The Long-Run Cost Curve

The long-run pro­duc­tion cost curve shows the rela­tion­ship between cost and out­put in the long run. In other words, it shows the total cost of pro­duc­tion for a given quan­tity of out­put. The term pro­duc­tion cost refers to aver­age total cost.

Gen­er­ally, when look­ing toward the long run, for each level of out­put, the firm can choose a dif­fer­ent level of invest­ment that would min­i­mize the aver­age total cost for that level of out­put. The firm invests in a level of capac­ity, say the size of the ware­house, or the acres of land, and that deter­mines the fir­m's short-run cost curve. It may, for instance, increase the fixed costs, but decrease the vari­able costs, allow­ing the firm to pro­duce larger and larger quan­ti­ties for a lower per-unit cost. This means that if a firm has a cer­tain level of out­put in mind, it must choose the invest­ment that results in the low­est aver­age total cost.

Most firms have sev­eral pos­si­ble lev­els of capac­ity to choose from. At any moment the firm is on one short-run aver­age total cost curve, set by its present capac­ity, but each other capac­ity level it could choose has its own curve. So a firm look­ing at its long-run options faces sev­eral pos­si­ble short-run aver­age total cost curves.

In the short run, a change in quan­tity is a move­ment along the short-run total cost curve. How­ever, in the long run, a change in quan­tity can be accom­pa­nied by a change in capac­ity level that increases fixed costs but decreases vari­able costs, such that in the long run, the aver­age total long-run cost for the new level of out­put is min­i­mized. That is, in the long run, the firm can choose to put itself on a dif­fer­ent short-run total cost curve.

The result is a long-run aver­age total cost curve that wraps around, or envelops, all the short-run aver­age total cost curves. The fig­ure below shows this.

In the fig­ure, the firm exam­ines this long-run aver­age total cost curve (LRATC) and tar­gets an out­put of eight units. How­ever, the firm also con­sid­ers two other options: two units of out­put and twelve units of out­put. The short-run aver­age total cost curves for these options are shown in the graph and labelled ATC.

By choos­ing an invest­ment level that min­i­mizes the short-run aver­age total cost for a quan­tity of eight, the firm will be at point C in the graph. How­ever, if the firm antic­i­pates a pro­duc­tion of two units in the long run, it will decrease its capac­ity invest­ment and instead be at point A in the graph.

Note that the min­i­mum point on ATC2 is not as low as the min­i­mum point on ATC8. There­fore, the aver­age total cost of pro­duc­tion is higher at point A than at point C. How­ever, point A rep­re­sents the low­est pos­si­ble aver­age total cost for the pro­duc­tion of two units.

Finally, if the firm antic­i­pates a pro­duc­tion of twelve units it will invest in get­ting to point E, by putting itself on the short-run curve ATC12. Note that if the firm decides to pur­sue a quan­tity of eight, and then wants to change to a quan­tity of two or twelve, then in the short run, the firm will be at point B or D, respec­tively, until it can get out of its short-run cost con­straints. This is why it's very impor­tant to choose opti­mally in the first place.

What all this is say­ing is that if the firm makes a long-run deci­sion and chooses a short-run cost curve that matches its planned level of out­put, then it will stay on the long-run aver­age total cost curve (in addi­tion to its exist­ing short-run cost curve). How­ever, if mar­ket con­di­tions change and the firm wants to pro­duce a dif­fer­ent quan­tity, then in the short run it will be off the long-run aver­age cost curve, at a higher cost, until it can adjust its capac­ity.

Key terms#

Long-run aver­age total cost curve (LRATC)

Long-run aver­age total cost is a busi­ness met­ric that rep­re­sents the aver­age cost per unit of out­put over the long run, where all inputs are con­sid­ered to be vari­able and the scale of pro­duc­tion is change­able.

Com­mon ques­tions#

Why is the long-run aver­age cost curve called an enve­lope curve?#

Because it touches each short-run aver­age total cost curve at one point and lies below or on all of them, it wraps around them like an enve­lope.