In the economy of Brightland, the commercial banks have deposits of $600 billion. Their reserves are $60 billion. All reserves are in deposits with the Central Bank and the commercial banks hold no excess reserves

There is $120 billion in Central Bank notes outside the banks, and there are no coins. a) What is the economy's monetary base? b) What is the quantity of money in the economy? c) Calculate the money multiplier. d) Suppose the Central Bank of Brightland undertakes an open market purchase of securities of so that the monetary base increases by $5 billion. By how much will the quantity of money change?

a) The monetary base is the sum of Central Bank notes and deposits at the Central Bank, so the monetary base is $120 billion + $60 billion= $180 billion.
b) The quantity of money equals notes plus deposits, which is $120 billion + $600 billion = $720 billion.
c) The money multiplier is (1+c)/(r + c), where c is the ratio of currency to deposits and r is the desired reserve ratio. In Brightland, the ratio of currency to deposits is
$120 billion/$600 billion = 0.2. Because there are no excess reserves, the desired reserve ratio is $60 billion/$600 billion = 0.1. So the money multiplier is (1 + 0.2 )/(0.1 + 0.2 ) = 4.0.
d) The quantity of money in the economy increases by the change in the monetary base multiplied by the money multiplier, so the quantity of money increases by
$5 × 4 billion = $20 billion.