“Money and Banking”
Suppose a coupon bond has a coupon rate of 5% per year, a face value of $10,000, and a maturity of 10 years; interest payments (coupon payments) are paid semi-annually. Furthermore, assume that you can invest all you want at a rate of 8%. How much is this bond worth today?
Coupon rate= 5%
Face value= $10,000
Maturity year= 10 years
Semiannual rate= 8%
Since the interest is paid semiannually the bond interest rate per period is 2.5% (= 5% ÷ 2), the market interest rate is 4% (= 8% ÷ 2) and number of time periods are 20 (= 2 × 10). Hence, the price of the bond is calculated as the present value of all future cash flows as shown below:
Price of Bond = 91000+45,662.1= $1, 36,662.1
It is the amount of times the money has created so that any bank can lend only after the statutory reserve which can be kept with the FED. Thus money multiplier is the ration of the change in total money supply to the change in monetary base or reserve.
The money multiplier refers to how the initial deposit will lead to more big and final increase in case of total money supply.
As for example, if the commercial banks gain a deposit of £1 million as well as this has increased to the final money for supplying £10 million. There is the money multiplier is 10.
The money multiplier is considered as the key element for the fractional banking system.
1.There is the initial increase in the bank deposits which is monetary base.
2.There is the bank holds that the fraction of the deposit has reserved and also it has lends out the other rest.
3.The loan of the bank thus would be redeposited in case of further increase in case of bank lending which increase with the money supply.
In fact, money multiplier is the reverse ratio of reserve ration in FED. If in any case the Federal Reserve ratio increases, the monetary base by one dollar and then the money supply increases by 1/f dollars. As for example, if the reserve requirement is maintained as f=0.10, then money supply has raised by ten dollars and that will confirm the money multiplier as ten.
The process of money multiplier: There is the money- multiplier that process explains in which way the monetary base has caused the money supply for increasing with multiplied amount. In that context, let Federal Reserve ratio has carried out with the open market operation, by the creation of $1 for buying $ 100 of Treasury securities from the bank. Therefore, the monetary base has risen by $100.
The seller has received the $90 as well as deposits in the bank. Bank has kept 0.10 * $90 as the reserves and the loans which is remaining by $81 for excess reserves, in that case borrower has used the money for buying purpose. In this case seller has received $81 as well as deposited that in the bank account and the process has continued.
The total increase in money supply has the sum of the increased price at each stage.
?M = 100 +90 +81 +··· = 100 +100 ×.90 +100 ×.90 2 +···, which is considered as the geometric sum (Oliner & Rudebusch, 1995).
(1) Total currency = (currency in circulation) + (vault cash)
(2) cu = (currency in circulation) / D (D = total deposits)
(3) Total reserves of banks = (vault cash) + (reserve deposits)
(4) R = (total reserves) / D
(5) M = (1 + cu) D
(6) MB = (currency in circulation) + (total reserves)
(7) MB = (cu + R) D
(8) mm = [(1 + cu)/ (R + cu)] (mm = money multiplier)
(9) M = (mm) MB
Suppose there is 200 worth of total currency, and 10% of it sits in the vaults of banks.
(a) How much currency is in circulation?
Suppose the “currency/deposit ratio" cu = 0.1.
(b) How large is the total amount of deposits in banks (D)?
(c) Given your answers above, how large is the money supply M?
Suppose the total of bank reserve deposits at the Fed is 196.
(d) How large are the total reserves of banks?
(e) Given the answers to (a) and (d), what is the value of the monetary base MB?
(f) Given the answers to (b) and (d), what is the “reserve/deposit ratio" R?
(g) Given the answer to (e) and prior information, what is the value of mm?
Now, suppose that, faced with a financial crisis that begins with a “credit crunch" and leads to a depressed level of GDP, the Fed attempts stimulus and launches a significant expansion of its balance sheet (known as “quantitative easing"), buying 396 worth of securities from banks, but the banks (weighed down with “toxic" assets and perceiving high risk involved with lending) simply hold all of the Feds payments as added reserves and do not alter their lending behavior.
(d') Repeat part (d) above, and find the new total reserves of banks.
(e') Repeat part (e) above, and find the new value of MB.
(f') Repeat part (f) above, and find the new value of R.
(g') Repeat part (g) above, and find the new value of mm.
(h) Given these results, how large is M now, after the Feds action and the banks reaction? (Here, use eq.(9)). Comparing (c) and (h), explain why the Delta M is what it is here.
(i) Sometimes, economic commentators (perhaps influenced by the legacy of Monetarism) argue that a large increase in MB will inevitably create significant price inflation (because the Fed is said to be “printing money"). Based on the numerical example here, is the claim of “inevitability" persuasive? Why or why not?
a)From Total currency = (currency in circulation) + (vault cash)
We have, currency in circulation = Total currency – vault in cash
= 200- 200*10%= 200- 20= 180
So currency in circulation is 180.
D= currency in circulation /cu= 180/ 0.1= 1800
c)From M = (1 + cu) D
M= (1+0.1) * 1800= 1.1 *1800= 1980
d)From Total reserves of banks = (vault cash) + (reserve deposits)
Total reserves of banks = 20 +196 = 216
e) From, MB = (currency in circulation) + (total reserves)
We get, MB= 180 + 216= 396
f)From R = (total reserves) / D, we get,
R= 216/ 1800= 0.12
g)From mm = [(1 + cu)/ (R + cu)], we get,
mm= (1 + 0.1)/ (0.12+ 0.1) = 5
(d') From Total reserves of banks = (vault cash) + (reserve deposits), we get,
Total reserves of banks= 20 +396 = 416
(e') From MB = (currency in circulation) + (total reserves), we get,
MB= 180 +416 = 596
(f') From R = (total reserves) / D, we get,
R= 416 / 1800 = 0.23
(g') From mm = [(1 + cu)/ (R + cu)], we get,
mm= (1+ 0.1) / (0.23 + 0.1)= 0.33
(h) From M = (mm) MB, we get,
M'= 0.33 * 596 = 196.68
So, change in M or Delta M = 1980- 196.68= 1783.32
On the other hand, the credit channel of monetary policy has generated the direct impact on the aggregate demand and output has been supported through certain fundamental assumptions.
It has been observed that within the credit channel, there are two channels, like, bank lending channel as well as balance sheet. The main contribution has been empirically differentiate in these two channels and in case of each channel, the effect of monetary policy has magnified as the change in lending. There is a theory regarding the bank lending channel has based on the model of Bernanke and Blinder. This theory is also related with contractionary monetary policy which leads to the reduction in case of bank deposits and that in turn has reduced the aggregate loan supply. The alternative channel thus described in Bernanke, Gilchrist and Gertler (1996). Therefore, the agency costs for the lending have changed endogenously with the monetary policy. The monetary contradiction has also decreased for net worth of the borrowers. Who leads with the increase in the agency costs? Also in primary, there are low-net-worth organisations. according to Gertler and Bernanke model, when the agency costs increase, the amount of credit has also increased, lenders decreases the amount of credits which is further extended to the risky firms for investing more in case of safe alternative (Apergis, Miller, & Alevizopoulou, 2012).
As there is no such lending possible in large amount (Economist's View, 2009)
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Economist's View. (2009). The Bank Lending Channel. Retrieved from http://economistsview.typepad.com/ http://economistsview.typepad.com/: http://economistsview.typepad.com/economistsview/2009/10/the-bank-lending-channel.html
Oliner, S., & Rudebusch, G. (1995). Is There aBank Lending Channel for Monetary Policy. Retrieved from https://www.frbsf.org/: https://www.frbsf.org/economic-research/files/95-2_3-20.pdf