Isabella David, Ilaria Laganą, Giorgia Romagnoli

Computer Science and Simulation for Economics

Project work on

"Money Multiplier."


The applet requires Java 1.4.1 or higher. It will not run on Windows 95 or Mac OS 8 or 9. Mac users must have OS X 10.2.6 or higher and use a browser that supports Java 1.4. (Safari works, IE does not. Mac OS X comes with Safari. Open Safari and set it as your default web browser under Safari/Preferences/General.) On other operating systems, you may obtain the latest Java plugin from Sun's Java site.

created with NetLogo

view/download model file: money_multiplier.nlogo


This model reproduces the mechanism of the " Money multiplier". Given a monetary base and a reserve ratio, we can observe the dynamics of the money supply curve thanks to the interaction between individuals and banks.
In our model when people go in a bank they deposit or borrow: according to the economical literature the reasons why people deposit/borrow don't matter.
To control the amount of money created by the system, central bank places
reserve ratios which set the proportion of primary deposits the banks can't lend.
We want to test if the model's results are consistent with the economical theory. Moreover our aim is to observe the variables' behaviour during the process.


At the beginning each turtle has got a fixed size (0.6) and an equal amount of currency.
When the system starts running, turtles interact with banks and on the strenght of the theory, turtles behave following few simple rules: when they are on a bank, if they have an higher amount of currency than that depending on the cash ratio they deposit it else they borrow. In the first case, according to the reserve ratio, bank makes available for loaning only a part of the deposit, which we call "loan" while the other one is defined as "fund". In the other case they borrow all the bank's resources available for loaning, so they have an excess of currency again that will be deposit the next time.
In order to make this process visible we associate each state (borrowing/depositing)to a specific turtle's size (0.6/0.3).
In order to observe how much time is necessary to reach the equilibrium we introduce two variables, called "cycles" and "time".
The first one represents the number of cycles done by the system; the second one starts increasing with cycles and it stops when the observed money supply is near to the theorical value.


Start the simulation by clicking "setup".
Then, after clicking "go", the turtles start moving and interacting in the way explained above; they keep on doing so until the "go" button remains pressed.

Buttons: setup
resets everything to the random-beginning values and releases in the simulated economy a number of turtles which can be chosen by the "number of turtles" slider.

Buttons: go
if clicked, the model starts running.

Buttons: go once
if clicked, the model runs once.

Sliders: turtles-number
on the bottom of the screen, this slider allows you to choose the number of turtles you'd like to start the simulation with.

Sliders: banks_number
this slider allows you to change the number of banks.

Sliders: money_base
this slider allows you to change the monetary base in the system.

Sliders: cash_ratio
this slider allows you to change the quota of money that turtles want to have as cash.

Sliders: reserve_ratio
this slider allows you to change the reserve ratio fixed by Central Banks.

on the left of the screen,
there are six monitors which show:
the total amount of currency
the total amount of deposit
the total amount of money supply
the total amount of fund

Plot: money supply, deposit and currency
this plot shows the trend of these three variables

Plot: fund and deposit
this plot indicates the trend of bank's funds and deposits.


First of all, we noticed that when two or more agents are at the same time on a bank, the sum of total fund and total currency excesses the amount of the initial money base. This result is in contrast with both theory and good sense.
Accordingly we have assumed that an agent interacts with the bank only if he is alone.
It's important to observe how some variables affect the model. In particular different values of the variables "banks_number", "reserve_ratio", "cash_ratio" and "money base" require a different number of cycles necessary to reach the equilibrium ("time"). For the reason expressed before, changing the number of turtles is not significant.

By running the model a lot of times it's possible to notice:
- an inverse proportion between cash ratio and "time"
- an inverse proportion between reserve ratio and "time"
- an inverse proportion between banks' number and "time" (in this case the relation between the two variables is not so strong as in the two case analysed before)
- relation between "money base" and "time" is not evident.


Move the slider of "banks_number". How does this variation affect the results of the model? Does the number of cycles change in a remarkable way?

Try different amount of "money_base". Which are the effects on the model?

Try different values of "reserve_ratio". Which are the effects on the model if Central Bank decreases the reserve ratio?

Try different values of "cash_ratio". How does the model change if cash ratio increases?


The model could be extended by making it more complex and near to reality.For example we could introduce an interaction between turtles making them exchange money so they borrow for a specific reason.


O. Blanchard "Macroeconomics", 3rd edition.