<blockquote>
<p>How is marginal utility interpreted as the additional &quot;happiness&quot; gained from consuming one more unit of some good?</p>
</blockquote>
<p>It is not. While it sounds somewhat intuititve, the concept of utility as a kind of psychological measure of &quot;happiness&quot; or &quot;satisfaction&quot; is outdated and no longer used in modern microeconomics. Instead of this cardinal utility concept, microeconomics relies on an ordinal utility concept. (Expected Utility Theory is an exception, but that's another story.) Since ordinal utility functions can be arbitrarily subjected to any positive monotonic transformation, marginal utility has no meaningful interpretation apart from its technical one. (Unfortunately, this is falsely presented even in some contemporary textbooks, e.g. in Pindyck-Rubinfeld.)</p>
<p>What still has a meaningful interpretation, though, is the ratio of marginal utilities, which is invariant under positive monotonic transformations and gives the negative MRS in the 2-goods case.</p>
<p>For the part of your question pertaining to the MRS see Giskard's answer.</p>

CC BY-SA 4.0
2021-05-25T07:49:33.930Z
2021-05-25T07:49:33.930Z
VARulle
<blockquote>
<p>How is marginal utility interpreted as the additional &quot;happiness&quot; gained from consuming one more unit of some good?</p>
</blockquote>
<p>Not sure what you mean. Utility is not interpreted as some biological measure of happiness. A bundle of goods with high utility is prefered by the consumer to bundles with lower utilities. This is all that utility describes; it is a modelling/storytelling tool.</p>
<blockquote>
<p>If marginal utility is the derivative of utility, then isn't it only measuring how the gains from an incredibly small consumption of some good?</p>
</blockquote>
<p>Yes, it is.</p>
<p>On your graph: kudos for using Desmos!</p>
<blockquote>
<p>The MRS at (20,5) is -1/4 which should mean that at (20,5) this person will be ok with trading in 4 units of good x for 1 unit of good y correct?</p>
</blockquote>
<p>Strictly speeking this is only true for marginal quantities (infinitesimally small quantities). Basically you are approximating the indifference curve with a linear curve (a line) at the (20,5) point. This line only coincides with the indifference curve at (20,5), and as you move farther away from this point, the line becomes a more and more imprecise approximation of the curve. (Note that 6.25 instead of 6 is not too bad as an approximation.)  <br>
The line about MRS representing the ratio at which a consumer is willing to trade is just to get the intuition across, it is not an exact definition.</p>

CC BY-SA 4.0
2021-05-25T09:40:19.970Z
+1 but I would just note that the above answer to first part holds under ordinal utility, under cardinal utility, utility is actually something that could be measured and subfields such as public economics heavily rely on notion that utility can be cardinal, and cardinal utility is (at least in principle) measurable even if we have no technical way of doing so
1muflon1
CC BY-SA 4.0
2021-05-25T13:54:43.680Z
Okay I think this clarified a lot for me thank you so much!
matt_
CC BY-SA 4.0
2021-05-25T14:42:22.963Z
Now, you can formally describe how well behaved the utility curve is, in order to be less hand-wavey about "the derivative is pretty good description".  The idea is that for many situations, people don't go from "I would really like more X" to "more X is horrible" at the scales in question.
Yakk
CC BY-SA 4.0
2021-05-25T15:13:11.110Z
@Yakk Sorry, but I  literally don't understand your comment. I also didn't find the quoted "the derivative is pretty good description" line anywhere in what I wrote. In case you want a different answer, feel free to post it! Otherwise please elaborate on what you want.
Giskard
CC BY-SA 4.0
2021-05-25T16:48:30.260Z
So, the degree of imprecision as you move away from infinitesimal amounts can be quantified.  In theory, the degree of imprecision (and how useless the derivative is) is unbounded, but in practice the kind of curves that you work with in economics are usually pretty smooth (at the scales you are working on them with).  To be more concrete, take a Taylor series around that point, and it will give you a bound on the error of the indifference line (and provide you with higher order indifference polynomials if you want them, together with a bounded error on them).
Yakk
CC BY-SA 4.0
2021-05-25T17:55:36.847Z
@Yakk Okay, I am familiar with [Taylor's Theorem](https://en.wikipedia.org/wiki/Taylor%27s_theorem#Statement_of_the_theorem); but I don't think I will add this to the answer. The level of precision was not part of the question, and this much detail seems unnecessary at this level. Please feel free to post your own answer.
Giskard
CC BY-SA 4.0
2021-05-25T06:39:51.413Z
2021-05-25T07:51:34.603Z
2021-05-25T07:51:34.603Z
Giskard
<p>I was just thinking back to some introductory economics courses, but now I'm extremely confused on a fundamental concept. How is marginal utility interpreted as the additional &quot;happiness&quot; gained from consuming one more unit of some good? If marginal utility is the derivative of utility, then isn't it only measuring how the gains from an incredibly small consumption of some good? And then I started thinking about indifference curves and the MRS. I'm not sure how the MRS tells you the slope at which you are willing to exchange 1 unit of good x for however many units of good y? Take this simple indifference for instance where y = 100/x:
<a href="https://i.sstatic.net/wNGeY.png" rel="nofollow noreferrer"><img src="https://i.sstatic.net/wNGeY.png" alt="enter image description here" /></a>
The MRS at (20,5) is -1/4 which should mean that at (20,5) this person will be ok with trading in 4 units of good x for 1 unit of good y correct? But this agent is only indifferent at (16,6.25) so I'm not really sure what the interpretation of the slope MRS here could be and how that differs from the indifference curve.</p>

