# Step-by-Step Solution Given Elasticities: - Own price elasticity of demand for X, \( E_P = -2 \) - Income elasticity of demand, \( E_I = 3 \) - Advertising elasticity of demand, \( E_A = 4 \) - Cross-price elasticity of demand (X with respect to Y), \( E_{XY} = -6 \) The general formula for percentage change in quantity demanded (\( \%\Delta Q \)) given an elasticity and a percentage change in the relevant variable (\( \%\Delta X \)) is: \[ \%\Delta Q = \text{Elasticity} \times \%\Delta X \] --- ## a. Price of good X increases by 5% - \( E_P = -2 \) - \( \%\Delta P_X = +5\% \) \[ \%\Delta Q_X = E_P \times \%\Delta P_X = (-2) \times 5\% = -10\% \] **Interpretation:** The consumption (quantity demanded) of good X will **decrease by 10%**. --- ## b. Price of good Y increases by 10% - \( E_{XY} = -6 \) - \( \%\Delta P_Y = +10\% \) \[ \%\Delta Q_X = E_{XY} \times \%\Delta P_Y = (-6) \times 10\% = -60\% \] **Interpretation:** The consumption of good X will **decrease by 60%**. --- ## c. Advertising decreases by 2% - \( E_A = 4 \) - \( \%\Delta A = -2\% \) \[ \%\Delta Q_X = E_A \times \%\Delta A = 4 \times (-2\%) = -8\% \] **Interpretation:** The consumption of good X will **decrease by 8%**. --- ## d. Income falls by 3% - \( E_I = 3 \) - \( \%\Delta I = -3\% \) \[ \%\Delta Q_X = E_I \times \%\Delta I = 3 \times (-3\%) = -9\% \] **Interpretation:** The consumption of good X will **decrease by 9%**. --- # Final Summary Table | Scenario | Calculation | Change in Q (%) | Interpretation | |--------------------------------------------------|---------------------------|-----------------|-------------------------------| | a. Price of X increases by 5% | \((-2) \times 5\) | \(-10\%\) | Decrease by 10% | | b. Price of Y increases by 10% | \((-6) \times 10\) | \(-60\%\) | Decrease by 60% | | c. Advertising decreases by 2% | \(4 \times (-2)\) | \(-8\%\) | Decrease by 8% | | d. Income falls by 3% | \(3 \times (-3)\) | \(-9\%\) | Decrease by 9% |