Monetary Circuit Model/Lending and Repayment

In this lesson, we will extend the skeleton model to include lending and repayment of loans, without interest or any other transactions.

The Code

First, we set up the parameters of the model. These go before the definition of the ODE system:

# Rate of cash outflow from the bank vault
bvo = 3.0 / 4.0
# Repayment rate of loans (debt turned over every 7 years)
rr = 1.0 / 7.0

lend = bvo * bv
repay = rr * fl

The variable "lend" represents the flow of money lent by the banking sector. We assume that this is proportional to the amount of capital the bank has available, its "cash in the vault." One possible interpretation is that as the bank lends out money, its desire for liquidity makes it less willing to finance investment projects, especially high risk ones.

Repayment is assumed to be proportional to the amount of outstanding debt. Both bvo and rr are annualized rates: banks lend 3/4 of their reserves per year and

Next, we modify our ODE system to include the new flows:

# ODE system
des = [
	diff(bv, t) == repay - lend,
	diff(bt, t) == 0,
	diff(fl, t) == lend - repay,
	diff(fd, t) == lend - repay,
	diff(wd, t) == 0
	]

What this says is that, when a loan is made, cash is transferred from the bank vault, bv, to firm deposits, fd. Similarly, when firms repay their loans, money is transferred from firm deposits back to the bank vault. fl serves to record the debt level of firms. In this model, fl and fd are equal since the only way for firms to get cash is to borrow it.

The result should look like this:

The model reaches an equilibrium when the rate of lending is equal to the rate of repayment. The exact level is determined by the liquidity preference of banks and firms. We will see in a later lesson how a sudden change in liquidity preference - a credit crunch - can affect the level of economic activity.

In the next lesson, we will add transactions between firms and workers.