Some Math: Difference between revisions
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The following explanatory model was presented by Lawrence H. White. | |||
These are the terms used in the formulation | |||
?= expected profit | ?= expected profit | ||
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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 | |||
S=B=N+D+K | |||
?=r<sub>b</sub>- r<sub>d</sub>D- C- L | |||
C= f (S,B,N,D) | C= f (S,B,N,D) | ||
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L= g (S, N, D) | L= g (S, N, D) | ||
L= ?<sub>s</sub> <sup>?</sup> p(X-S) P(X? N,D) | L= ?<sub>s</sub><sup>?</sup> p(X-S) P(X? N,D)dx | ||
L(s)<0 | L(s)<0 | ||
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TRY TO WRITE THIS DIRECTLY ON THE WEBSITE- PG 43 OF COMPETITION AND CURRENCY | TRY TO WRITE THIS DIRECTLY ON THE WEBSITE- PG 43 OF COMPETITION AND CURRENCY | ||
Revision as of 22:19, 4 December 2006
The following explanatory model was presented by Lawrence H. White.
These are the terms used in the formulation
?= expected profit
r b =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
S=B=N+D+K
?=rb- rdD- C- L
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
