2 Models of money creation
2.1 The static multiplier
Standard macroeconomic theory explains the amount of money available in an
economy starting from the monetary base (H), which is composed of currency
held by the public (CU) and reserves held by the banking sector (R).5 The money
multiplier is simply derived as the ratio between the monetary base provided
by the central bank and a monetary aggregate (M), composed of currency (CU)
and deposits (D):6
H = CU + R
M = CU + D,
(1)
(2)
= CU∕D, re = R∕D, it
(3)
from which, dividing everything by D and defining cu
follows that
M 1 + cu
m = H = cu + re ’
The standard money multiplier represents therefore an aggregate characteris-
tic of the economy, with essentially no behavioural content. Nevertheless, the
ratios re and cu are often taken to represent agents’ individual preferences, as-
sumed constant and homogeneous. The whole approach is essentially static and
neglects completely the process through which money is created.
2.2 A dynamic version of the multiplier
We present here a different way to obtain the multiplier: instead of using ratios
of aggregate quantities, we consider the dynamic process that unfolds through
monetary and credit transactions. We start with an increase in monetary base,
in the form of an increase in funds available to the public. Suppose we are in
a situation where households have exactly the proportion of cash∕deposits (cu)
that they wish, and banks have the proportion of reserve∕deposit (re) that they
want to hold. Therefore households will split the additional funds they receive
between deposits and cash, in the proportion cu. Banks in turn will keep a
fraction (re) of the additional deposits they receive as reserves and use the rest
to extend new loans (L) to the public, who will split them again into cash and
deposits, and the process continues.7
From the definitions above, we get that at each step i of the process:8
5It is customary not to distinguish between households and firms, and consider them as an
aggregate entity (the public). We will follow here this simplification as well.
6In this work we will refer to a generic monetary aggregate M, which could be understood
as Ml in US or Europe.
7The following restrictions apply: 0 ≤ re ≤ 1, cu ≥ 0.
8Here CUi is the additional amount of cash available at time i with respect to time i-1,
not the total cash available at time i. The same for the other variables here used.