To determine the change in the currency-deposit ratio resulting from a change in the reserve-deposit ratio, we can follow these steps:

### 1. ### Break Down the Problem
We need to identify the relationship between the currency-deposit ratio (c) and the reserve-deposit ratio (r). The overall money supply can be affected by changes in these ratios. First, we will define the ratios:

- Initial reserve-deposit ratio $ r_1 = 0.5 $
- New reserve-deposit ratio $ r_2 = 0.2 $
- We need to find the change in the currency-deposit ratio $ c $.

### 2. ### Relevant Concepts
In a simple model of money supply, the following relationships hold:

- The money supply $ M $ can be represented as:
$$
M = C + D
$$
where $ C $ is currency and $ D $ is deposits.

- The reserve-deposit ratio $ r $ is defined as:
$$
r = \frac{R}{D}
$$
where $ R $ is reserves.

- The currency-deposit ratio $ c $ is defined as:
$$
c = \frac{C}{D}
$$

The total money in circulation can be also represented in terms of these ratios:
$$
M = \frac{C}{c} + \frac{D}{r}
$$

### 3. ### Analysis and Detail
To analyze the change, we can use the given initial and new reserve-deposit ratios to infer how changes might affect the currency-deposit ratio through the money supply.

1. Initial money supply involving the reserve-deposit ratio and currency-deposit ratio:
$$
M_1 = \frac{C}{c} + \frac{D}{r_1}
$$

2. New money supply with the new reserve-deposit ratio:
$$
M_2 = \frac{C}{c} + \frac{D}{r_2}
$$

Assuming the money supply stays constant, we can set $ M_1 = M_2 $ and solve for the changes in $ c $.

### 4. ### Verify and Summarize
Given that the reserve-deposit ratio decreased from 0.5 to 0.2, it implies that banks are holding fewer reserves relative to deposits, which generally leads to an increase in loan-making and potentially an increase of currency relative to deposits.

In this simplified model, we can't pinpoint $c$ exactly without additional data. However, a substantial decrease in the reserve-deposit ratio typically corresponds to an increase in the currency-deposit ratio, suggesting $c$ will go up.

### Final Answer
The change in the currency-deposit ratio cannot be specified numerically without more information but is expected to increase as the reserve-deposit ratio decreases from 0.5 to 0.2.

Question

To determine the change in the currency-deposit ratio resulting from a change in the reserve-deposit ratio, we can follow these steps:

### 1. ### Break Down the Problem
We need to identify the relationship between the currency-deposit ratio (c) and the reserve-deposit ratio (r). The overall money supply can be affected by changes in these ratios. First, we will define the ratios:

- Initial reserve-deposit ratio $ r_1 = 0.5 $
- New reserve-deposit ratio $ r_2 = 0.2 $
- We need to find the change in the currency-deposit ratio $ c $.

### 2. ### Relevant Concepts
In a simple model of money supply, the following relationships hold:

- The money supply $ M $ can be represented as:
  $$
  M = C + D
  $$
  where $ C $ is currency and $ D $ is deposits.

- The reserve-deposit ratio $ r $ is defined as:
  $$
  r = \frac{R}{D}
  $$
  where $ R $ is reserves.

- The currency-deposit ratio $ c $ is defined as:
  $$
  c = \frac{C}{D}
  $$

The total money in circulation can be also represented in terms of these ratios:
$$
M = \frac{C}{c} + \frac{D}{r}
$$

### 3. ### Analysis and Detail
To analyze the change, we can use the given initial and new reserve-deposit ratios to infer how changes might affect the currency-deposit ratio through the money supply.

1. Initial money supply involving the reserve-deposit ratio and currency-deposit ratio:
   $$
   M_1 = \frac{C}{c} + \frac{D}{r_1}
   $$

2. New money supply with the new reserve-deposit ratio:
   $$
   M_2 = \frac{C}{c} + \frac{D}{r_2}
   $$

Assuming the money supply stays constant, we can set $ M_1 = M_2 $ and solve for the changes in $ c $.

### 4. ### Verify and Summarize
Given that the reserve-deposit ratio decreased from 0.5 to 0.2, it implies that banks are holding fewer reserves relative to deposits, which generally leads to an increase in loan-making and potentially an increase of currency relative to deposits.

In this simplified model, we can't pinpoint $c$ exactly without additional data. However, a substantial decrease in the reserve-deposit ratio typically corresponds to an increase in the currency-deposit ratio, suggesting $c$ will go up.

### Final Answer
The change in the currency-deposit ratio cannot be specified numerically without more information but is expected to increase as the reserve-deposit ratio decreases from 0.5 to 0.2.

Knowee AI · Accepted Answer