This curve is used to determine the possible projections of cost and output for the long term. While a short-term curve does exist, the factors that go into determining a short-term curve are a mixture of fixed inputs and variable inputs. However, given the sheer unpredictability of the future, the long-run average cost curve is mostly constructed using variable inputs. The long-run average total cost curve is used to determine productivity and cost in the long run.
Derivation of Long-run Average Cost Curve
To understand the reasoning behind the derivation of a long-run average cost curve, it is preferable to start with three short-run average cost curves.
As the term suggests, short term average cost curves can be used for any firm in the short run. The firm can modify the increase or decrease in output and cost by changing the variable inputs appropriately. However, planning for the long run involves a little more creativity and understanding.
After closely examining each SAC (also referred to as plants, there may be more than 3 for a single firm), the firm will need to determine the most optimal curve to maximize production and minimize cost. To this end, the firm will need to choose the most optimal SAC, which will then be projected into the long term. While one SAC might give the firm the required results, another SAC might give them greater returns. This is why it is essential to consider multiple variables and create multiple SACs to determine the best cost vs output scenario. SACs are the key to how to find the long-run average total cost curve.
Long Run Average Cost Curve Definition
To define the long-run average cost curve, consider an array of SACs that will vary only slightly to form a specific gradation. In such a case, the curve that is formed by connecting the lowest points of each SAC will form the long-run average cost curve. Given that this long-run curve is drawn tangentially to all the increasingly graded SAC, it showcases the points with the lowest cost and thus gives the firm an idea of what SAC it can use to achieve the desired output.
So if any point on the LAC is what the goal the firm wishes to reach, then the firm will employ the corresponding SAC that is closest to the point along the tangent. Multiple SACs along the tangent will be able to sustain a specific output, but only one will be able to do it at the lowest cost. Using the wrong SAC or improperly grading the curve will result in increased cost for the same output or (in cases of a faulty LAC) result in a decreased output for the expected cost.
The long-run average cost curve is used to plan the desired output for a specific cost, granting it the title of the planning curve. This is because a firm can plan their cost and productivity by choosing the right plant along the long-run average cost curve.