If the monetary base of a country is $7,000. People hold half of their money in the form of currency, and commercial banks hold a quarter of their deposits in reserve. Context: long run, closed economy（use the econ 211 knowledge) c) To restore money supply to the original level, should the central bank buy or sell government bonds? Calculate, in dollars, how much the central bank needs to transact
Question
If the monetary base of a country is $7,000. People hold half of their money in the form of currency, and commercial banks hold a quarter of their deposits in reserve. Context: long run, closed economy（use the econ 211 knowledge) c) To restore money supply to the original level, should the central bank buy or sell government bonds? Calculate, in dollars, how much the central bank needs to transact
Solution
To answer this question, we first need to understand the concept of the money multiplier. In this case, the money multiplier is determined by the reserve ratio and the public's preference for holding cash.
Given that people hold half of their money in the form of currency and banks hold a quarter of their deposits in reserve, the money multiplier (m) can be calculated as follows:
m = 1 / (Currency ratio + Reserve ratio) m = 1 / (0.5 + 0.25) m = 1 / 0.75 m = 1.33
The money supply (MS) is the product of the monetary base (MB) and the money multiplier (m). So, the original money supply was:
MS = MB * m MS = 9,310
If the central bank wants to restore the money supply to this original level, it will need to adjust the monetary base through open market operations, i.e., buying or selling government bonds.
Let's say the new monetary base is MB'. If the money supply is to remain the same, we have:
MS = MB' * m $9,310 = MB' * 1.33
Solving for MB', we get:
MB' = 7,000
Since the new monetary base (MB') is the same as the original monetary base (MB), the central bank does not need to buy or sell government bonds. The money supply is already at its original level.
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