Price Elasticity
1. **State the problem:** Calculate the Price Elasticity of Demand (PED) as the price of T-Shirts increases from $8 to $14 when income is $15M.
2. **Recall the formula for PED:**
$$\text{PED} = \frac{\% \text{ change in quantity demanded}}{\% \text{ change in price}} = \frac{\frac{Q_2 - Q_1}{Q_1}}{\frac{P_2 - P_1}{P_1}}$$
3. **Identify values from the table for income = $15M:**
- Initial price $P_1 = 8$
- Final price $P_2 = 14$
- Initial quantity demanded $Q_1 = 22$
- Final quantity demanded $Q_2 = 16$
4. **Calculate percentage changes:**
- Percentage change in quantity demanded:
$$\frac{16 - 22}{22} = \frac{-6}{22} = -0.2727$$
- Percentage change in price:
$$\frac{14 - 8}{8} = \frac{6}{8} = 0.75$$
5. **Calculate PED:**
$$\text{PED} = \frac{-0.2727}{0.75} = -0.3636$$
6. **Interpretation:**
The PED is approximately $-0.36$, which means demand is inelastic in this price range for income $15M$. A 1% increase in price leads to about a 0.36% decrease in quantity demanded, indicating consumers are relatively unresponsive to price changes here.