Cost Output Relationship in the Long Run

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Cost Output Relationship in the Long Run


The long-run cost-output implies the relationship between the changing scale of the firm and the total output. In the long run, only the average cost is important and considered in taking long term output decisions.

The long-run average cost is the long-run total cost divided by the level of output. It is the least possible cost of producing the given level of output when all the factors are variable. Long-run average cost curves will normally be U-shaped just as short-run curves are, but they will always be flatter than the short-run ones. The reason is obvious that the scale of operations of the firm can be changed and all the costs become variable because there are no fixed factors in the long run. Over a long period, the size of the plant can be changed, unwanted buildings can be sold, and administrative and marketing staff can be increased or decreased to deal efficiency and can be used more economically. Thus, the average cost will be lower and variable costs will not rise as sharply as in a short period. That’s why LAC curve is flatter than short-run ones.

The long-run cost curves are influenced by the law of returns to scale. Each time the scale of the operations of the firm is changed, a new short-run cost curve will have to be drawn for the firm. In the short run, there will be only one AC curve to represent one fixed scale of output and the short-run average cost curve [SAC] is applicable to only one plant while the long-run average cost [LAC] takes many plants into consideration because of the changes in the scale of operations.




LAC curve will be tangent to all the SAC curves and will touch each SAC curve at its minimum point at optimum output. The  LAC curve is also known as the ‘Envelope Curve’ or  ‘Planning Curve’ as it serves as a guide to the producer in his plans to expand production.


Production cost in the short and long run both:




In this diagram, SAC1, SAC2, and SAC3 are the three possible plants and the LAC curve is drawn according to these plants. For the output OQ1, plant SAC2 cost P1Q1 is more than plant SAC1 R1Q1 which is a long-run cost also. For OQ2 output, the cost will be the same [R2Q2] for the short run and long run both.

If the firm increase the production OQ3, it can be obtained at the higher average cost P3Q3 in plant SAC2 but the same output OQ3 can be produced at a lower average cost R3Q3 in the long run because the scale of the production can be modified in the long-run according to the requirements.


Important features of LAC and cost-output relationship in the long run:

  1. LAC curve will be tangent to all the SAC curves and will touch each SAC curve at its minimum point at the optimum output. SAC curve cannot be lower than the LAC curve for any given level of output.
  2. The LAC curve is also known as the ‘Envelope Curve’ because it envelops a group of SAC curves.
  3. The LAC curve is also known as the ‘Planning Curve’ as it serves as a guide to the producer in his plans to expand production and represents the least cost of production for the various possible level of output.
  4. Long-run average cost curves will normally be U-shaped or dish-shaped but they will always be flatter than the short-run ones.
  5. The LAC helps the producer to select the optimum size of the plant so that the factors can be utilized properly and economically.


Dr. Swati Gupta



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