1. If the return on scale remains unchanged, LAC=LMC, which is the straight line of LAC and the lowest point of SAC.

2. When the scale gains increase or decrease: LMC and LAC meet the lowest point of LAC, that is, the lowest point of SA corresponding to the output. The points on the left and right sides of this intersection are not the lowest SAC points of the corresponding output. On the left is the point where SAC falls, namely SAC & gtSMC, and on the right is the point where SAC rises, namely sac < SMC.

3. Only the lowest point of LAC is tangent to the lowest point of SAC.

The three short-term cost curves represent the change of average cost under different production scales. The farther to the right, the larger the production scale. Each SAC and LAC do not intersect but are tangent, and there is only one tangent point, thus forming an envelope curve. This is the result of choosing the production scale in order to reduce the cost.

Extended data

Derivation of long-term average cost curve

(1) Long-term average cost curve with limited scale change: it is the connection of the line segments below the intersection of all short-term average cost curves.

(2) Infinitely subdivided long-term average cost curve: it is the lower envelope of short-term average cost curve. Because of the different curvatures, only the lowest point of LAC curve is tangent to the lowest point of SAC curve.

Relationship between long-term average cost curve and short-term average cost curve

The long-term average cost curve is the locus of the tangent points of countless short-term average cost curves, and it is the envelope of all short-term average cost curves. Every point on the long-term average cost curve represents the lowest average cost of producing the corresponding output level.

Both the short-term average cost curve and the long-term average cost curve are U-shaped curves that first drop and then rise. The difference is that the short-term average cost curve is steep whether it falls or rises, while the long-term average cost curve is flat whether it falls or rises; The short-term average cost curve is determined by the law of diminishing marginal income, and the long-term average cost curve is determined by economies of scale.

Baidu Encyclopedia-Long-term Average Cost Curve