with these equations: ( = 230 +0₂66d₁ F = 420₁6 = 280-0₁13Y₁ X=470₁ M=555, and T = 13 +0.25Y What is the tax multiplier?

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**Problem Statement:**

With these equations:
- \( C = 230 + 0.66Y_d \)
- \( F = 470 \)
- \( G = 280 - 0.13Y \)
- \( X = 470 \)
- \( M = 555 \)
- \( T = 13 + 0.25Y \)

**Question:** What is the tax multiplier?

**Educational Explanation:**

To solve for the tax multiplier, you'll need to understand how changes in taxes affect the overall economy. The tax multiplier is a measure of the change in output resulting from a change in taxes. It's calculated using various economic factors, including consumption, saving, and government spending. To compute it, you'll typically apply the following formula:

\[ \text{Tax Multiplier} = -\frac{MPC}{1 - MPC \times (1 - t)} \]

Where:
- MPC is the marginal propensity to consume,
- \( t \) is the tax rate.

You'll need to determine these values from the equations given.

Note:
- \( Y_d \) stands for disposable income.
- \( C \) is the consumption function.
- \( G \) is government spending, which here is a function of income \( Y \).
- \( X \) and \( M \) are exports and imports, respectively.
- \( T \) represents taxes, with a fixed and a variable component linked to income \( Y \).
Transcribed Image Text:**Problem Statement:** With these equations: - \( C = 230 + 0.66Y_d \) - \( F = 470 \) - \( G = 280 - 0.13Y \) - \( X = 470 \) - \( M = 555 \) - \( T = 13 + 0.25Y \) **Question:** What is the tax multiplier? **Educational Explanation:** To solve for the tax multiplier, you'll need to understand how changes in taxes affect the overall economy. The tax multiplier is a measure of the change in output resulting from a change in taxes. It's calculated using various economic factors, including consumption, saving, and government spending. To compute it, you'll typically apply the following formula: \[ \text{Tax Multiplier} = -\frac{MPC}{1 - MPC \times (1 - t)} \] Where: - MPC is the marginal propensity to consume, - \( t \) is the tax rate. You'll need to determine these values from the equations given. Note: - \( Y_d \) stands for disposable income. - \( C \) is the consumption function. - \( G \) is government spending, which here is a function of income \( Y \). - \( X \) and \( M \) are exports and imports, respectively. - \( T \) represents taxes, with a fixed and a variable component linked to income \( Y \).
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