Question

2. How does the envelope relationship relate short run average cost and long run average cost?

Answer 1

To know the relationship between short run average cost curve and long run average cost curve, first we would see short run and long run.

Short run is that period for a firm when it wants its output to increase, it can only do same with the variable factors like raw material, labour, etc. The fixed factors like land, building, machine can not vary or changed for output increase.

While in the long run, when output increase is needed both factors, variable and fixed both can be changed as per necessity. Be it labour, raw material, land, machine, capital etc.

This makes clear that in short run only variable costs can vary for output increase while in long run, both variable and fixed costs can be changed for desired output increase.

Both curves, whether short or long are U in shape because as the output increases cost of production starts falling resulting in various economies of scale. Once it reaches lowest point which is optimum level it starts rising and keeps rising if the production is continued after optimum point.

Short run cost curves are drawn every time new for the firm as SAC1, SAC2, SAC3, etc. which has U shape. This is because, firms output increase is based on variable factors, and every time variable factors are changed, scale of operations also changes. And with every change in scale of operation new short run cost curve is created.

While long run cost curves have all costs as variable in the firm. The firm has long time so have larger type of scale or machinery/plant to produce the output. Long run cost curves shape is also U but its flatter than the short run cost curves. The U shape of the cost curves will be less pronounced if the period is longer to which curve relates.

Both the curves have been illustrated in the diagram and example below.

Short run average cost curve as SAC. If the desired output is 10 units, the firm will select the lowest plant and it will build the scale of plant by SAC1 and work at point A. This is because cost per unit of the plant is lower and size is smaller. If the output is increased to 20 units, the size of plant will increase and output will be attained at scale of plant represented by SAC2 at point B which is the lowest. The optimum output is obtained at point B. If the desired out is 30 units, it will be attained at point C, represented by SAC3.

And now to get the long run average cost curve LAC, if we draw tangent to all short run average cost curves we get long run average cost curves. Thus, the diagram itself makes it clear that long run average cost curve is sum of all short run average cost curves and thus we say long run average cost curve is total of short run cost curves because it envelops all short run cost curves.

Hence the ENVELOPE relationship relates short run average cost curves and long run average cost curves where long run average cost curve is sum of all short run average cost curves.