Introduction
The relationship between short-run and long-run cost structures is crucial to understanding firm behavior. In the short run, at least one factor of production is fixed. In contrast, in the long run, all inputs are variable. The Long-run Average Cost (LAC) curve is derived from various Short-run Average Cost (SAC) curves and represents the minimum average cost of production at different output levels.
Short-Run Average Cost Curves (SAC)
Each SAC curve represents a specific plant size or scale of operation. Due to the law of diminishing returns, each SAC is U-shaped. Firms can only operate on one SAC at a time in the short run.
Long-Run Average Cost Curve (LAC)
The LAC curve is also known as the ‘envelope curve’ because it envelopes all SAC curves. It shows the lowest cost at which any output level can be produced when a firm has full flexibility to choose the most efficient plant size.
Derivation of LAC from SAC
To derive the LAC:
- Plot several SAC curves representing different plant sizes.
- Identify the lowest point on each SAC where the firm can produce each output level efficiently.
- Join these lowest points smoothly to form the LAC curve.
Shape of the LAC Curve
The LAC is typically U-shaped due to economies and diseconomies of scale:
- Falling segment: Represents economies of scale (spreading fixed costs, specialization, etc.).
- Rising segment: Reflects diseconomies of scale (management issues, inefficiencies).
Graphical Illustration
Imagine SAC1, SAC2, SAC3 as different short-run curves. The LAC curve touches each SAC at its tangency point, indicating the least-cost output for that plant size. The result is a smooth, U-shaped curve that lies below or touches the SACs.
Conclusion
The Long-run Average Cost curve is a strategic guide for firms, helping them select the most cost-effective production scale in the long run. It encapsulates all possible short-run cost situations, guiding optimal plant size choices as output needs change.