Some Math: Difference between revisions
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S=B=N+D+K | S=B=N+D+K | ||
?=rbB- rdD- C- L | ?=rbB- rdD- C- L | ||
where: | where: | ||
?= expected profit | ?= expected profit | ||
rb=rate on bills | rb=rate on bills | ||
rd=rate on deposits | rd=rate on deposits | ||
C= operating costs | C= operating costs | ||
L=expected liquidity costs | L=expected liquidity costs | ||
S=specie | S=specie | ||
P= % adjustment cost for impending specie deficiency. Assumed to be constant | P= % adjustment cost for impending specie deficiency. Assumed to be constant | ||
X= net specie outflow during the given period | X= net specie outflow during the given period | ||
P(X? N,D)= the pdf of X given N and D | P(X? N,D)= the pdf of X given N and D | ||
C= f (S,B,N,D) | C= f (S,B,N,D) | ||
L= g (S, N, D) | L= g (S, N, D) | ||
L= s ? p(X-S) P(X? N,D)dX | L= s ? p(X-S) P(X? N,D)dX | ||
L(s)<0 | L(s)<0 | ||
L(n)>0 | L(n)>0 | ||
L(d)>0 | L(d)>0 | ||
Revision as of 06:09, 4 December 2006
S=B=N+D+K
?=rbB- rdD- C- L
where:
?= expected profit
rb=rate on bills
rd=rate on deposits
C= operating costs
L=expected liquidity costs
S=specie
P= % adjustment cost for impending specie deficiency. Assumed to be constant
X= net specie outflow during the given period
P(X? N,D)= the pdf of X given N and D
C= f (S,B,N,D)
L= g (S, N, D)
L= s ? p(X-S) P(X? N,D)dX
L(s)<0
L(n)>0
L(d)>0
From these partial derivatives, it follows that expected liquidity costs decrease when S increases. Also, L increases when N and D increase. Finally, let us solve this using a Lagrangian:
TRY TO WRITE THIS DIRECTLY ON THE WEBSITE- PG 43 OF COMPETITION AND CURRENCY
This model was presented by Lawrence H. White.
