Long Run Average Cost Curve

In the short run, some inputs are fixed while the others are variable. On the other hand, in the long run, the firm can vary all of its inputs. Long run cost is the minimal cost of producing any given level of output when all individual factors are variable. The long run cost curve helps us understand the functional relationship between out and the long run cost of production. In this article, we will look at understanding the long run average cost curve.

Deriving a Long Run Average Cost Curve

To understand the derivation of a long run average cost curve, let’s consider three short run average cost curves (SACs) as shown in Fig. 1 below.

These SACs are also called plant curves. In the short run, a firm can operate on any SAC, given the size of the plant. For the sake of our understanding, let’s assume that there are only three plants that are technically possible. Therefore, the firm increases or decreases its outputs by changing the amount of the variable inputs.

However, in the long run, the firm examines each SAC to find the curve that allows it to produce a given level of output at the minimum cost. Hence, it chooses between SAC₁, SAC₂, and SAC₃. From Fig. 1 above, you can see that to generate OB amount of output, the firm can choose between SAC₁ and SAC₂. Note that the firm will choose SAC₁ due to the lower costs as compared to SAC₂.

Further, you can also see that if the firm tries to produce an output OA, then it costs

• AL per unit with SAC₁
• AH per unit with SAC₂

Clearly, AH > AL. Therefore, the firm chooses SAC₁. Similarly, if the firm tries to produce an output which is greater than OB but less than OD, then it chooses SAC₂ since SAC1 involves higher costs. Also, for outputs larger than OD, the firm uses SAC₃. Summing up, we can say that in the long run, the firm employs the plant yielding maximum output at minimum cost per unit.

Long Run Average Cost Curve

Imagine if a firm has a choice of varying a plant by infinitely small gradations leading to infinite average cost curves. In such a case, the smooth curve enveloping all these short-run average cost curves is a long run average cost curve.

As you can see in the figure above, the long run average cost curve is drawn tangential to all SACs. In other words, every point on the long run average cost curve is a tangent point on some SAC. Hence, whenever a firm desires to produce a certain output, it operates on the corresponding SAC.

From the Fig. 2 above, you can observe that to produce an output OM, the corresponding point on the long run average cost curve is ‘G’. Also, the corresponding SAC is SAC₂.

Therefore, the firm operates on SAC₂ at point G. Similarly, the firm chooses different SACs based on its output requirement. It is also possible for the firm to produce the output OM with SAC₃.

However, this will lead to a higher cost of production as compared to SAC₂. On the other hand, to produce a higher output OV, the firm requires SAC₃. If the firm uses SAC2 for the same, then it results in higher unit similarity.

Note:

The long run average cost curve is not tangent to the minimum points of the SACs. For that matter, the long run average cost curve is tangential to

• the falling portions of the SACs while it is declining and
• the rising portions of the SACs while it is rising

Therefore, to produce an output less than OQ at the least cost, the firm operates the plant at less than its full capacity or less than its minimum cost of average production. To produce an output larger than OQ at the least cost, the firm operates the plant beyond its optimum capacity.

OQ is the optimum point because the output OQ is produced at the minimum point of the long run average cost curve and the corresponding SAC (SAC₄). While other plants are used at less than or more than their full capacity, only SAC₄ is operated at the minimum point.

A long run average cost curve is known as a planning curve. This is because a firm plans to produce an output in the long run by choosing a plant on the long run average cost curve corresponding to the output. It helps the firm decide the size of the plant for producing the desired output at the least possible cost.

Why does a long run average cost curve have a U-shape?

From Fig. 2, you can see that the LAC curve (long run average cost curve) is a U-shaped curve. This shape depends on the returns to scale. We know that, as a firm expands, the returns to scale increase.

Then they remain constant for some time and eventually decrease. On the same lines, the LAC curve first declines and eventually rises. Returns to scale have an inverse relationship with the long run average costs. Usually, a firm experiences

• Falling long run average costs and increasing economies to scale due to internal and external economies of scale.
• Rising long run average costs and diminishing economies to scale due to internal and external diseconomies of scale.

Now, the LAC curve shown in Fig. 2 is based on the traditional economic analysis. It is a flattened U-shape which exists only when the state of technology remains constant. However, empirical evidence shows that in the long run, the state of technology changes. Therefore, modern firms face an L-shaped LAC curve as opposed to a U-shaped curve as shown below.

As you can see above, over the AB range, the curve is perfectly flat. This implies that over this range, all sizes of plant have the same minimum cost of production.

Solved Question on Long Run Average Cost Curve

Q1. The positively sloped (i.e. rising) part of the long run average total cost curve is due to which of the following?

1. Diseconomies of scale.
2. Increasing returns.
3. The firm being able to take advantage of large-scale production techniques as it expands its output.
4. The increase in productivity that results from specialization.

Answer: While analyzing the U-shape of a long run average cost curve, we can identify that the rising part of the LAC curve is due to both internal and external diseconomies of scale. Hence, the answer is Option a.