<p>If a consumer's demand for a good is perfectly inelastic with respect to the price, this means that the consumer is prepared to spend all his available income to that one good, even if this means that he won't consume anything else. This means that the consumer has <em>lexicographic preferences</em>, with this one good above everything else.  </p>

<p>Lexicographic preferences are not continuous, and so they cannot be represented by a continuous utility function. They have indifference "curves" that are single points, etc. </p>

<p>So the case of perfectly inelastic demand represents an "exception" at a  deeper level than for example Giffen goods represent. Giffen goods are manageable in the context of "usual" preferences, tweaked but not scrapped altogether.</p>

<p>Finally, note that "perfectly inelastic demand" represented as a straight vertical line, does not answer the question "what will happen if, given his budget constraint, the consumer cannot afford to buy the specific quantity $\bar q$?" Will he buy as much as his budget $B$ allows, or will he buy nothing?</p>

<p>If, when he cannot afford the desired quantity $\bar q$, he buys as much as he can, then in reality the demand curve becomes negatively sloped after a price level, and it acquires a "forced" elasticity, dictated by the budget constraint:</p>

<p><a href="https://i.sstatic.net/SSB3S.png" rel="nofollow noreferrer"><img src="https://i.sstatic.net/SSB3S.png" alt="enter image description here"></a></p>

<p>The above represents that case of truly lexicographic preferences. In the case where, if the consumer cannot afford $\bar q$, then he buys no quantity of the good, things are more complicated.</p>

CC BY-SA 3.0
2015-09-13T14:28:45.050Z
2015-09-13T14:28:45.050Z
Alecos Papadopoulos
<p>Because although some goods have perfect inelasticity over some interval, they are not perfectly inelastic over the whole demand curve - over the rest of the curve, quantity and demand will be strictly inversely related. And the law of demand doesn't have a "strictly" in there. Price and quantity are inversely related, but not <em>strictly</em> so, which (in the mathematical sense) means that parts of the demand curve are allowed to be perfectly inelastic.</p>

CC BY-SA 3.0
2015-09-13T10:56:48.857Z
2015-09-13T10:56:48.857Z
410 gone
<p>Assume a case of perfect price inelasticity of demand. </p>

<p><a href="https://i.sstatic.net/PAXFR.png" rel="nofollow noreferrer"><img src="https://i.sstatic.net/PAXFR.png" alt="Graph depicting perfect price inelasticity"></a>
<br> 
In such a case, </p>

<blockquote>
  <p>PED = 0</p>
</blockquote>

<p>The quantity demanded does not respond to changes in price, i.e. it remains constant, even when price increases or decreases (instead of falling or rising, as it should if it conformed to the inverse relation defined by the law of demand).</p>

<p>Thus, shouldn't perfect price inelasticity also be considered as an exception to the law of demand, just as Giffen goods and Veblen goods are?</p>

CC BY-SA 3.0
2015-09-15T14:31:01.070Z
@denesp:  Veblen goods are not Giffen goods.
Steven Landsburg
CC BY-SA 3.0
2015-09-15T17:37:23.203Z
@StevenLandsburg You are correct. (Had to read up on this.) Deleting my earlier comment.
Giskard
<supply-and-demand><elasticity>
Why is perfect price inelasticity of demand not considered an exception to the law of demand?
user3182445
# Why is perfect price inelasticity of demand not considered an exception to the law of demand?

(Asked by: username_0 on 2015-09-13)

Assume a case of perfect price inelasticity of demand.

[![Graph depicting perfect price inelasticity](https://i.sstatic.net/PAXFR.png)](https://i.sstatic.net/PAXFR.png)
  
In such a case,

> PED = 0

The quantity demanded does not respond to changes in price, i.e. it remains constant, even when price increases or decreases (instead of falling or rising, as it should if it conformed to the inverse relation defined by the law of demand).

Thus, shouldn't perfect price inelasticity also be considered as an exception to the law of demand, just as Giffen goods and Veblen goods are?

**Tags:** supply-and-demand, elasticity
> **Comments:**
> **username_1**: @denesp:  Veblen goods are not Giffen goods.  
> **username_2**: @StevenLandsburg You are correct. (Had to read up on this.) Deleting my earlier comment.  

---

## 2 answers

### Answer by username_4 on 2015-09-13. Score: 4 | Accepted answer

Because although some goods have perfect inelasticity over some interval, they are not perfectly inelastic over the whole demand curve - over the rest of the curve, quantity and demand will be strictly inversely related. And the law of demand doesn't have a "strictly" in there. Price and quantity are inversely related, but not *strictly* so, which (in the mathematical sense) means that parts of the demand curve are allowed to be perfectly inelastic.


---

### Answer by username_3 on 2015-09-13. Score: 0

If a consumer's demand for a good is perfectly inelastic with respect to the price, this means that the consumer is prepared to spend all his available income to that one good, even if this means that he won't consume anything else. This means that the consumer has *lexicographic preferences*, with this one good above everything else.

Lexicographic preferences are not continuous, and so they cannot be represented by a continuous utility function. They have indifference "curves" that are single points, etc.

So the case of perfectly inelastic demand represents an "exception" at a deeper level than for example Giffen goods represent. Giffen goods are manageable in the context of "usual" preferences, tweaked but not scrapped altogether.

Finally, note that "perfectly inelastic demand" represented as a straight vertical line, does not answer the question "what will happen if, given his budget constraint, the consumer cannot afford to buy the specific quantity $\bar q$?" Will he buy as much as his budget $B$ allows, or will he buy nothing?

If, when he cannot afford the desired quantity $\bar q$, he buys as much as he can, then in reality the demand curve becomes negatively sloped after a price level, and it acquires a "forced" elasticity, dictated by the budget constraint:

[![enter image description here](https://i.sstatic.net/SSB3S.png)](https://i.sstatic.net/SSB3S.png)

The above represents that case of truly lexicographic preferences. In the case where, if the consumer cannot afford $\bar q$, then he buys no quantity of the good, things are more complicated.


---

