#### Summary

As economies near perfection, costs efficiency becomes increasingly crucial, so much so that investment plays a greater role. But just how and where that investment in cost management should be directed is the subject of our second LP on cost analysis.#### Short run:

#### Long run:

- Returns to scale
- Elasticity of scale
- Economies of scale
**Long run cost analysis**- Subadditivity

In the *long run*, no cost is *fixed*. We can determine our *production* level and adjust plant sizes, investment in capital and labour accordingly. As we can see in the diagrams below, this gives us unlimited options. Depending on the scale we choose to implement, each level of production will be associated to new, *short run cost* curves. When we exhaust the infrastructure these provide us, we can upgrade to a new production level and so forth. The actual long run cost curve is made up of all of these individual scenarios, built up year after year.

If we look at *average costs*, the curve these draw is also the build up of the individual short run curves. These form a U shape, as we can see in the diagram. When average cost is decreasing with each additional investment, we are enjoying economies of scale, but not yet working at maximum efficiency. We reach this maximum efficiency at the minimum point, before the average cost per unit begins growing again.

*Marginal costs* only really make sense in the long run for each individual level of production. At optimal levels of production for each level, they intersect the long run average cost curve where this meets the short run average cost curve. This is what determines our optimal level of production. In summary, at our optimal level of production:

*AC _{SR} = AC_{LR} = MC_{SR} = MC_{LR}*

which is known as Le Châtelier’s principle.

The other important lesson to take away from this is the fact that, when we reach the optimal point where efficiency is at its best, average and marginal costs are the same, as happened in the short run (see detailed graph below these lines). At this point, the slope of the tangent line, that is, the derivative, of the short run total cost (TC_{SR}) is equal to zero, which is consequent with the fact that we are operating at maximum efficiency. What we can also glean from the graph is the fact that TC_{SR }and TC_{LR }are tangent where short run average cost (AC_{SR}) and AC_{LR} also meet, which is not necessarily an optimum. In fact, the only time where these junctions do suppose an optimum is in case 2.