Introduction
Hello and welcome back. In our last lesson, we defined and calculated the various short-run costs a firm faces, such as fixed, variable, total, and average costs. We established that in the short run, at least one input—typically capital, like the size of a factory—is fixed. This has significant implications for a firm's cost structure.
Today, we transition from the short run to the long run. In the long run, all inputs are variable. A firm can build a bigger factory, lease more space, or downsize its operations. This flexibility is key. Our objective for this lesson is to describe the relationship between short-run and long-run average cost curves. We will see that the long-run average cost curve is derived directly from the many possible short-run scenarios a firm can choose from. This concept is crucial for understanding how firms plan for growth and achieve optimal production scales.
1. From One Short-Run Curve to Many
Let's quickly recall the shape of the Short-Run Average Total Cost (SRATC) curve. It's typically U-shaped. This is because, with a fixed plant size, adding more variable inputs (like labor) initially leads to efficiencies (falling average cost), but eventually, the law of diminishing marginal returns kicks in, causing marginal and average costs to rise.
The key insight for today is that a firm doesn't just have one SRATC curve; it has a different potential SRATC curve for every possible level of fixed inputs. A small factory has its own SRATC curve. A medium-sized factory has another. A large factory has yet another.
In the long run, the firm is no longer "stuck" on one of these curves. It can choose the factory size (and thus, the SRATC curve) that is best for its planned level of production.
To visualize this, let's watch a video that explains how the long-run average cost curve is derived from this family of short-run curves.
The Long Run Average Cost Curve as the Lower Envelope of our Short Run Average Cost Curves
This video from econhelp provides an excellent graphical derivation of the Long-Run Average Cost (LRAC) curve. It methodically builds up the concept from the foundational difference between short-run and long-run production.
Please watch the video from the beginning to 07:34. As you watch, focus on these key ideas: The core distinction: capital is fixed in the short run but variable in the long run. How each short-run average cost (SRAC) curve corresponds to a specific, fixed level of capital (e.g., a specific factory size). The crucial step: how the firm, in the long run, chooses the level of capital that minimizes the average cost for any given quantity of output, thereby tracing out the lowest possible costs.
2. The "Envelope Curve"
As the video explained, the Long-Run Average Cost (LRAC) curve is often called an envelope curve. It "envelops" or wraps around the entire family of SRATC curves from below.
This is because for any specific quantity of output you want to produce, the LRAC tells you the absolute lowest possible average cost you can achieve in the long run, once you've had time to adjust all your inputs (like building the perfectly sized factory).
Let's formalize this with a reading and a clear diagram.
7.4 The Structure of Costs in the Long Run
This reading from a university-level economics textbook provides a clear textual explanation of the LRAC as an envelope curve. It reinforces the concept you just saw in the video.
Please read the section titled 'Shapes of Long-Run Average Cost Curves'. Focus on the text explaining Figure 7.4b, which describes how the LRAC is built from the group of SRAC curves and why a firm would be 'foolish' to choose a non-optimal factory size for a given output.
The key takeaway is that for any point on the LRAC curve, it is tangent to one of the SRATC curves. This point of tangency represents the optimal plant size for producing that specific quantity of output. For any other level of output, that same plant size will be suboptimal, resulting in a higher average cost (i.e., you would be at a point on the SRATC curve that is above the LRAC curve).
This is shown clearly in the diagram below. If the firm wants to produce quantity Q1, it will choose the small plant size represented by SRAC1. If it expects to produce Q2, it will build the larger plant represented by SRAC2 to achieve the lowest possible average cost for that output level. The LRAC curve (in black) connects all these lowest-cost points.
3. The Shape of the LRAC: Economies and Diseconomies of Scale
Just like the SRATC curve, the LRAC curve is also typically U-shaped. However, the reasons for its shape are different.
The shape of the LRAC curve is determined by economies of scale, constant returns to scale, and diseconomies of scale.
- Economies of Scale: The downward-sloping portion of the LRAC. Here, as a firm increases its scale of operations (i.e., all inputs), its long-run average cost per unit decreases. This is why larger factories can often produce goods more cheaply.
- Constant Returns to Scale: The flat portion of the LRAC. In this range, increasing the scale of operations does not change the long-run average cost.
- Diseconomies of Scale: The upward-sloping portion of the LRAC. Beyond a certain point, a firm can become too large. The complexities of managing a massive organization can lead to inefficiencies, causing the long-run average cost per unit to increase.
The following resource, from a CFA prep provider, illustrates this clearly.
Topics in Demand and Supply Analysis
This reading from IFT directly connects the concepts of economies and diseconomies of scale to the shape of the LRAC curve, using terminology and diagrams you can expect to see on the CFA exam.
Read the sections titled 'Defining Economies of Scale and Diseconomies of Scale' and the 'Interpretation of the graph'. Focus on how the LRATC curve's downward-sloping, flat, and upward-sloping sections correspond to economies of scale, constant returns to scale, and diseconomies of scale, respectively.
It is essential not to confuse the reason for the U-shaped LRAC (economies/diseconomies of scale) with the reason for the U-shaped SRATC (diminishing marginal returns).
- Diminishing Marginal Returns (Short Run): Occurs when you add more of a variable input to a fixed input.
- Diseconomies of Scale (Long Run): Occurs when you increase all inputs and the scale of operation becomes inefficiently large.
To solidify this distinction, quickly read the "Clear it Up" box in the BCCampus resource you looked at earlier.
7.4 The Structure of Costs in the Long Run
This brief section clarifies a very common point of confusion for students.
Read the box titled 'How do economies of scale compare to diminishing marginal returns?'. This will help you clearly separate these two important concepts.
Conclusion
In this lesson, we have bridged the gap between short-run and long-run cost analysis. You now understand how a firm's long-run planning involves choosing among many possible short-run scenarios to minimize costs.
Key Takeaways:
- In the short run, a firm operates on a single SRATC curve determined by its fixed inputs (e.g., plant size).
- In the long run, a firm can choose its level of all inputs, effectively selecting the optimal SRATC curve for its desired output level.
- The Long-Run Average Cost (LRAC) curve is the "envelope" of all possible SRATC curves, representing the lowest possible average cost for each level of output.
- The U-shape of the LRAC curve reflects economies of scale (falling average cost), constant returns to scale (constant average cost), and diseconomies of scale (rising average cost).
- An important implication is that the long-run average cost of producing a certain quantity will always be less than or equal to the short-run average cost.
Preview of the Next Lesson:
We have established that the LRAC's shape is due to economies and diseconomies of scale. The next logical question is why do these phenomena occur? What factors allow a larger firm to reduce its average costs, and what causes them to eventually rise? In the next lesson, we will answer these questions by exploring the specific causes of economies and diseconomies of scale, such as specialization, technological advantages, and managerial challenges.