Question

The total money supply M has two components: bank deposits D and cash holdings C which we assume to bear a constant ratio C/D money H is defined as the sum of cash holdings held by the public and the reserves held by the banks. Bank reserves are a fraction of bank deposits, determined by the reserve ratio r, 0 <r<1 c, 0 < c< 1. The high-powered (a) Express the money supply M as a function of high-powered money H. (b) Would an increase in the reserve ratio r raise or lower the money supply? (c) How would an increase in the cash-deposit ratio caffect the money supply!?

Answer 1

a)

When people can hold both currency and chequable deposit then the demand for money malies a steps: people must decide how much money to hold they must decide how much of this money to hold in currency and in chequeable deposit. the overall money demand tn. can be expressed as Md = PYL(2) Assume that people hold a fixed propoction of their money in currency and remaining in choqueable deposit suppose that people hold a fraction ic'in

. currency and remaining fraction Clov) in chequeable of deposit ! . Demand fou, currency and demand for chequeable deposit can be expressed as: cudz c Mid - o g le+ (1-0) of PYLOW D C i- c ) Md ② Larger will be the amount of chequable debout, lager will be the amount of reserve that banks must hold fore precautionary season and legal Meason, Let o be rescere eatio, so we get following on - R Q - o zrlD OP D RO'D - R = OD - 7 of people want to hold deposit Dd then barks must hold leserwes equal to oD. sine, demende for deposit es Da Cl-) Mo 2. Demand foll Meslewe will be R = 0 [l-cmd - andet het demand fou central bank money be Hd and it has 2 components ie, demand fore werrency and the demand fore ressure of so Hd = Cudt Rd a ic Md t o [C-ond] Ho a Maric to Cl-(c) ] 6. finee money demand fr. is indo pyli) se Ha=PY . Li) [ ct OC l-UE) 4.

Let supply of central bank money be t so, at equilibrin demand fore central bank, money must be equal to supply of centeal bank money. 45=Hd & H = /uct Cro) o JPY Lci) i, date at which central bank gives money to commerid Mda Cult Rd banks. AS Dividing both side of egn. by Iuct Ciclo L 4 = PY Pci-M Iic+Cl-co
The last equation gives the required relation.

B)

From the last equation it can be seen that the reserve ratio is indirectly proportional to money supply. Thus, an increase in reserve ratio decreases the money supply.

C) An increase in Cash-deposit ratio would also lower the money supply.