The Demand for Money When Firms Hold Balances As Payment for Services

Cover The Demand for Money When Firms Hold Balances As Payment for Services
The Demand for Money When Firms Hold Balances As Payment for Services
David Sullins
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(M)) Minimizing cost as' before, we find C* at M* such that '-'' \-^ =^L-^F^M=^L-^S = -i* 3R, Wlici-G i-g= -^, tlic marp. Innl savings resulting from a small increment in M, is again the shadow rate on deposits from the firm's viewpoint.
'Hie sufficient condition for a minimum is satisfied since, from our assumptions.
S^C, -T ™y, , 2, '^', 3^ 3R' Again 5. 12 71 = r (1 - A)M - R„(S, (M)) L B M 5. 13 J = TT - C* = -r 6M'^ ^6M* _ T(M*) + R^, (Sj^j(M*)) - Rg(Sj^^(M*)) and now from 5. 2 and 5. 3 37
...5. U J = - r_ 6M* - T(M*) -f (P^('%, ) - P^(^M^^ (S, (M*)) for S^^ > S'V 'llie bank inin Ltiii zes J by deterininirii; S' M 8r M ( r f. -'^ + R'c;' _R'ctN iljl S 3S' " ^' \^ SM ^ ^F^M ^B^M-* Or, 3S' M b M and substituting for - —7— from 5. 11 dn 8r ^ = (r (1 -, S) - R'S') — -4 M b M 3M ^''S Since it is demonstrated in tlie appendix that -r —, > J* is found at 5. 15 ^^'q^^^'' = r^^d - «) (Note that R^S^^ = r^ from 5. 4) or 3S„ ^ r^ (1-6) r, (1-6) r, (1-6) 5. 16a S'* = ( —~t) M 3M*-' 0R„ r; c •> S B S dp ^ 'It'- , 2, Unfortunately, the sign of — ^ is no longer unambiguous.

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