The relationship between borrowed reserves (BR), the nonborrowed monetary base (MBn), and the monetary base (MB) is

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The question asks about the relationship among borrowed reserves (BR), the nonborrowed monetary base (MBn), and the monetary base (MB).
First, recall the standard decomposition of the monetary base: MB is the sum of the nonborrowed base MBn and the borrowed reserves BR, i.e., MB = MBn + BR.
From this, we can algebraically derive BR = MB − MBn. This expresses borrowed reserves as what remains of the total monetary base after subtracting the nonborrowed portion.
Now, evaluate what this implies about the components:
- BR ≥ 0, because you can’t have negative borrowed reserves; if there are no borrowings, BR = 0 and MB = MBn.
- MBn ≤ MB, since MBn is a portion of MB; the nonborrowed base cannot exceed the total base.
- The alternative but equivalent formulations are MB = MBn + BR and BR = MB − MBn, both consistent with the decomposition of MB into nonborrowed and borrowed parts.
In contexts where a statement asserts MB = BR − MBn, that would be incorrect because subtracting MBn from BR would not yield MB; it would misplace the components. Similarly, stating MBn = MB − BR is algebraically equivalent to BR = MB − MBn, so it would be correct, but only if interpreted as the same relationship; if presented as a standalone claim without recognizing the addition, it could be misleading.
Because the provided answer text identifies the relation as 'BR = MB - MBn', the correct understanding aligns with the fundamental identity MB = MBn + BR and its rearrangement BR = MB − MBn, which accurately captures how the monetary base is partitioned into nonborrowed and borrowed reserves.

The relationship between borrowed reserves (BR), the nonborrowed monetary base (MBn), and the monetary base (MB) is

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