At Price \(=\$ \mathrm{q}\), quantity demanded, \(\mathrm{Q}_{\mathrm{D}}=11 .\) At Price \(=\) \(\$ 11, \mathrm{QD}=9\). Find the elasticity of demand using a) \(\mathrm{P}=9, \mathrm{Q}_{\mathrm{D}}=11\) as a base b) \(\mathrm{P}=11, \mathrm{Q}_{\mathrm{D}}=9\) as a base c) average values as a base.

To compute elasticity of demand, we need the percentage change in quantity demanded and percentage change in price for each case (a, b and, c). a) Using \(P = \$9\) and \(QD = 11\) as a base: - Percentage change in Quantity Demanded \(= \frac{11 - 9}{11} \times 100 = \frac{2}{11} \times 100\) - Percentage change in Price \(= \frac{11 - 9}{9} \times 100 = \frac{2}{9} \times 100\) b) Using \(P = \$11\) and \(QD = 9\) as a base: - Percentage change in Quantity Demanded \(= \frac{9 - 11}{9} \times 100 = \frac{-2}{9} \times 100\) - Percentage change in Price \(= \frac{9 - 11}{11} \times 100 = \frac{-2}{11} \times 100\) c) Using average values as a base: - Average Price \(= \frac{9 + 11}{2} = \$10\) - Average Quantity Demanded \(= \frac{9 + 11}{2} = 10\) - Percentage change in Quantity Demanded \(= \frac{11 - 9}{10} \times 100 = \frac{2}{10} \times 100\) - Percentage change in Price \(= \frac{11 - 9}{10} \times 100 = \frac{2}{10} \times 100\)

Now, we can calculate the elasticity of demand for each case (a, b, and c) using the percentage changes we calculated in step 1: a) \(E = \frac{(\frac{2}{11} \times 100)}{(\frac{2}{9} \times 100)}= \frac{\frac{2}{11}}{\frac{2}{9}}\) b) \(E = \frac{(\frac{-2}{9} \times 100)}{(\frac{-2}{11} \times 100)}= \frac{\frac{-2}{9}}{\frac{-2}{11}}\) c) \(E = \frac{(\frac{2}{10} \times 100)}{(\frac{2}{10} \times 100)}= \frac{\frac{2}{10}}{\frac{2}{10}}\)

Finally, we simplify the elasticity values we calculated in step 2: a) Elasticity of demand using \(P = \$9\) and \(QD = 11\) as a base: \(E = \frac{2}{11} \times \frac{9}{2} = \frac{9}{11}\) b) Elasticity of demand using \(P = \$11\) and \(QD = 9\) as a base: \(E = \frac{-2}{9} \times \frac{11}{-2} = \frac{11}{9}\) c) Elasticity of demand using average values as a base: \(E = \frac{2}{10} \times \frac{10}{2} = 1\) So, the elasticity of demand using: a) \(P = \$9\), \(QD = 11\) as a base is \(\frac{9}{11}\). b) \(P = \$11\), \(QD = 9\) as a base is \(\frac{11}{9}\). c) Average values as a base is \(1\).