A tax on an item is diminished by 20% and its consumption increases by 15%, then the effect on revenue is:

Question

Accepted Answer

To determine the effect on revenue when a tax on an item is diminished by 20% and its consumption increases by 15%, we need to analyze the impact of these changes on the overall revenue.

1. **Explanation for Option 3 (Correct Answer: decreased by 8%)**:
   - Let's assume the original price of the item is $ P $ and the original tax rate is $ T $. Therefore, the original tax amount is $ P \times T $.
   - The original revenue from the tax is the product of the tax amount and the quantity consumed. Let the original quantity consumed be $ Q $. Thus, the original revenue is $ P \times T \times Q $.
   - When the tax is diminished by 20%, the new tax rate becomes $ 0.8T $.
   - The consumption increases by 15%, so the new quantity consumed is $ 1.15Q $.
   - The new revenue is $ P \times 0.8T \times 1.15Q = 0.92 \times (P \times T \times Q) $.
   - This shows that the new revenue is 92% of the original revenue, indicating a decrease of 8%.

2. **Explanation for why other options are incorrect**:
   - **Option 1 (increased by 8%)**: This option suggests that the revenue increases, which contradicts the calculation showing a decrease. The reduction in tax rate outweighs the increase in consumption, leading to a net decrease in revenue.
   - **Option 2 (increased by 11%)**: Similar to Option 1, this option implies an increase in revenue. However, the combined effect of a 20% decrease in tax and a 15% increase in consumption results in a net decrease, not an increase.
   - **Option 4 (decreased by 11%)**: While this option correctly identifies a decrease in revenue, the magnitude of the decrease is incorrect. The calculation shows a decrease of 8%, not 11%.

In conclusion, the correct answer is Option 3, as the revenue decreases by 8% due to the combined effects of a 20% reduction in tax and a 15% increase in consumption.