Long run average cost curve

What Is the Long Run Average Cost Curve?

The long run average cost curve (LRAC) is a fundamental concept in microeconomics that illustrates the lowest possible average cost of producing any given level of output when all inputs are variable. Unlike the short run, where at least one factor of production is fixed costs, in the long run, a firm can adjust all its inputs, including plant size, machinery, and labor, to achieve the most efficient production function for each output level. The shape of the long run average cost curve typically reflects the presence of economies of scale, constant returns to scale, and diseconomies of scale as production volume changes. This curve is crucial for understanding a firm's optimal scale of operation and its long-term pricing strategy.

History and Origin

The foundational concepts underpinning the long run average cost curve, particularly the distinction between short-run and long-run costs and the analysis of a firm's cost structure, can be traced back to the work of English economist Alfred Marshall. Marshall, a prominent figure in neoclassical economics, published his influential work, Principles of Economics, in 1890. In this treatise, he laid much of the groundwork for modern cost theory, emphasizing how firms adjust their inputs over different time horizons to minimize costs and optimize output.¹⁸ Marshall's contributions included the law of diminishing returns and a comprehensive analysis of supply and demand, which provided the context for understanding how costs influence production decisions in the long run.¹⁵, ¹⁶, ¹⁷

Key Takeaways

• The long run average cost curve (LRAC) represents the minimum average cost of production when all inputs are variable.
• Its shape is influenced by economies of scale (decreasing costs), constant returns to scale (stable costs), and diseconomies of scale (increasing costs).
• The LRAC helps businesses determine the most efficient scale of operation to achieve the lowest per-unit cost over the long term.
• Technological advancements and changes in input prices can shift the LRAC, making production more or less efficient.
• Understanding the LRAC is vital for strategic planning, investment decisions, and assessing a firm's long-term competitive advantage.

Formula and Calculation

While the long run average cost curve itself is a graphical representation rather than a single formula, each point on the curve represents the minimum average cost for a specific level of output, given that all inputs can be optimally adjusted. The average cost at any given output level is calculated by dividing the total cost of production by the quantity of output.

The total cost in the long run comprises all variable costs since no inputs are fixed. Therefore, for any given output (Q), the long run average cost (LRAC) is:

To determine the points on the LRAC, a firm hypothetically considers all possible plant sizes and combinations of inputs to produce each output level at the lowest possible cost. This involves evaluating the short run average total cost (SRATC) curves for various plant sizes and then constructing an "envelope" curve that is tangent to the lowest points of these SRATC curves. This envelope curve forms the LRAC.

Interpreting the Long Run Average Cost Curve

Interpreting the long run average cost curve involves understanding its distinct phases, which reflect how a firm's average costs behave as it changes its scale of operations. Initially, as a firm increases its output and expands its production capacity, it typically experiences economies of scale. This is represented by the downward-sloping portion of the LRAC, where the average cost per unit decreases. Such efficiencies often arise from specialization of labor, bulk purchasing of raw materials, and more efficient use of machinery.

After achieving a certain scale, a firm may enter a phase of constant returns to scale, where further increases in output do not significantly change the average cost. This segment of the LRAC appears relatively flat. Beyond this optimal range, if a firm continues to expand, it may encounter diseconomies of scale. This is depicted by the upward-sloping portion of the LRAC, indicating that average costs per unit begin to rise. Diseconomies can result from managerial inefficiencies, communication breakdowns in large organizations, or increased bureaucratic hurdles.¹³, ¹⁴

Therefore, the LRAC helps identify the most efficient scale of production for a firm, which is typically found at the lowest point or the flat portion of the curve, representing the optimal plant size where costs are minimized. Businesses use this analysis to make strategic decisions regarding expansion, capital expenditure, and overall resource allocation.

Hypothetical Example

Consider a hypothetical company, "WidgetCo," which manufactures widgets. WidgetCo currently produces 10,000 widgets per month using a small facility. Its total long-run costs (including rent, machinery leases, and raw materials) amount to $100,000, making its LRAC $10 per widget.

Scenario 1: Economies of Scale
WidgetCo decides to expand its operations to 20,000 widgets per month by investing in a larger factory and more efficient assembly lines. Due to bulk discounts on materials and improved labor specialization, its total costs increase to $150,000.
$LRAC = $150,000 / 20,000 = $7.50 \text{ per widget}$
In this case, WidgetCo experienced economies of scale, as its average cost per unit decreased.

Scenario 2: Constant Returns to Scale
Encouraged by its success, WidgetCo expands further to 30,000 widgets per month. It manages to scale its operations proportionally, with total costs rising to $225,000.
$LRAC = $225,000 / 30,000 = $7.50 \text{ per widget}$
Here, WidgetCo exhibits constant returns to scale; the average cost per unit remains stable despite increased output.

