The average tax rate and marginal tax rate are the same under a proportional tax rate structure.

Question

BlackTom AI · Accepted Answer

Under a proportional (flat) tax, every additional dollar of income is taxed at the same constant percentage, so the marginal and average rates coincide.

Relevant concepts:
- Proportional (flat) tax: a constant tax rate t applied to all income levels. Tax paid = t × income.
- Average tax rate (ATR): total tax paid divided by total income.
- Marginal tax rate (MTR): the tax on an additional dollar of income; formally the derivative d(tax)/d(income) or Δtax/Δincome.

Step-by-step reasoning with algebra and a numeric example:
1. Let income be Y and the constant proportional tax rate be t (for example t = 0.20 or 20%).
2. Total tax paid = T = t × Y.
3. Average tax rate = ATR = T/Y = (t × Y)/Y = t. This shows the ATR equals t for any Y.
4. Marginal tax rate = MTR = dT/dY. Since T = tY and t is constant, dT/dY = t. Alternatively, for a small income increment ΔY: ΔT = t × ΔY, so ΔT/ΔY = t.
5. Hence ATR = t and MTR = t, so ATR = MTR.

Why the correct answer is correct:
Because a proportional tax applies the same constant percentage to each dollar, the proportion of income paid in tax (ATR) is exactly that percentage, and the tax on one more dollar (MTR) is the same percentage.

Why the other option (False) is incorrect:
ATR and MTR differ under non-proportional systems. In a progressive tax, MTR typically exceeds ATR; in a regressive system MTR can be lower than ATR. But those cases do not apply to a proportional tax.

Conclusion: The statement is True. This matches the provided correct answer.

The average tax rate and marginal tax rate are the same under a proportional tax rate structure.True/False

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