1. **State the problem:** We need to find the Average Tax Rate (ATR) for Alice, Ben, and Carrie given a tax rule: for each dollar earned above 500000, the worker pays 50% tax on that excess income.
2. **Formula and explanation:**
- Tax paid = 0 if income \( \leq 500000 \)
- Tax paid = 0.5 \( \times \) (income - 500000) if income \( > 500000 \)
- Average Tax Rate (ATR) = \( \frac{\text{Tax paid}}{\text{Income}} \times 100\% \)
3. **Calculate for Alice:**
- Income = 160000 \( < 500000 \), so Tax paid = 0
- ATR = \( \frac{0}{160000} \times 100\% = 0\% \)
4. **Calculate for Ben:**
- Income = 250000 \( < 500000 \), so Tax paid = 0
- ATR = \( \frac{0}{250000} \times 100\% = 0\% \)
5. **Calculate for Carrie:**
- Income = 800000 \( > 500000 \)
- Tax paid = 0.5 \( \times \) (800000 - 500000) = 0.5 \( \times \) 300000 = 150000
- ATR = \( \frac{150000}{800000} \times 100\% = 18.75\% \)
6. **Summary:**
- Alice's ATR = 0%
- Ben's ATR = 0%
- Carrie's ATR = 18.75%
7. **Check options:** None of the options match these exact values, so likely the problem expects tax only on income above 500000, but Alice and Ben earn less than 500000, so their ATR is 0%. Carrie pays 18.75% ATR.
**Final answer:** Alice's ATR is 0%, Ben's ATR is 0%, Carrie's ATR is 18.75%.
Average Tax Rate
Step-by-step solutions with LaTeX - clean, fast, and student-friendly.