Let's walk through the step-by-step solution **with explanations** for the scenario described: --- ### **Background** - **PREPA is a natural monopoly**: This means its ATC (average total cost) is downward sloping over the relevant range. - **Given curves on the graph**: - **D**: Market demand curve - **MR**: Marginal revenue curve - **MC**: Marginal cost curve - **ATC**: Average total cost curve PREPA is **regulated by a price cap** that allows it to **break even** (earn zero economic profit). --- ### **Step 1: Find the Break-Even (Zero Profit) Price and Quantity** A firm breaks even where **Price = ATC**. #### **How to find the point:** - The regulatory authority sets the **price cap** at the level where the **demand curve (D)** intersects the **ATC** curve. - At this price, the firm can sell a quantity where **P = ATC**, so **total revenue = total cost**, and **economic profit = 0**. #### **On the graph:** - **Find the intersection of the ATC curve and the demand curve (D).** - **Draw a horizontal line** at this price across the graph—this is the **price cap**. --- ### **Step 2: Mark the Firm’s Output and Price** - **At the price cap**, move down vertically to the **demand curve** to find the **quantity sold**. - **Put a dot** (●) at the intersection of **price cap** and **demand**—this is **(Q, P)** under regulation. --- ### **Step 3: Show Deadweight Loss (DWL)** - In a natural monopoly, **allocative efficiency** is at **P = MC**. - But under break-even regulation, **P = ATC > MC**, so **Q is less than the allocatively efficient quantity**. - **DWL** is the triangle between: 1. The **demand curve** 2. The **MC curve** 3. The vertical line at the regulated quantity (Q). - **Shade this triangle** and label it **DWL**. --- ### **Step 4: Show Consumer Surplus (CS)** - **Consumer surplus** is the area **below the demand curve** and **above the price cap** line, from **Q = 0 up to the regulated quantity**. - **Draw this area** and label it **CS**. --- ### **Step 5: Economic Profit** - **At the break-even price cap:** \[ \text{Economic profit} = 0 \] --- ### **Summary Table** | | What to Draw | |---|---| | Price Cap | Horizontal line at P = ATC where D and ATC intersect | | Regulated Output | Dot at intersection of price cap and demand curve | | Deadweight Loss (DWL) | Triangle between D, MC, and vertical line at Q | | Consumer Surplus (CS) | Area between D and price cap, up to Q | | Economic Profit | $0 | --- ## **Final Answer** - **Draw a horizontal line at the price where the demand curve intersects the ATC curve (this is the price cap).** - **Draw a point at the intersection of the price cap and the demand curve (this is the regulated price and quantity).** - **Shade and label the triangle between the demand curve, the MC curve, and the vertical at the regulated quantity as DWL (deadweight loss).** - **Shade and label the area between the demand curve and price cap, up to the regulated quantity, as CS (consumer surplus).** - **Economic profit is $0.** --- **If you provide the graph, I can mark these directly.** If not, follow these steps to draw the required lines, points, and shapes!