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## (5.9)

In this model we continue to assume that commercial banks want no excess legal reserves. They will expand or contract their outstanding loans any time total reserves differ from required reserves. We now define the monetary base

where

where RR D are reserves legally required against demand deposit liabilities and RRT are reserves legally required against time deposit liabilities. Thus RRD=rDD and RR T=bTD where TD is total time deposits and b is the average legal reserve requirement on commercial bank time deposit liabilities. Thus

Hence B=R+C=rDD+bTD+C. In terms of differences,

We want again to get the total increase in money supply in response to an increase in the monetary base. Suppose that the public maintains fixed proportions between time and demand deposits where the factor of proportionality is ?, i.e. TD=?DD. Hence

so that

This gives us the increase in demand deposits. We know that ? TD= ?? DD=?[1/ (r+b?+s)]? B and ? C=[s/(r+b?+s)]? B. We know that

Equation (5.14) then relates total change in money supply to a change in monetary base.