Question

The money supply \((M)\) is the sum of bank deposits \((D)\) plus currency in the hands of the public (call that \(C\) ). Suppose the required reserve ratio is 20 percent and the Fed provides 50 billion in bank reserves \((R=\$ 50\) billion \()\) a. First assume that people hold no currency (C=0). How large will the money supply (M) be? If the Fed increases bank reserves to R=60 billion, how large will M be then? b. Next, assume that people hold 20 cents worth of currency for each dollar of bank deposits; that is, C=0.2 D . Define the monetary base (B) as the sum of bank reserves (R) plus currency: B=R+C. If the Fed now creates 50 billion worth of monetary base, how large will M be? (Hint: You will need a little bit of algebra to figure this out. Remember that the 50 billion monetary base is divided between two purposes: bank reserves and currency.) Now, if the Fed increases the monetary base to B= 60 billion, how large will M be? c. What do you notice about the relationship between M and B?

Short answer

Answer: In both scenarios, when the monetary base increases, the money supply also increases. However, the increase is larger in the scenario without currency held by the public. When the public holds more currency, the impact of an increase in the monetary base on the money supply is smaller.

Step-by-step solution

Part a: Money Supply without Currency

In this case, we are given that C=0, so the money supply (M) is the sum of bank deposits (D). Since the required reserve ratio is 20 percent, banks can create 1/0.2 = 5 times their reserves in deposits. So, if the Fed provides 50 billion in bank reserves (R), the money supply will be: M = D = 5*R = 5*50 = 250 billion Now, if the Fed increases bank reserves to R=60 billion, the money supply will be: M = D = 5*R = 5*60 = 300 billion #Step 2: Money Supply with Currency#

Part b: Money Supply with Currency

In this case, we are given that people hold 20 cents worth of currency for each dollar of bank deposits, so C=0.2*D. The monetary base (B) is defined as the sum of bank reserves (R) plus currency (C), or B=R+C. If the Fed creates 50 billion worth of monetary base (B=50), we can set up an equation for R, D, and C: \(B = R + C = R + 0.2*D\) Since D = 5*R (from the 20% reserve ratio), we can substitute this into the equation above: \(50 = R + 0.2*5*R \Rightarrow 50 = R*(1+1) \Rightarrow R = \$25\) billion Now, we can calculate D and M: D = 5*R = 5*25 = \$125 billion M = D + C = 125 + 0.2*125 = \$150 billion Next, if the Fed increases the monetary base to B=60 billion, we can repeat the previous process: \(60 = R + 0.2*5*R \Rightarrow 60 = R*(1+1) \Rightarrow R = \$30\) billion Now, we can calculate D and M for this scenario: D = 5*R = 5*30 = \$150 billion M = D + C = 150 + 0.2*150 = \$180 billion #Step 3: Relationship between M and B#

Part c: Relationship between M and B

To analyze the relationship between M and B, let's observe how M changes when B increases by 10 billion in both scenarios: 1. Without currency (Part a): M increased from 250 billion to 300 billion 2. With currency (Part b): M increased from 150 billion to 180 billion In both cases, when the monetary base increased by 10 billion, the money supply also increased. However, the increase was larger in the scenario without currency. This means that when the public holds more currency, the impact of an increase in the monetary base on the money supply is smaller.

Key concepts

Monetary Base

The monetary base, often called 'high-powered money,' is a fundamental concept in understanding how the central bank influences the overall money supply. It is the sum of two critical components: bank reserves and currency in circulation. This can be mathematically expressed as \( B = R + C \), where \( B \) is the monetary base, \( R \) denotes bank reserves, and \( C \) represents currency.

The monetary base serves as the foundation upon which banks can create additional money through lending. When a central bank, like the Federal Reserve, adjusts the monetary base, it indirectly changes the capacity of banks to make loans and thereby alter the money supply. This is a crucial tool for monetary policy. For instance, when the Fed injects money into the economy, it essentially boosts bank reserves and can lead to a multiplied increase in the money supply depending on the reserve ratio and other factors.

Understanding the monetary base is essential for recognizing how central banks control the supply of money and consequently influence economic activities such as inflation, employment, and overall economic growth.

Bank Reserves

Bank reserves are pivotal in ensuring a stable banking system. These are the portions of deposits that banks hold and do not lend out. They fall into two categories: required reserves and excess reserves.

Specifically, required reserves are the minimum amounts that banks must legally hold, determined by the central bank's required reserve ratio. This system helps in averting bank runs, where too many depositors attempt to withdraw funds simultaneously.

When a bank receives a deposit, it must retain a fraction of it as reserves. For instance, if the reserve ratio is 20%, and a bank receives $1,000 in deposits, it must keep $200 as reserves. Banks have the freedom to lend the rest, thus creating new money in the economy by making loans. This process of holding reserves enables banks to manage liquidity and meet withdrawal demands while contributing to the overall money creation process.

Further, excess reserves are any reserves banks hold over the required minimum. With the financial landscape's dynamism, these reserves sometimes act as buffers in times of financial uncertainty or economic downturns.

Required Reserve Ratio

The required reserve ratio is a regulatory tool used by central banks to control the amount of funds that commercial banks must hold. It represents the fraction of deposit liabilities that banks need to retain as reserves.

This ratio directly influences how much money banks can generate from their deposits through the process of lending. For example, with a reserve ratio of 20%, banks can lend 80% of their deposits. By altering this ratio, central banks possess a powerful means to increase or decrease banks' lending capabilities and thus the money supply. A lower reserve ratio permits banks to lend more, potentially stimulating economic growth, while a higher ratio restricts lending, serving as a means to curb inflationary pressures.

Historically, the reserve ratio has played a central role in maintaining financial system stability. It acts as a safeguard, assuring that banks have enough liquidity to meet everyday withdrawal demands and withstand economic shocks. The balance between stimulating economic activity and ensuring financial stability is delicately managed through adjustments to the required reserve ratio.