<p>I struggle to find formal mathematical expressions for long run average costs and long run marginal costs. All ressources I see take a finite number of short run average costs and draw the envelop curve to it. Is this really the right way to define it formally ? Since there is a finite number of curves, the envelop is not well-defined right ? So is it implicit that there are infinitely many short run average costs so that there is only one possible envelop curve : the LRAC ?</p>
<p>The LRMC is then the derivative of this curve. Is there a formal mathematical expression for theses curves ?</p>

CC BY-SA 4.0
2022-12-24T13:24:49.460Z
A related discussion is given here: https://economics.stackexchange.com/questions/53166/where-does-the-short-run-and-long-run-costs-intersect-if-k-is-fixed/53183#53183
Bertrand
CC BY-SA 4.0
2022-12-24T13:52:06.747Z
You can also check this playlist: https://youtube.com/playlist?list=PLUJGfL_499TJ4xlOvpKeAqo4M5xYkq6wi
Amit
<marginal><long-run>
Mathematical expression for long run costs curves
Kilkik
# Mathematical expression for long run costs curves

(Asked by: username_0 on 2022-12-24)

I struggle to find formal mathematical expressions for long run average costs and long run marginal costs. All ressources I see take a finite number of short run average costs and draw the envelop curve to it. Is this really the right way to define it formally ? Since there is a finite number of curves, the envelop is not well-defined right ? So is it implicit that there are infinitely many short run average costs so that there is only one possible envelop curve : the LRAC ?

The LRMC is then the derivative of this curve. Is there a formal mathematical expression for theses curves ?

**Tags:** marginal, long-run
> **Comments:**
> **username_1**: A related discussion is given here: https://economics.stackexchange.com/questions/53166/where-does-the-short-run-and-long-run-costs-intersect-if-k-is-fixed/53183#53183  
> **username_2**: You can also check this playlist: https://youtube.com/playlist?list=PLUJGfL_499TJ4xlOvpKeAqo4M5xYkq6wi  

---

## 0 answers

