Tuesday  April 24, 2018
 AmosWEB means Economics with a Touch of Whimsy!
 TANGENCY: A geometric condition that occurs when two curves touch at a single point with identical slopes at that point. This condition of tangency surfaces in several different areas of economic analysis, including indifference curve analysis (tangency between an indifference curve and budget line) and monopolistic competition (tangency between demand curve and long-run average cost curve). The tangency between two curves should be contrasted with the condition of intersection, in which two cross at a single point but do not have identical slopes.

DEPOSIT EXPANSION MULTIPLIER:

The ratio of the change in checkable deposits to the change in reserves, which indicates the magnified change in deposits resulting from a change in reserves. The deposit expansion multiplier indicates how many checkable deposits are created with an injection of additional reserves into the banking system. As the name suggests, the change in checkable deposits is typically a multiple of the initial change in reserves. The size of the deposit expansion multiplier depends on the reserve requirement ratio. The deposit expansion multiplier also forms the core of the money multiplier.
The deposit expansion multiplier measures the change in checkable deposits resulting from a given change in bank reserves. The term "multiplier" indicates that the change in deposits is inevitably a "multiple" of the initial change in bank reserves. This multiplier arises through the money creation activities made possible by fractional-reserve banking. That is, banks create money (checkable deposits) by "expanding" a given amount of reserves into a larger amount of checkable deposits.

### Money Creation

An understanding of the deposit expansion multiplier begins with the money creation process undertaken by the banking system. Fractional-reserve banking makes it possible for banks to create checkable deposits in the process of lending excess reserves. The amount of loans made and checkable deposits created depend on the proportion of reserves banks need to keep to back up deposits--the reserve requirement ratio.

If the reserve requirement ratio is lower, then banks either need fewer reserves to back up a given amount of checkable deposits or they can back up more checkable deposits with a given amount of reserves. This further means that banks can create more checkable deposits with a given amount of reserves.

Suppose, for example, that the Federal Reserve System injects \$100 of excess reserves into the banking system. In addition, suppose that the reserve requirement ratio is 10 percent, meaning that banks must keep reserves equal to at least 10 percent of deposits. The banking system will use this \$100 of excess reserves to back up, or create, ten times the amount of checkable deposits.

### The Multiplier Equation

The amount of checkable deposits created with a given amount of reserves is indicated by a simple equation:
D = mR
In this equation D represents the number of checkable deposits created, R is the number of excess reserves added to the banking system, and m is the multiplier. Based on the numbers above, m has a value of 10.

### The Reserve Requirement Ratio

The key to the value of the deposit expansion multiplier is the reserve requirement ratio--the proportion of reserves banks need to keep to back up deposits. First and foremost, the reserve requirement ratio determines the amount of reserves that banks need for existing deposits. However, this ratio also indicates how many additional deposits can be created when banks receive additional reserves.

If, for example, the reserve requirement ratio is 10 percent, then banks need \$1 of reserves for each \$10 of deposits, a reserve to deposit ratio of 1 to 10. Flipping this ratio around generates a deposit to reserve ratio of 10 to 1. That is, banks can have \$10 of deposits for each \$1 of reserves.

This further means that the deposit expansion multiplier m is the inverse of the reserve requirement ratio. If the reserve requirement ratio is 10 percent (that is, 0.10), then the deposit expansion multiplier is 10 (= 1/0.10). If the reserve requirement ratio is 5 percent (0.05), then the deposit expansion multiplier is 20 (= 1/0.05). If the reserve requirement ratio is 20 percent (0.20), then the deposit expansion multiplier is 5 (= 1/0.20).

Why is the deposit expansion multiplier is the inverse of the reserve requirement ratio.

• The key to the deposit creation process is that each bank keeps only a fraction of any new deposits that it receives (as reserves), then sends along the rest to another bank.

• If banks keep a SMALLER slice of deposits (as reserves), they send MORE to other banks, which is used to create more deposits.

• If banks keep a LARGER slice of deposits (as reserves), they send LESS to other banks, which is used to create fewer deposits.

### Other Magnified Changes

The deposit expansion multiplier is one example of a more general multiplier phenomenon that surfaces throughout the study of macroeconomics. In general a multiplier captures the magnified relationship between one activity and a triggering event. Another set of multipliers reflect the magnified change in aggregate output resulting from a change in aggregate expenditures--what are termed expenditure multipliers.

At the top of this list is the simple investment multiplier, which is the ratio of the change in change in aggregate production (gross domestic product) resulting from a given change in investment expenditures. A comparable expenditures multiplier is for government purchases, the ratio of the change in change in gross domestic product resulting from a given change in government purchases.

### The Money Multiplier

The deposit expansion multiplier forms the foundation of the money multiplier. Whereas the deposit expansion multiplier indicates the change in checkable deposits resulting from a given change in bank reserves, the money multiplier indicates the change in money resulting from a given change in bank reserves.

These two multipliers differ in part because money includes both checkable deposits and currency. A portion of the checkable deposits created by banks is often taken out in currency or transferred into savings accounts, both of which cause the money multiplier be different from the inverse of the reserve requirement ratio.

 <= DEMAND SPACE DERIVATION, AGGREGATE EXPENDITURES LINE =>

Recommended Citation:

DEPOSIT EXPANSION MULTIPLIER, AmosWEB Encyclonomic WEB*pedia, http://www.AmosWEB.com, AmosWEB LLC, 2000-2018. [Accessed: April 24, 2018].

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