1. Explain the difference between discretionary and automatic spending by the go
ID: 1177756 • Letter: 1
Question
1. Explain the difference between discretionary and automatic spending by the government. Please give an example of discretionary spending and automatic spending.
2. Calculate the Money Multiplier, Excess Reserves, Required Reserves and Total Potential Deposit Creation given the following information.
rrr = .12
Total Deposits: $6300
Total Reserves: $5500
3. What is the goal of supply side policy? Describe how deregulation works as a supply side policy tool. Why is it unlikely that we will eliminate food and drug standards?
Explanation / Answer
In monetary economics, a money multiplier is one of various closely related ratios of commercial bank money to central bank money under a fractional-reserve banking system.[1] Most often, it measures the maximum amount of commercial bank money that can be created by a given unit of central bank money. That is, in a fractional-reserve banking system, the total amount of loans that commercial banks are allowed to extend (the commercial bank money that they can legally create) is a multiple of reserves; this multiple is the reciprocal of the reserve ratio, and it is an economic multiplier.[2]
In equations, writing M for commercial bank money (loans), R for reserves (central bank money), and RR for the reserve ratio, the reserve ratio requirement is that R/M geq RR; the fraction of reserves must be at least the reserve ratio. Taking the reciprocal, M/R leq 1/RR, which yields M leq R imes (1/RR), meaning that commercial bank money is at most reserves times (1/RR), the latter being the multiplier.
If banks lend out close to the maximum allowed by their reserves, then the inequality becomes an approximate equality, and commercial bank money is central bank money times the multiplier. If banks instead lend less than the maximum, accumulating excess reserves, then commercial bank money will be less than central bank money times the theoretical multiplier.
In the United States since 1959, banks lent out close to the maximum allowed for the 49-year period from 1959 until August 2008, maintaining a low level of excess reserves, then accumulated significant excess reserves over the period September 2008 through the present (November 2009). Thus, in the first period, commercial bank money was almost exactly central bank money times the multiplier, but this relationship broke down from September 2008.
As a formula and legal quantity, the money multiplier is not controversial %u2013 it is simply the maximum that commercial banks are allowed to lend out. However, there are various heterodox theories concerning the mechanism of money creation in a fractional-reserve banking system, and the implication for monetary policy.
Jaromir Benes and Michael Kumhof of the IMF Research Department, report that: the %u201Cdeposit multiplier%u201C of the undergraduate economics textbook, where monetary aggregates are created at the initiative of the central bank, through an initial injection of high-powered money into the banking system that gets multiplied through bank lending, turns the actual operation of the monetary transmission mechanism on its head.
At all times, when banks ask for reserves, the central bank obliges. Reserves therefore impose no constraint. The deposit multiplier is simply, in the words of Kydland and Prescott (1990), a myth. And because of this, private banks are almost fully in control of the money creation process. [3]
Contents [hide]
1 Definition
2 Mechanism
2.1 Reserves first model
2.1.1 Formula
2.1.2 Table
2.1.3 Example
2.2 Loans first model
3 Implications for monetary policy
4 References
5 Notes
Definition[edit]
The money multiplier is defined in various ways.[1] Most simply, it can be defined either as the statistic of "commercial bank money"/"central bank money", based on the actual observed quantities of various empirical measures of money supply,[4] such as M2 (broad money) over M0 (base money), or it can be the theoretical "maximum commercial bank money/central bank money" ratio, defined as the reciprocal of the reserve ratio, 1/RR.[2] The multiplier in the first (statistic) sense fluctuates continuously based on changes in commercial bank money and central bank money (though it is at most the theoretical multiplier), while the multiplier in the second (legal) sense depends only on the reserve ratio, and thus does not change unless the law changes.
For purposes of monetary policy, what is of most interest is the predicted impact of changes in central bank money on commercial bank money, and in various models of monetary creation, the associated multiple (the ratio of these two changes) is called the money multiplier (associated to that model).[5] For example, if one assumes that people hold a constant fraction of deposits as cash, one may add a "currency drain" variable (currency%u2013deposit ratio), and obtain a multiplier of (1+CD)/(RR+CD).
