Do you know that every 1 dollar spending will affect the output by 5 dollar

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In the **IS curve** equation, the term \( \frac{1}{1 - c} \) plays a crucial role in determining how changes in **government spending (G)**, **taxes (T)**, and other components of aggregate demand affect the overall **output (Y)**.

### What Does \( \frac{1}{1 - c} \) Mean?
The term \( \frac{1}{1 - c} \) is known as the **multiplier**. Here, \( c \) represents the **marginal propensity to consume (MPC)**. The **multiplier** tells us how much total output (GDP) will increase in response to an initial change in spending, such as an increase in government spending, investment, or consumption.

### Role of the Multiplier:
- The **multiplier** amplifies the initial change in spending because the initial increase in spending leads to **increased income**, which leads to more **consumption**, and that, in turn, increases **income** further, creating a feedback loop.

- The size of the multiplier depends on the **MPC** (\( c \)). A higher MPC means that people spend a larger portion of their income, leading to a **larger multiplier**.

### Example:
If the **MPC (c)** is **0.8**, the multiplier becomes:
\[
\text{Multiplier} = \frac{1}{1 - 0.8} = \frac{1}{0.2} = 5
\]
This means that for every **$1 increase in spending**, the total increase in output (GDP) will be **$5**.

The logic behind this is:
1. An initial **$1 of spending** creates **$1 of income** for someone else.
2. Since their **MPC is 0.8**, they will spend **$0.80** of that new income.
3. That $0.80 becomes someone else’s income, and they spend **80% of that**, or **$0.64**, and so on.

The total effect on output becomes a multiple of the initial spending increase.

### In the IS Curve Equation:
The IS curve equation typically looks something like:
\[
Y = \frac{1}{1 - c} \times (G - T - b \times r)
\]
Where:
- **\( Y \)**: Output (GDP).
- **\( G \)**: Government spending.
- **\( T \)**: Taxes.
- **\( r \)**: Interest rate.
- **\( b \)**: Sensitivity of investment to changes in the interest rate.
- **\( c \)**: Marginal propensity to consume (MPC).

### Meaning of \( \frac{1}{1 - c} \) in IS Curve:
- The term \( \frac{1}{1 - c} \) amplifies the effect of **government spending** and **tax changes** on output.
- A higher **MPC (c)** means that a given change in **government spending (G)** or **taxes (T)** will have a **greater effect on output (Y)**.

If the MPC is high, the multiplier effect is larger, and the economy is more sensitive to changes in fiscal policy (government spending and taxes). If the MPC is low, the multiplier is smaller, and fiscal policy has a weaker effect on overall output.

### Summary:
- \( \frac{1}{1 - c} \) is the **multiplier** in the IS curve, where **\( c \)** is the **marginal propensity to consume (MPC)**.
- The **multiplier** shows how much total output (Y) will change in response to changes in government spending, taxes, or investment.
- A higher **MPC** leads to a larger multiplier, meaning the economy is more responsive to fiscal changes.

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