Microeconomics,, 16th Canadian Edition

35. Suppose the public wants to hold a fraction, c, of deposits in cash,
    C. Now suppose that X dollars are injected into the system.
    Ultimately, this money will be held either as reserves by the
    banking system or as cash by the public. Thus, we have

From the banking system’s reserve behaviour, we have

, and from the public’s cash behaviour, we have

. Substituting into the above equation, we get the
result that

From this we can also relate the change in reserves and the

change in cash holdings to the initial injection:

For example, when and , an injection of $100
will lead to an increase in reserves of $80, an increase in cash in
the hands of the public of $20, and an increase in deposits of
$400.
36. Let d be the government’s debt-to-GDP ratio and let be the
annual change in d. The percentage change in d over the year is

ΔC+ΔR=X

ΔR=v⋅ΔD

ΔC=c⋅ΔD

ΔD=vX+c

ΔR = ⋅X

ΔC = ⋅X

v+vc

v+cc

v=0.20 c=0.05

Δd