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'''Long run average cost''' is the cost per unit of output when all inputs are variable, so that the firm can choose the optimal scale and combination of inputs for each level of output. The long-run average cost curve is the envelope of the short-run average total cost curves, each corresponding to a different level of the fixed input.

== Shape and Interpretation ==
The long-run average cost curve is typically U-shaped. At low levels of output, average cost falls as output rises, reflecting economies of scale from specialisation, indivisible inputs, and learning. Beyond some point, average cost rises, reflecting diseconomies of scale from coordination and management problems in large organisations.

The output at which long-run average cost is minimised defines the minimum efficient scale, the smallest output at which a firm can achieve the lowest achievable average cost. The shape and location of the curve have important implications for market structure, since a large minimum efficient scale relative to market demand implies that only a few firms can operate efficiently.

== Relation to Short Run ==
The long-run curve is the lower envelope of the short-run curves. For each level of the fixed input, there is a short-run average total cost curve, and the long-run curve is the lowest point of each of these curves. The point of tangency between a short-run curve and the long-run curve indicates the output at which the given level of the fixed input is optimal.

The relationship implies that the firm's optimal scale changes with the level of output, and that in the long run the firm adjusts all inputs to minimise cost for the chosen output. In the short run, the firm is constrained by its fixed inputs and operates on a particular short-run curve.

== Economies of Scale and Scope ==
Economies of scale refer to reductions in average cost as output expands. They arise from a variety of sources, including technical indivisibilities, specialisation of labour and machinery, bulk purchasing, and the spreading of fixed costs. They are limited by diseconomies arising from coordination and complexity at large scale.

Economies of scope refer to cost savings from producing multiple products jointly rather than separately. They arise from shared inputs and joint production and are relevant to multi-product firms, including utilities, banks, and transport operators. The analysis of scope economies informs decisions about diversification and about the regulation of multi-product firms.

== Applications ==
The long-run average cost curve informs the analysis of natural monopoly, where average cost falls over the entire range of demand, so that a single firm can serve the market at lower cost than multiple firms. It also informs merger analysis, since economies of scale may justify consolidation, and the analysis of entry barriers, since a large minimum efficient scale relative to the market can deter entry.

== Determinants of the Shape ==
The shape of the long-run average cost curve is determined by the balance of economies and diseconomies of scale. Economies arise from specialisation, indivisible inputs, bulk purchasing, and learning by doing. Diseconomies arise from coordination and incentive problems in large organisations, from the difficulty of managing complex operations, and from the depletion of scarce managerial talent.

The relative strength of these forces varies across industries. In some industries, economies of scale continue to very large outputs, so the curve is downward-sloping over the relevant range. In others, economies are exhausted at low output and diseconomies set in early, so the curve rises quickly.

== Empirical Estimation ==
Estimating long-run average cost curves requires data on costs and outputs across firms and over time. Statistical cost estimation faces challenges, including the measurement of output in multi-product firms, the treatment of input prices, and the endogeneity of output and costs.

Alternative methods include engineering estimates, which specify the cost of producing at different scales based on technical relationships, and survivor analysis, which infers efficient scale from the sizes of firms that survive in competitive markets. Each method has limitations, and estimates of the same industry can differ substantially.

== Scale and Scope in Practice ==
In practice, firms often produce multiple products, and the analysis of cost must consider economies of scope as well as scale. A firm may achieve lower cost by producing related products jointly, sharing inputs and spreading fixed costs. The assessment of efficiency therefore requires attention to the product mix as well as the scale of output.

Industries with significant scope economies include banking, where deposits and loans share operational infrastructure; utilities, where generation and distribution may be integrated; and transportation, where networks serve multiple routes. The analysis of scope economies informs decisions about diversification and regulation.

== Implications for Regulation and Policy ==
The shape of the long-run average cost curve informs the regulation of natural monopoly, where a single firm can serve the market at lower cost than multiple firms. In such cases, regulation seeks to prevent the exercise of monopoly power while allowing the realisation of scale economies, through price controls, rate-of-return regulation, or incentive mechanisms.

The concept also informs merger review, since economies of scale may justify consolidation, and the analysis of entry conditions, since a large minimum efficient scale relative to the market can deter entry. The assessment of these issues requires careful estimation of costs and of the relevant market, and the conclusions can be sensitive to the assumptions made.

== See also ==
* [[Cost Function]]
* [[Minimum Efficient Scale]]
* [[Market structure]]

== References ==

<ref name="r1">Textbooks on cost theory and industrial organisation.</ref>
<ref name="r2">Research on economies of scale and scope.</ref>
<ref name="r3">Studies of market structure and natural monopoly.</ref>

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[[Category:Microeconomics]]
[[Category:Production economics]]
[[Category:Cost accounting]]