The Relation between Long-Run and Short-Run Average Costs

The short-run cost of production must always be higher than the long-run cost, except for at one certain point where they are the same. In Figure 8.3 the short-run cost and the long-run cost of producing 100 units is the same, given that one has chosen an amount of capital equal to K*. For every other choice of capital, it is more expensive to produce 100 units in the short run than in the long run.

If this is true about the cost, it must also be true about the average cost, i.e. the long-run average cost must always be smaller than the short-run average cost, except for at one point where they are the same. If we draw a few different curves for short-run average costs, where each curve is valid for different long run investments in capital, we get a picture as the one in Figure 8.4.

We have three different short-run average cost curves, SRAC₁, SRAC₂, and SRAC₃ (Short Run Average Cost) and one long-run average cost curve, LRAC (Long Run Average Cost). Each SRAC curve has one point where it is optimal in the long run as well. For example, SRAC₁ is optimal at point a, where it touches LRAC and the average cost is 12. If one had instead chosen a different amount of capital, for instance, such that one would have been constrained to SRAC₂, one would have ended up at point b if one wanted to produce the quantity q1.

Average cost would then have been 18. SRAC₂ is instead long-run optimal if one wants to produce q₂. If one takes all such points where the short-run average cost is optimal, i.e. for all possible SRAC curves, not just the ones drawn here, one will get the curve for the long-run average cost, LRAC. Just as the short-run marginal cost curves must intersect the SRAC curves at their lowest points, the long-run marginal cost curve, LRMC, must intersect LRAC at its lowest point.

The LRAC curve in Figure 8.4 has another interesting property. To the left of the quantity q₂, LRAC slopes downwards (towards q₂), but to the right it slopes upwards. That means that the lowest cost per unit of the good is achieved at the quantity q₂ and at point c in the diagram. To the left of q₂, we have economies of scale and to the right we have diseconomies of scale. Note that this can be very important if there is competition in the market. If the firm is at a point to the left of q₂, it can lower its cost per unit by increasing the scale of production. In the next step, it can undercut the price of its competitors.

To get more help in The Relation between Long-Run and Short-Run Average Costs click the button below to submit your homework assignment