T/F = If the excess to reserve deposit ratio goes up along with the currency to deposit ratio, all else constant, then we are unsure what happens to the money multiplier since the money multiplier...
T/F = If the excess to reserve deposit ratio goes up along with the currency to deposit ratio, all else constant, then we are unsure what happens to the money multiplier since the money multiplier is negatively related to the excess reserve to deposit ratio but positively related to the currency to deposit ratio.
Description of Money Multiplier
The Money Multiplier (m1) is a key element of the fractional banking system used by central banks, and refers to the increase (or decrease) of the total money supply in response to an initial deposit (monetary base). The function of M is exhibited in bank retention of a percentage of an initial deposit on reserve. This allows the bank to lend the remainder, and re-deposit loan payments with interest to the bank, establishing a basis future lending and a further increase in the money supply.
The formula for m1:
Money Multiplier = Change in total money supply / Change in total monetary base
The same as:
m1 = 1/r, where r = the reserve ratio
To answer the T/F Problem:
"If the excess to reserve deposit ratio goes up with the currency to deposit ratio, all else constant, then we are 'unsure' what happens to the money multiplier since is is negatively related to the excess reserve to deposit ratio but positively related to the currency to deposit ratio" is: FALSE
We are 'sure' what happens to the money multiplier since the excess to reserve deposit ratio [ER/D] increases with the currency to deposit ratio [C/D], all else is constant.
The required reserve ratio (RRR) is found in the formula:
m1 = 1 + (C/D)/[rr + (ER/D) + (C/D)].
Note: the currency "drain ratio" or percentage of banknotes held by individual consumers in cash instead of bank depository accounts, creates the conditions for the money multiplier to be negatively related to the total reserve, and positively related to the currency deposit ratio, and this is a reliable function.
The money multiplier m is related to the currency-deposit ratio [C/D], the excess-reserves ratio [ER/D)] and to the required reserve ratio [RRR] by the formula: m = (1 + [C/D])/([RRR] + [C/D]+[ER/D]).
If the excess-reserves ratio and the currency-deposit ratio go up with all other variables remaining the same, there is a decrease in the money multiplier. This is a result of the fact that the currency-deposit ratio is present both in the numerator as well the denominator but the excess-reserves ratio is present only in the denominator. As two terms of the denominator are going up with the third remaining same and only one term goes up in the numerator, the denominator becomes larger at a rate greater than that at which the numerator increases.
The given statement is therefore false. For the conditions that are given, the money multiplier becomes smaller.
False, because the laws of algebra and calculus apply to currency calculations and we can therefore know the behavior of the money multiplier m in principle.
We can unpack the relationship m=(1+[C/D])/([RRR+[C/D]+[E/R]) to see the relationship among and between terms. It is sometimes easier to see these when written by hand rather than text line typing, so you might find it helpful to copy this equation onto a scrap paper to see it more clearly because you can write out all of the fractions vertically:
The two terms in the denominator on the right of the above equation can be separated:
m=1/([RRR]+[C/D]+[ER/D]) + (C/D)/([RRR]+[C/D]+[ER/D])
Now we can represent the relations of each term more generally in terms of trends:
m~1/⬆️⬆️ + ⬆️/⬆️⬆️
From this we can see that the first term on the right of the equation will become negative as the C/D rate and ER/D rates increase and will do so faster than the second term (due to the C/D rate being in the numerator and denominator there).
Therefore, the money multiplier is a known quantity that can be calculated precisely and behavior estimated dynamically.
Therefore we are not at all unsure of what happens to the money multiplier m, and therefore to assert this claim is False!