An economy has a monetary base of 1,000 $1 bills. Calculate the money supply in scenarios a-d an the answer part e . a) all the money is held as currency b) all the money is held as demand deposits. Banks hold 100 percent of all deposits as reserves. c)All the money is held as demand deposits. Banks hold 20 percent of deposits as reserves. d) people hold equal amount of currency and demand deposits. Banks hold 20 percent of deposits as reserves. e) the central bank decides to increase the money supply by 10 percent. in each of the above four scenarios, how much should i increase the monetary base.
The correct answer and explanation is:
Calculation of Money Supply
(a) All the money is held as currency
Here, the entire monetary base is held as currency, so the money supply equals the monetary base.
Money supply = $1,000.
(b) All the money is held as demand deposits; banks hold 100% of deposits as reserves
Since banks hold 100% reserves, they cannot lend out any money. The money supply equals the deposits.
Money supply = $1,000.
(c) All the money is held as demand deposits; banks hold 20% of deposits as reserves
Banks hold 20% of deposits as reserves, meaning the reserve ratio (rrrr) is 0.2. The money multiplier is: Money multiplier=1rr=10.2=5\text{Money multiplier} = \frac{1}{rr} = \frac{1}{0.2} = 5
Money supply is the monetary base multiplied by the money multiplier: Money supply=1,000×5=5,000\text{Money supply} = 1,000 \times 5 = 5,000
(d) People hold equal amounts of currency and demand deposits; banks hold 20% of deposits as reserves
Let the monetary base (MB=1,000MB = 1,000) be split equally between currency (CC) and reserves (RR): C=500,R=500C = 500, \quad R = 500
With a reserve ratio (rr=0.2rr = 0.2), total deposits (DD) satisfy R=rr×DR = rr \times D: 500=0.2×D⇒D=2,500500 = 0.2 \times D \quad \Rightarrow \quad D = 2,500
The money supply is the sum of currency and demand deposits: Money supply=C+D=500+2,500=3,000\text{Money supply} = C + D = 500 + 2,500 = 3,000
Part (e): Increasing Money Supply by 10%
The new money supply needs to be 1.10×current money supply1.10 \times \text{current money supply}. The central bank must adjust the monetary base (MBMB) accordingly:
- Scenario (a): MBnew=1,100MB_{\text{new}} = 1,100. Increase by 100100.
- Scenario (b): MBnew=1,100MB_{\text{new}} = 1,100. Increase by 100100.
- Scenario (c): MBnew=New money supplyMoney multiplier=1.10×5,0005=1,100MB_{\text{new}} = \frac{\text{New money supply}}{\text{Money multiplier}} = \frac{1.10 \times 5,000}{5} = 1,100. Increase by 100100.
- Scenario (d): Solve iteratively: New money supply=1.10×3,000=3,300\text{New money supply} = 1.10 \times 3,000 = 3,300 With currency-demand deposits split and a reserve ratio of 0.2, the central bank must increase MBMB to approximately 1,1001,100, an increase of 100100.
Explanation
The money supply depends on how the monetary base (MBMB) circulates in the economy. In scenario (a), since all money is held as currency, there is no multiplier effect, and the money supply equals MBMB. In (b), deposits are fully backed by reserves, so banks cannot lend, and the money supply remains the same as MBMB. Scenario (c) introduces fractional-reserve banking, where banks hold only 20% of deposits as reserves, allowing them to lend the rest. This lending creates a multiplier effect, significantly increasing the money supply. In (d), the mix of currency and deposits affects the multiplier: currency does not generate additional deposits, so the multiplier effect is smaller than in (c).
When the central bank increases the money supply by 10% in part (e), it adjusts the MBMB to achieve the desired money supply under each scenario. The adjustment is straightforward in (a) and (b), where there is no multiplier. In (c) and (d), the central bank must account for the money multiplier and the split between currency and reserves. The increase in MBMB is proportional to the existing money supply, adjusted for the multiplier. Each scenario highlights the crucial role of banking behavior and public preferences in determining how changes in MBMB translate into changes in the broader money supply.