<p>The minimum point of a short run cost curve will be above the long run average cost curve at the left section of the LRAC, because at this section, the firm is expoiting economies of scale which cannot be exploited in the short run. Therefore in the long run, the firm can achieve cost less than the short run minumum cost.</p>
<p>If you see it graphically and mathematically as well, it will also be the same, it's very difficult, or rather impossible, to make the LRAC curve pass through all those minimum points of the infinite SRAC curves without cutting through them.</p>

CC BY-SA 4.0
2021-12-10T06:35:21.133Z
2021-12-10T06:42:22.863Z
2021-12-10T06:42:22.863Z
Stelios Mili
<p>The diagram is fine as an illustration of a possible relation between the long run average cost curve and <em>one particular</em> short run average cost curve.</p>

<p>Long run in the context of a firm's cost functions means that all inputs are free to vary, so it makes sense to refer to <em>the</em> long run cost curve.  Short run means that one or more inputs (eg capital equipment) are fixed.  Since these inputs could be fixed at different levels, there are many different short run cost curves. The long run cost curve is the <em>envelope</em> of these curves. Unless it has been specified at what level they are considered fixed (which could implicitly be whatever is their current level), it makes no sense to refer to <em>the</em> short run average cost curve.</p>

<p>In most cases, the minimum point of a short run cost curve will be above the long run cost curve.  This should not be surprising: it just means that, for the relevant output, it's possible to obtain lower costs if all inputs are free to vary than if only some are free to vary.</p>

<p>There will however be one short run cost curve corresponding to the levels of fixed inputs at which the long run cost curve is at its minimum.  The lowest point of that particular short run cost curve <em>will</em> be tangent to the long run cost curve (and incidentally the short and long run marginal cost curves will also pass through the same point).</p>

<p>A diagram showing multiple short run average cost curves, with one having its lowest point tangent to the lowest point of the long run cost curve may be found in Nicholson W (9th edn 2005) <em>Microeconomic Theory</em>.  For an online source see <a href="http://www.policonomics.com/long-run-cost-analysis/" rel="nofollow noreferrer">here</a>.</p>

CC BY-SA 4.0
2019-10-31T08:30:05.997Z
By "the minimum point of a short run cost curve will be above the long run cost curve", do you mean that the minimum point of a short run cost curve does not touch the long run cost curve? How would it be so?
Aqqqq
CC BY-SA 4.0
2019-10-31T08:48:35.520Z
Just asked the question here: https://economics.stackexchange.com/questions/32513/is-it-possible-that-the-minimum-point-of-a-short-run-cost-curve-does-not-touch-t
Aqqqq
CC BY-SA 3.0
2017-01-05T12:10:45.263Z
2017-01-05T12:52:37.383Z
2017-01-05T12:52:37.383Z
Adam Bailey
<p>The diagram from the Varian textbook shows that the SRAC curve is tangent to the LRAC curve at a point which is not the bottom of the SRAC curve. It would be really helpful if someone could explain this.</p>

<p><a href="https://i.sstatic.net/4lQBF.png" rel="nofollow noreferrer"><img src="https://i.sstatic.net/4lQBF.png" alt="enter image description here"></a></p>

CC BY-SA 3.0
2017-01-04T11:38:38.017Z
The SAC is tangent to the LAC but not at the lowest point of SAC?
user2229066
<microeconomics><cost>
Why is the short run average cost curve not a tangent to the long run average cost curve at the lowest point on the short run average cost curve?
user2229066
# Why is the short run average cost curve not a tangent to the long run average cost curve at the lowest point on the short run average cost curve?

(Asked by: username_0 on 2017-01-04)

The diagram from the Varian textbook shows that the SRAC curve is tangent to the LRAC curve at a point which is not the bottom of the SRAC curve. It would be really helpful if someone could explain this.

[![enter image description here](https://i.sstatic.net/4lQBF.png)](https://i.sstatic.net/4lQBF.png)

**Tags:** microeconomics, cost

> **Comments:**
> **username_0**: The SAC is tangent to the LAC but not at the lowest point of SAC?  

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## 2 answers

### Answer by username_2 on 2017-01-05. Score: 3 | Accepted answer

The diagram is fine as an illustration of a possible relation between the long run average cost curve and *one particular* short run average cost curve.

Long run in the context of a firm's cost functions means that all inputs are free to vary, so it makes sense to refer to *the* long run cost curve. Short run means that one or more inputs (eg capital equipment) are fixed. Since these inputs could be fixed at different levels, there are many different short run cost curves. The long run cost curve is the *envelope* of these curves. Unless it has been specified at what level they are considered fixed (which could implicitly be whatever is their current level), it makes no sense to refer to *the* short run average cost curve.

In most cases, the minimum point of a short run cost curve will be above the long run cost curve. This should not be surprising: it just means that, for the relevant output, it's possible to obtain lower costs if all inputs are free to vary than if only some are free to vary.

There will however be one short run cost curve corresponding to the levels of fixed inputs at which the long run cost curve is at its minimum. The lowest point of that particular short run cost curve *will* be tangent to the long run cost curve (and incidentally the short and long run marginal cost curves will also pass through the same point).

A diagram showing multiple short run average cost curves, with one having its lowest point tangent to the lowest point of the long run cost curve may be found in Nicholson W (9th edn 2005) *Microeconomic Theory*. For an online source see [here](http://www.policonomics.com/long-run-cost-analysis/).

> **Comments:**
> **username_3**: By "the minimum point of a short run cost curve will be above the long run cost curve", do you mean that the minimum point of a short run cost curve does not touch the long run cost curve? How would it be so?  
> **username_3**: Just asked the question here: https://economics.stackexchange.com/questions/32513/is-it-possible-that-the-minimum-point-of-a-short-run-cost-curve-does-not-touch-t  

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### Answer by username_1 on 2021-12-10. Score: 2

The minimum point of a short run cost curve will be above the long run average cost curve at the left section of the LRAC, because at this section, the firm is expoiting economies of scale which cannot be exploited in the short run. Therefore in the long run, the firm can achieve cost less than the short run minumum cost.

If you see it graphically and mathematically as well, it will also be the same, it's very difficult, or rather impossible, to make the LRAC curve pass through all those minimum points of the infinite SRAC curves without cutting through them.


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