These concepts are not generally distinguished by different names; if one wishes to distinguish them, one may gloss them by names such as empirical (or observed) multiplier, legal (or theoretical) multiplier, or model multiplier, but these are not standard usages.[4]
Similarly, one may distinguish the observed reserve%u2013deposit ratio from the legal (minimum) reserve ratio, and the observed currency%u2013deposit ratio from an assumed model one. Note that in this case the reserve%u2013deposit ratio and currency%u2013deposit ratio are outputs of observations, and fluctuate over time. If one then uses these observed ratios as model parameters (inputs) for the predictions of effects of monetary policy and assumes that they remain constant, computing a constant multiplier, the resulting predictions are valid only if these ratios do not in fact change. Sometimes this holds, and sometimes it does not; for example, increases in central bank money may result in increases in commercial bank money %u2013 and will, if these ratios (and thus multiplier) stay constant %u2013 or may result in increases in excess reserves but little or no change in commercial bank money, in which case the reserve%u2013deposit ratio will grow and the multiplier will fall.[6]
Mechanism[edit]
For more details on this topic, see Fractional-reserve banking.
There are two suggested mechanisms for how money creation occurs in a fractional-reserve banking system: either reserves are first injected by the central bank, and then lent on by the commercial banks, or loans are first extended by commercial banks, and then backed by reserves borrowed from the central bank. The "reserves first" model is that taught in mainstream economics textbooks,[1][2] while the "loans first" model is advanced by endogenous money theorists.
Reserves first model[edit]
The expansion of $100 through fractional-reserve lending at varying rates, under the re-lending model. Each curve approaches a limit. This limit is the value that the money multiplier calculates.
In the "reserves first" model of money creation, a given reserve is lent out by a bank, then deposited at a bank (possibly different), which is then lent out again, the process repeating[2] and the ultimate result being a geometric series.
Formula[edit]
The money multiplier, m, is the inverse of the reserve requirement, RR:[2]
m= rac{1}{RR}
This formula stems from the fact that the sum of the "amount loaned out" column above can be expressed mathematically as a geometric series[7] with a common ratio of 1-RR.
To correct for currency drain (a lessening of the impact of monetary policy due to peoples' desire to hold some currency in the form of cash) and for banks' desire to hold reserves in excess of the required amount, the formula:
m= rac{(1+Currency Drain Ratio)}{(Currency Drain Ratio + Desired Reserve Ratio)}
can be used, where "Currency Drain Ratio" is the ratio of cash to deposits, i.e. C/D, and the Desired Reserve Ratio is the sum of the Required Reserve Ratio and the Excess Reserve Ratio.[5]
The formula above is derived from the following procedure. Let the monetary base be normalized to unity. Define the legal reserve ratio, lpha inleft(0, 1 ight);, the excess reserves ratio, eta inleft(0, 1 ight);, the currency drain ratio with respect to deposits, gamma inleft(0, 1 ight);; suppose the demand for funds is unlimited; then the theoretical superior limit for deposits is defined by the following series:
Deposits = sum_{n = 0}^{infty}left[left(1 - lpha - eta - gamma ight) ight]^{n} = rac{1}{lpha + eta + gamma}
.
Analogously, the theoretical superior limit for the money held by public is defined by the following series:
Publicly Held Currency = gamma cdot Deposits = rac{gamma}{lpha + eta + gamma}
and the theoretical superior limit for the totale loans lent in the market is defined by the following series:
Loans = left(1 - lpha - eta ight) cdot Deposits = rac{1 - lpha - eta}{lpha + eta + gamma}
By summing up the two quantities, the theoretical money multiplier is defined as
m = rac{Money Stock}{Monetary Base} = rac{Deposits + Publicly Held Currency}{Monetary Base} = rac{1 + gamma}{lpha + eta + gamma}
where lpha + eta = Desired Reserve Ratio and gamma = Currency Drain Ratio
The process described above by the geometric series can be represented in the following table, where
loans at stage k; are a function of the deposits at the precedent stage: L_{k} = left(1 - lpha - eta ight) cdot D_{k - 1}
publicly held money at stage k; is a function of the deposits at the precedent stage: PHM_{k} = gamma cdot D_{k - 1}
deposits at stage k; are the difference between additional loans and publicly held money relative to the same stage: D_{k} = L_{k} - PHM_{k};
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