ECON 102: Monetary System Formulas
In this document, we present the most important formulas used in Module 10.
Money Creation
We first define the following variables:
• M: Money Supply
• r: The reserve ratio (it could be required or desired). ri is used when we refer to a single bank.
• c: The average proportion of money held by individuals in the form of currency.
• C: The value of coins and bank notes in circulation outside banks.
• R: The amount kept by commercial banks in reserve. Ri is used when we refer to a single bank.
• D: Total value of deposits in commercial banks. Di is used when we refer to deposits in a single bank.
Steady State
The steady state is when no commercial banks can make new loans without exceeding their reserve ratio. In the module, we refer to the steady state as: many periods or infinitely many periods following a change in the monetary system.
The Effect of an Injection of Money
If X dollars in liquidity is injected in the economy, the following formula can be used to calculate the effect on the money supply at the steady state:
∆M = X 1 + c(1 − r) , 1−(1−r)(1−c)
where ∆M means change of money supply. If individuals hold no money in the form of currency (c=0)
the formula is:
Computing the Reserve Ratio
∆M = X r
In simple models with a few banks, the reserve ratio at the steady state for each bank is: ri = Ri .
Di
If all banks have the same ratio, it is equal to
r=R.
D
Econ 102 Module 10: Formulas Page 1 of 2
The Money Supply
Quantity Equation
The quantity equation is
M=D+C
M×V=Y×P,
where V is the velocity of money, Y is the real GDP and P is the price level. The right hand side (Y × P ) is the nominal GDP. Using the growth rate approximation for the product of two variables, the equation implies the following:
∆%M + ∆%V ≈ ∆%Y + π
∆%M + ∆%V ≈ growth rate of nominal GDP ,
and
where ∆%M is the growth rate of the money supply, ∆%V is the growth rate of the velocity, ∆%Y is
the growth rate of real DGP and π is the inflation rate.
Econ 102 Module 10: Formulas Page 2 of 2