Scenario 3: Diseconomies of Scale
WidgetCo attempts to reach 40,000 widgets per month, but its large size leads to coordination issues, increased managerial layers, and bottlenecks in its supply chain. Its total costs jump to $350,000.
$LRAC = $350,000 / 40,000 = $8.75 \text{ per widget}$
In this final scenario, WidgetCo encounters diseconomies of scale, as the average cost per widget increased due to inefficiencies stemming from its excessive size. This example illustrates how the LRAC would initially fall, then flatten, and eventually rise, demonstrating the importance of finding the optimal scale for production and efficient return on investment.

Practical Applications

The long run average cost curve has numerous practical applications for businesses, investors, and policymakers. For businesses, understanding the LRAC helps in strategic planning, particularly when making decisions about expansion or contraction. Firms can identify the most efficient scale of operation where their per-unit costs are minimized, aiding in long-term production planning and resource allocation. For instance, large retailers like Walmart and e-commerce giants like Amazon leverage their massive scale to achieve significant economies of scale, enabling them to negotiate lower prices with suppliers and spread high fixed costs over a vast output, thus lowering their average costs per unit.¹⁰, ¹¹, ¹² This allows them to offer competitive prices and gain a competitive advantage.

Investors analyze the LRAC to assess a company's long-term profitability and sustainability. A company operating near its minimum LRAC typically indicates efficient management and a strong market position. Conversely, a company experiencing rising average costs due to diseconomies of scale might signal potential future challenges. Policymakers also consider LRAC concepts when evaluating market structures, competition, and the potential for natural monopolies, where economies of scale are so extensive that a single firm can supply the entire market at a lower cost than multiple firms.

Limitations and Criticisms

While the long run average cost curve is a valuable theoretical tool, it has several limitations and criticisms in its practical application. One major critique is the assumption that all inputs are perfectly variable in the long run and that a firm can instantaneously shift between different plant sizes without incurring additional adjustment costs. In reality, significant capital expenditure and time are often required to expand or contract operations, which are not always fully captured by the static LRAC model.

Furthermore, empirical studies have sometimes presented a different picture than the traditional U-shaped LRAC. Many studies suggest that the LRAC for a large number of industries is more L-shaped, meaning that average costs fall rapidly initially due to economies of scale but then tend to remain constant or decrease only slightly as production increases, rather than rising significantly due to diseconomies of scale.⁸, ⁹ This implies that the managerial and organizational challenges that lead to diseconomies of scale may be offset by continuous technical efficiencies or improvements in management practices in very large firms.⁶, ⁷

Critics also point out that the LRAC assumes a given level of technology. Technological advancements can continually shift the entire curve downwards, making previous optimal scales less efficient. Moreover, the concept might not fully account for external factors beyond the firm's control, such as changes in input prices across the entire industry or shifts in regulatory environments, which can impact costs independently of a firm's scale decisions. The complexity of real-world operations, including communication breakdowns and bureaucracy in very large organizations, can also lead to inefficiencies that are difficult to predict or quantify precisely within the theoretical framework.³, ⁴, ⁵

Long Run Average Cost Curve vs. Short Run Average Cost Curve

The distinction between the long run average cost curve (LRAC) and the short run average cost curve (SRATC) is fundamental to cost theory. The primary difference lies in the flexibility of inputs.

In essence, the SRATC illustrates costs for a firm operating with its current, fixed capacity, showing how average costs change as variable inputs are added. The long run average cost curve, on the other hand, represents a series of optimal choices, showing the lowest average cost achievable for various output levels when a firm has the flexibility to choose any plant size.

FAQs

What causes the long run average cost curve to be U-shaped?

The traditional U-shape of the long run average cost curve is attributed to the presence of economies of scale at lower output levels, leading to decreasing average costs, followed by constant returns to scale in an intermediate range, and eventually diseconomies of scale at very high output levels, causing average costs to rise.

How do economies of scale affect the LRAC?

Economies of scale cause the initial downward-sloping portion of the long run average cost curve. As a firm increases its output, it can achieve lower average costs per unit due to factors like specialization, bulk purchasing, and more efficient use of technology.

What are diseconomies of scale?

Diseconomies of scale occur when a firm's average cost per unit increases as it expands its output beyond a certain point. This typically happens due to managerial inefficiencies, communication challenges, increased bureaucracy, or coordination problems in very large organizations, making it harder to manage effectively.

Can the LRAC ever be L-shaped?

Yes, some empirical studies suggest that the long run average cost curve can be L-shaped.¹, ² This implies that while average costs fall quickly due to initial economies of scale, they then tend to remain relatively constant or decrease at a much slower rate over a wide range of output, rather than rising significantly due to diseconomies of scale. This might be due to continuous technological improvements or effective management offsetting potential inefficiencies in large firms.

Why is understanding the LRAC important for businesses?

Understanding the long run average cost curve is crucial for businesses because it helps them identify the most efficient scale of production. It guides strategic decisions regarding investment in new facilities, determining optimal plant size, and assessing the long-term viability and competitiveness of their operations within the market, impacting their overall opportunity cost and profitability.