Question

Assume that money demand takes the form 𝑀 𝑃 = 𝑌[1 − (𝑟 + 𝜋 𝑒 )] where Y = 1000 and r = 0.1.

a. Assume that, in the short run, 𝜋 𝑒 is constant and equal to 25%. Calculate the amount of seignorage for each rate of money growth, ΔM/M, listed below. i. 25% ii. 50% iii. 75%

b. In the medium run, 𝜋 𝑒 = 𝜋 = ΔM/M. Compute the amount of seignorage associated with the three rates of money growth in part (a). Explain why the answers differ from those in part (a). 

Answer 1

(a)In the short run

Signorage = $\Delta$ M/M $*M/P$

If  is 25% then amount Seigniorage is

M/P= Y(1-(r+π^e )

= 1000(1-(0.1+0.25)

=650 (0.25)

= 162.5

If  is 50% then amount Seigniorage is

=650 (0.50)

=325

If  is 75% then amount Seigniorage is

=650(0.75)

=487.5

b) In the medium

$\Delta$ M/M= π=π^e

If  is 25% then amount Seigniorage is

= 1000(1-(0.1+0.25)

=650 (0.25)

= 162.5

If  is 50% then amount Seigniorage is

= 1000(1-(0.1+0.5)

=400 (0.5)

=200

If  is 75% then amount Seigniorage is

= 1000(1-(0.1+0.75)

=150 (0.75)

=112.5

The values differ because overtime, the melt value changes as market demands shift. In the short we assume that π^e is fixed while $\Delta$ M/M is changing. In the medium run, the two are changing and equal.