimal places.) b. Repeat Part (a) for the case in which Y 700 and r 0.08. What inflation rate maximizes seignorage? 0.13 (Round to two decimal places.) What is the maximum amount of seignorage revenue? 8.55 (Round to two decimal places.)

Answer 1

Real money demand equation is given as:

Ld0 0.25Y 520i

(i here is nominal interest rate)

Real money supply equation is given as:

$L^s = \frac{M}{P}$

Using fischer's equation, we know:

irT

where r is real interest rate and is rate of inflation.

71

a)

Given Y = 600 and r = 0.07

Equilibrium is given as:

LdL 0.25 600 520(0.07 T)= M/P L

Seigniorage is the process of printing money by the government to finance deficits.

Mathematically Seigniorage is calculated as:

S T L(T

In our case, this will be:

ST L(T T (0.25 600 520(0.07T) T (113.6 -520T

Maximizing this with respect to inflation rate, we get:

d = 0113.6 1040 0 T = 113.6 / 1040 0.109 0.11

Seigniorage revenue is calculated as:

STL(T T(113.6 520 0.11(113.6 520 0.11) = 6.20

b)

Given Y = 700 and r = 0.08

Equilibrium is given as:

Ld L0.25 700 520(0.08 ) M/P = L

Seigniorage is calculated as:

ST L(T T (0.25 700 520(0.08 T) T (133.4 -520T

Maximizing this with respect to inflation rate, we get:

$\frac{\mathrm{d} }{\mathrm{d} \pi} = 0 \Rightarrow 133.4 - 1040\pi^* = 0 \Rightarrow \pi^* = 133.4/1040 = 0.128 \approx 0.13$

Seigniorage revenue is calculated as:

$S = \pi L(\pi) = \pi(133.4 - 520\pi) = 0.13(133.4-520*0.13) = 8.55$