<utility><marginal>
Fundamental question on marginal utility
matt_
# Fundamental question on marginal utility

(Asked by: username_0 on 2021-05-25)

I was just thinking back to some introductory economics courses, but now I'm extremely confused on a fundamental concept. How is marginal utility interpreted as the additional "happiness" gained from consuming one more unit of some good? If marginal utility is the derivative of utility, then isn't it only measuring how the gains from an incredibly small consumption of some good? And then I started thinking about indifference curves and the MRS. I'm not sure how the MRS tells you the slope at which you are willing to exchange 1 unit of good x for however many units of good y? Take this simple indifference for instance where y = 100/x:
[![enter image description here](https://i.sstatic.net/wNGeY.png)](https://i.sstatic.net/wNGeY.png)
The MRS at (20,5) is -1/4 which should mean that at (20,5) this person will be ok with trading in 4 units of good x for 1 unit of good y correct? But this agent is only indifferent at (16,6.25) so I'm not really sure what the interpretation of the slope MRS here could be and how that differs from the indifference curve.

**Tags:** utility, marginal

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## 2 answers

### Answer by username_2 on 2021-05-25. Score: 7 | Accepted answer

> How is marginal utility interpreted as the additional "happiness" gained from consuming one more unit of some good?

Not sure what you mean. Utility is not interpreted as some biological measure of happiness. A bundle of goods with high utility is prefered by the consumer to bundles with lower utilities. This is all that utility describes; it is a modelling/storytelling tool.

> If marginal utility is the derivative of utility, then isn't it only measuring how the gains from an incredibly small consumption of some good?

Yes, it is.

On your graph: kudos for using Desmos!

> The MRS at (20,5) is -1/4 which should mean that at (20,5) this person will be ok with trading in 4 units of good x for 1 unit of good y correct?

Strictly speeking this is only true for marginal quantities (infinitesimally small quantities). Basically you are approximating the indifference curve with a linear curve (a line) at the (20,5) point. This line only coincides with the indifference curve at (20,5), and as you move farther away from this point, the line becomes a more and more imprecise approximation of the curve. (Note that 6.25 instead of 6 is not too bad as an approximation.)   
The line about MRS representing the ratio at which a consumer is willing to trade is just to get the intuition across, it is not an exact definition.

> **Comments:**
> **username_3**: +1 but I would just note that the above answer to first part holds under ordinal utility, under cardinal utility, utility is actually something that could be measured and subfields such as public economics heavily rely on notion that utility can be cardinal, and cardinal utility is (at least in principle) measurable even if we have no technical way of doing so  
> **username_0**: Okay I think this clarified a lot for me thank you so much!  
> **username_4**: Now, you can formally describe how well behaved the utility curve is, in order to be less hand-wavey about "the derivative is pretty good description".  The idea is that for many situations, people don't go from "I would really like more X" to "more X is horrible" at the scales in question.  
> **username_2**: @Yakk Sorry, but I  literally don't understand your comment. I also didn't find the quoted "the derivative is pretty good description" line anywhere in what I wrote. In case you want a different answer, feel free to post it! Otherwise please elaborate on what you want.  
> **username_4**: So, the degree of imprecision as you move away from infinitesimal amounts can be quantified.  In theory, the degree of imprecision (and how useless the derivative is) is unbounded, but in practice the kind of curves that you work with in economics are usually pretty smooth (at the scales you are working on them with).  To be more concrete, take a Taylor series around that point, and it will give you a bound on the error of the indifference line (and provide you with higher order indifference polynomials if you want them, together with a bounded error on them).  
> **username_2**: @Yakk Okay, I am familiar with [Taylor's Theorem](https://en.wikipedia.org/wiki/Taylor%27s_theorem#Statement_of_the_theorem); but I don't think I will add this to the answer. The level of precision was not part of the question, and this much detail seems unnecessary at this level. Please feel free to post your own answer.  

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### Answer by username_1 on 2021-05-25. Score: 3

> How is marginal utility interpreted as the additional "happiness" gained from consuming one more unit of some good?

It is not. While it sounds somewhat intuititve, the concept of utility as a kind of psychological measure of "happiness" or "satisfaction" is outdated and no longer used in modern microeconomics. Instead of this cardinal utility concept, microeconomics relies on an ordinal utility concept. (Expected Utility Theory is an exception, but that's another story.) Since ordinal utility functions can be arbitrarily subjected to any positive monotonic transformation, marginal utility has no meaningful interpretation apart from its technical one. (Unfortunately, this is falsely presented even in some contemporary textbooks, e.g. in Pindyck-Rubinfeld.)

What still has a meaningful interpretation, though, is the ratio of marginal utilities, which is invariant under positive monotonic transformations and gives the negative MRS in the 2-goods case.

For the part of your question pertaining to the MRS see Giskard's answer.


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