Chapter 29: Problem 8

In Westlandia, the public holds $50 \%$ of $\mathrm{M} 1$ in the form of currency, and the required reserve ratio is $20 \%$. Estimate how much the money supply will increase in response to a new cash deposit of $\$ 500$ by completing the accompanying table. (Hint: The first row shows that the bank must hold $\$ 100$ in minimum reserves $-20 \%$ of the $\$ 500$ deposit- against this deposit, leaving $\$ 400$ in excess reserves that can be loaned out. However, since the public wants to hold $50 \%$ of the loan in currency, only $\$ 400 \times 0.5=\$ 200$ of the loan will be deposited in round 2 from the loan granted in round 1.) How does your answer compare to an economy in which the total amount of the loan is deposited in the banking system and the public doesn't hold any of the loan in currency? What does this imply about the relationship between the public's desire for holding currency and the money multiplier?

Short Answer

Expert verified

Answer: The money supply increases by $320 in response to a new cash deposit of $500 in Westlandia.

Step by step solution

1. Calculate the initial required reserves and excess reserves from the new deposit

First, we need to calculate the amount of required reserves and excess reserves after the cash deposit of $500. The required reserve ratio is $20\%$, so the required reserves will be $500\times0.20=\$100$. This leaves $500-100=\$400$ in excess reserves that can be loaned out.

2. Determine the loan amount that will be deposited in each round

In each round, the bank will lend out the excess reserves and then half of the loan will be deposited back into the banking system because the public wants to hold $50\%$ of the loan in currency. So we have: Round 1: $400\times0.5=\$200$ Round 2: $200\times0.5=\$100$ Round 3: $100\times0.5=\$50$ and so on...

3. Calculate the increment in the money supply for each round

In each round, the money supply in the banking system increases by the amount of loan that is deposited back in the system: Increment in round 1: $200\times(1-0.20)=\$160$ Increment in round 2: $100\times(1-0.20)=\$80$ Increment in round 3: $50\times(1-0.20)=\$40$ and so on...

4. Calculate the total increase in money supply

Sum the increments for all the rounds to find the total increase in the money supply: Total increase = $160+80+40+\cdots$ The sum is a geometric series, so we can use the formula for the sum of an infinite geometric series: $S = \frac{a}{1-r}$, where $a$ is the first term and $r$ is the common ratio. Here, $a=\$160$ and $r=\frac{1}{2}$, so the total increase in money supply is: $S = \frac{160}{1-0.5}=\$320$

5. Comparing with the scenario where the public doesn't hold any of the loan in currency

In this scenario, the entire loan amount would be deposited back into the banking system, and the money multiplier would be higher. If required reserves are still $20\%$, then the money multiplier would be: $MM = \frac{1}{0.20}=5$. In this case, the total increase in money supply due to the $500 deposit would be: $Increase = 500\times (MM-1) = 500\times 4=\$2000$

6. Implications of public's desire to hold currency on the money multiplier

As the public's desire to hold currency increases, the money multiplier decreases. This means that there is less potential for bank loans to increase the money supply, leading to a slower expansion of the credit in the economy. So, the money supply increases by $\$320$ in response to a new cash deposit of $\$500$ in Westlandia. This increase is smaller than the increase in an economy where the public does not hold any of the loan in currency ($\$2000$). The public's desire to hold currency has a negative effect on the money multiplier, leading to a slower growth in the money supply and credit expansion in the economy.