Question
\begin{tabular}{l} Suppose a \( 9 \% \) increase in income led to a \( 49 \% \) increase in quantity demanded for smartwatches. Smartwatches have an income elasticity \\. Include a negative sign if applicable, and round your answer to two decimal places. \\ \hline\end{tabular}
Ask by Vaughan Osborne. in the United States
Feb 26,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
The income elasticity of demand for smartwatches is 5.44.
Solution
The income elasticity of demand (Ey) is calculated as the percentage change in quantity demanded divided by the percentage change in income. Given a 49% increase in quantity demanded and a 9% increase in income, the calculation is:
Ey = 49% ÷ 9% ≈ 5.44
Since both changes are increases, the elasticity is positive. Thus, the income elasticity for smartwatches is 5.44.
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Simplify this solution Bonus Knowledge
To calculate the income elasticity of demand, you can use the formula: \[ \text{Income Elasticity of Demand (E)} = \frac{\%\text{ Change in Quantity Demanded}}{\%\text{ Change in Income}} \] Substituting in the values: \[ E = \frac{49\%}{9\%} \approx 5.44 \] The income elasticity of smartwatches is approximately \(5.44\). This signifies that smartwatches are a luxury good, as the elasticity is greater than 1, indicating that demand increases more than the increase in income.
