# Step-by-Step Solution ## Assumptions & Given Data To solve the problem, we **need information about the supply and demand schedules** for used DVDs. Typically, these questions provide a table or equations for quantity demanded and supplied at different prices. Since the problem statement doesn't include specific data, I'll **illustrate the general method** and provide a hypothetical example. If you can provide the demand and supply data, I can use that instead. --- ## a. Calculating the Weekly Shortage **Shortage** occurs when the quantity demanded exceeds the quantity supplied at the imposed price ceiling. ### Steps: 1. **Find quantity demanded at $7.50** (`Q_d`). 2. **Find quantity supplied at $7.50** (`Q_s`). 3. **Calculate shortage**: \[ \text{Shortage} = Q_d - Q_s \] ### Hypothetical Example Suppose the data is: | Price | Quantity Demanded | Quantity Supplied | |-------|-------------------|------------------| | $9 | 100 | 180 | | $8 | 120 | 160 | | $7.50 | 135 | 140 | | $7 | 150 | 120 | #### At $7.50: - \( Q_d = 135 \) - \( Q_s = 140 \) **Shortage**: \[ \text{Shortage} = Q_d - Q_s = 135 - 140 = -5 \] But a negative value suggests a surplus, which contradicts the usual effect of a price ceiling. Let's check the values again. At a lower price, quantity supplied should be less than quantity demanded. Suppose at $7.50: - \( Q_d = 160 \) - \( Q_s = 100 \) **Shortage**: \[ \text{Shortage} = 160 - 100 = 60 \] **Final Answer (using example data):** > **60 used DVDs** --- ## b. Calculating Total Economic Surplus Lost (Deadweight Loss) The **deadweight loss (DWL)** is the lost surplus due to transactions that no longer occur because of the price ceiling. ### Steps: 1. **Find the equilibrium price and quantity** (where supply = demand). 2. **Find the quantity exchanged at the price ceiling** (\( Q_{ceiling} = Q_s \) at $7.50). 3. **Calculate DWL**: The DWL is the area of the triangle between the supply and demand curves from \( Q_{ceiling} \) to \( Q_{equilibrium} \). \[ \text{DWL} = \frac{1}{2} \times (\text{Price difference at those quantities}) \times (\text{Quantity difference}) \] ### Hypothetical Example Suppose equilibrium is at $8.50 and quantity 130. - **Equilibrium quantity:** 130 - **Quantity at ceiling:** 100 (from earlier) - **Demand price at Q=100:** $10 (price buyers would pay for the 130th DVD) - **Supply price at Q=100:** $7.50 (price sellers are willing to accept for the 100th DVD) \[ \text{DWL} = \frac{1}{2} \times (130 - 100) \times (10 - 7.50) = \frac{1}{2} \times 30 \times 2.5 = 37.5 \] **Final Answer (using example data):** > **$37.50 per week** --- ## Summary Table | Part | Formula Used | Example Answer | |------|------------------------|--------------------| | a | \( Q_d - Q_s \) | 60 used DVDs | | b | \( \frac{1}{2} \times (Q^* - Q_{ceiling}) \times (P_{demand} - P_{supply}) \) | $37.50 per week | --- ## **Note:** **If you provide the actual supply and demand data, I can give the precise numeric answers for your specific problem.**