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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