# Part One: Calculate Price Elasticity of Demand (Midpoint Method) **Step 1: Apply the Midpoint Formula** The midpoint method formula for price elasticity of demand is: \[ \text{Elasticity} = \frac{\frac{Q_2 - Q_1}{(Q_2 + Q_1)/2}}{\frac{P_2 - P_1}{(P_2 + P_1)/2}} \] Where: - \(Q_1 = 180\), \(Q_2 = 150\) - \(P_1 = \$4\), \(P_2 = \$5\) Calculate percentage change in quantity and price: \[ \text{Percentage change in quantity} = \frac{150 - 180}{(150 + 180)/2} = \frac{-30}{165} \approx -.182 \] \[ \text{Percentage change in price} = \frac{5 - 4}{(5 + 4)/2} = \frac{1}{4.5} \approx .222 \] **Explanation:** We use the averages of the starting and ending values to get a consistent measure of percentage change. --- **Step 2: Calculate Elasticity** \[ \text{Elasticity} = \frac{-.182}{.222} \approx -.82 \] **Explanation:** The price elasticity of demand is approximately \(-.82\), indicating the percentage change in quantity demanded for a 1% change in price. --- # Part Two: Classify Demand as Elastic or Inelastic **Step 1: Interpret the Elasticity Value** - If \(|\text{Elasticity}| > 1\): Demand is elastic. - If \(|\text{Elasticity}| < 1\): Demand is inelastic. Here, \(|-.82| = .82 < 1\). **Explanation:** Since the absolute value of elasticity is less than 1, the demand is **inelastic**. --- # Part Three: Total Expenditure Before and After the Price Change **Step 1: Calculate Initial and New Expenditure** - **Initial Expenditure:** \(P_1 \times Q_1 = \$4 \times 180 = \$720\) - **New Expenditure:** \(P_2 \times Q_2 = \$5 \times 150 = \$750\) **Explanation:** Total expenditure is simply price times quantity for each situation. --- **Final Answers:** - **Price elasticity of demand:** \(-.82\) (inelastic) - **Classification:** Inelastic demand - **Total expenditure:** *Before:* \$720 *After:* \$750