Question

Consider a simple economy in which money supply (think of M1) is determined through actions of the central bank, non-bank public, and commercial banks. Assume that the central bank influences the size of the monetary base and the public and commercial banks decide on the value of deposits and excess reserves.

i) Imagine that in a given point in time the value of the monetary base is equal to 100, the public chooses not to hold any currency, and commercial banks hold only required reserves, which are supposed to be equal to 10% of checkable deposits. What is the value of money supply in this case?

ii) Now, assume that commercial bank choose to hold excess reserves. Specifically, assume that they hold twice as much as they are required. What do you expect the money supply to be now?

iii) Now, assume that the public chooses to split their portfolios equally between currency and deposits. What is the value of the money multiplier in this case?

iv) Continue with assumptions of ii) and iii). What would be the instantaneous impact on money supply if the central bank engaged in a purchase of securities worth 10 through an open market operation?

Answer 1

Answer i

Money supply = Monetary Base/ Reserve Requirement (RR) = 100/10% = 100/0.1 =1000

Hence money supply =1000

Answer ii

If Banks are holding twice the reserve requirement means reserve for banks is 10%*2 =20%

Hence Money supply = Monetary Base/ Reserve = 100/20% = 100/0.2 =500

Hence money supply =500

Answer iii

When public is splitting the portfolio equally between currency and deposits means currency holding ratio (CR) is 50%

Money Supply = Monetary Base* (CR+1)/(CR=RR) = 100*(50%+1)/(50%+20%)=100*(1+0.5)/(0.5+0.2)= 100*1.5/0.7 = 214.286

Hence money supply =214.286

Answer iv

If central bank purchased securities worth 10 means it has increased the monetary base by 10. Hence new monetary base will be 100+10 =110

Hence Money Supply = Monetary Base* (CR+1)/(CR+RR) = 110*(50%+1)/(50%+20%)=110*(1+0.5)/(0.5+0.2)= 110*1.5/0.7 = 235.7

Hence money supply =235.7

Hence money supply has increased by 235.7-214.286 = 21.42