. Profit maximization in the cost-curve diagram Suppose that the market for sports watches is a competitive market. The following graph shows the daily cost curves of a firm operating in this market. Hint: After placing the rectangle on the graph, you can select an endpoint to see the coordinates of that point. 100 90 Profit or Loss 80 70 60 50 40 ATC 30 20 AVC MC 10 10 20 30 40 50 60 80 90 100 70 QUANTITY (Thousands of watches per day) In the short run, at a market price of $45 per watch, this firm will choose to produce watches per day. On the preceding graph, use the blue rectangle (circle symbols) to shade the area representing the firm’s profit or loss if the market price is $45 and the firm chooses to produce the quantity you already selected. Note: In the following question, enter a positive number, even if it represents a loss. would be $ thousand per day in the short run. The area of this rectangle indicates that the firm’s 3
The Correct Answer and Explanation is:
To answer this question, we’ll walk through how a firm determines its profit-maximizing quantity, identifies whether it’s making a profit or loss, and then calculate the total dollar amount of profit or loss using the cost curves provided.
Step 1: Identify the Market Price
The market price is \$45 per watch.
Step 2: Apply the Profit Maximization Rule
In a perfectly competitive market, firms maximize profit where:
Price (P) = Marginal Cost (MC)
From the graph:
- Locate where MC intersects the horizontal line at \$45.
- This happens at a quantity of 70,000 watches per day.
Step 3: Determine the Average Total Cost (ATC) at this Quantity
At 70,000 watches per day, trace vertically up to the ATC curve:
- ATC at 70,000 units is about \$60 per watch (as shown on the graph).
Step 4: Calculate Profit or Loss per Unit
- Price = \$45
- ATC = \$60
So,
Profit (or loss) per unit = Price – ATC = \$45 – \$60 = -\$15 (loss)
Since the firm is losing \$15 per watch, it is incurring a loss.
Step 5: Total Profit (Loss) = Per Unit Loss × Quantity
- Per unit loss = \$15
- Quantity = 70,000 watches
Total loss = 70,000 × \$15 = \$1,050,000 or \$1,050 thousand per day
Step 6: Shading the Area (Rectangle)
On the cost-curve graph:
- Base of the rectangle = 70 (quantity in thousands)
- Height = \$60 (ATC) – \$45 (Price) = \$15
- Area = Base × Height = 70 × 15 = \$1,050 (thousand)
This rectangle represents the firm’s daily economic loss.
✅ Final Answers:
- Quantity produced: 70 thousand watches per day
- Total loss: \$1,050 thousand per day
Explanation Summary (300+ Words):
In a perfectly competitive market, firms are price takers—they cannot set their own prices. They must accept the market price, which in this case is \$45 per watch. To maximize profits, a firm produces where the market price equals marginal cost (MC). From the graph, we see that at a price of \$45, the firm’s MC curve intersects the price line at a quantity of 70,000 units.
At this production level, the firm’s average total cost (ATC) is \$60 per unit. Since the firm is selling each watch for \$45 but it costs \$60 to make, it loses \$15 on each watch sold. This loss per unit, when multiplied by the number of units produced (70,000), gives a total daily loss of \$1,050,000. Because the firm is operating in the short run, it might continue producing despite this loss if it can cover its average variable costs (AVC), which appear to be below \$45 on the graph. Continuing to operate allows it to minimize losses in the short run, as shutting down would result in a loss equal to total fixed costs.
Graphically, this loss is represented by the area of a rectangle. The rectangle’s height is the difference between ATC and price (\$15), and the base is the quantity produced (70). The area (70 × 15 = 1,050) shows the total loss in thousands of dollars.
Thus, even though the firm operates at the profit-maximizing rule (P = MC), it incurs a loss due to high average total costs at that output level.