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The tax on a commodity is reduced by 10%, but its consumption is increased by 20%. The percentage increase in the tax revenue derived from it is:
15%
8%
20%
10%
8%
The total revenue is the product of the tax rate per unit and the quantity consumed. When two percentage changes x and y are applied to the components of a product, the overall percentage change is calculated using the formula x+y+100xyтАЛ.
The total revenue is the product of the tax rate per unit and the quantity consumed. When two percentage changes x and y are applied to the components of a product, the overall percentage change is calculated using the formula x+y+100xyтАЛ.
Think of it like buying groceries: if the price of an item drops slightly but you decide to buy significantly more because it's cheaper, your total bill will increase because the volume of purchase outweighed the price reduction.
Use the 'Successive Change Rule': Sum plus product-divided-by-hundred.
Total┬аRevenue=Taxperunit├ЧQuantity
Net┬аPercentage┬аChange=x+y+100xyтАЛ
The principle of successive percentage changes operates on multiplicative factors. If the tax is reduced by 10%, the multiplier is 0.90. If the consumption increases by 20%, the multiplier is 1.20. The total effect is the product of these multipliers: 0.90├Ч1.20=1.08, which represents an 8% increase over the original value of 1.
A reduction is treated as a negative percentage (x=тИТ10).
An increase is treated as a positive percentage (y=+20).
Multiplicative effects always use the successive change formula rather than simple addition.
Quickly estimates the impact of variable economic or physical factors.
Only applicable for two variables in a product relationship.
Calculating total flux in physics (Area ├Ч Intensity).
Calculating net change in power (Voltage ├Ч Current) due to fluctuations.
Calculated as: тИТ10+20+100(тИТ10)(20)тАЛ=10тИТ2=8%.
Option A is incorrect as it ignores the multiplicative interaction. Option C ignores the price reduction. Option D assumes the effects cancel out simply.
B is correct тАФ The successive change formula accurately reflects the multiplicative nature of price and quantity on total revenue, resulting in an 8% net increase.
Always convert percentage increases/decreases into decimal multipliers (e.g., 1.2 and 0.9) to avoid sign errors when dealing with complex successive changes.
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