Question

The tax on a commodity is diminished by 10% and its consumption increased by 10%. The effect on the revenue derived from it changes by \( K %\). Find the value of \( K \).

• A. 1
• B. -2
• C. -1
• D. 2

Hint:

Use successive percentage changes formula: \( % \text{ Change} = a + b + \frac{ab}{100} \) for quick calculations.

Answer 1

The Correct Option is C

Let the initial tax be \( T \) and the initial consumption be \( C \), so the initial revenue is: \[ R = T \times C \] When the tax decreases by 10%, the new tax is: \[ T' = 0.9T \] When the consumption increases by 10%, the new consumption is: \[ C' = 1.1C \] The new revenue: \[ R' = T' \times C' = (0.9T) \times (1.1C) = 0.99TC \] Percentage change in revenue: \[ \frac{R' - R}{R} \times 100 = \frac{0.99TC - TC}{TC} \times 100 = -1% \] Thus, \( K = -1 \).