<p>You are right, Varian defines <span class="math-container">$MRS=dy/dx$</span>, while Wikipedia and Snyder/Nicholson (or Pindyck/Rubinfeld, Mas-Colell/Whinston/Green and almost all others) define <span class="math-container">$MRS=-dy/dx$</span>. There are pros and cons to both variants, but the latter one is the de facto standard nowadays, maybe just because it is easier to work with positive numbers.</p>

CC BY-SA 4.0
2022-06-30T00:11:16.497Z
Thanks! I suppose everything stays the same when we compare the absolute value of the MRS, so at the end there is no big difference. I just wanted to know if I was missing something since in my lectures the MRS is the slope, and the book I am self studying with gives a different definition.
Javier H
CC BY-SA 4.0
2022-06-28T23:52:51.997Z
2022-06-28T23:52:51.997Z
VARulle
<p>It is not different definition. MRS between x and y is given by:</p>
<p><span class="math-container">$$-\frac{dy}{dx} = \frac{MU_x}{MU_y} \Leftrightarrow \frac{dy}{dx} = -\frac{MU_x}{MU_y} $$</span></p>
<p>Varian in his textbooks likes to use (see Varian Microeconomic Analysis pp 97):</p>
<p><span class="math-container">$$\frac{dy}{dx} = -\frac{MU_x}{MU_y},$$</span> but that is not different definition from Wikipedia's definition:</p>
<p><span class="math-container">$$-\frac{dy}{dx} = \frac{MU_x}{MU_y} $$</span></p>

CC BY-SA 4.0
2022-06-27T19:13:49.940Z
But in the screenshot shown, Varian appears to define MRS $= \frac{dy}{dx}$. I think the answer to this question is useful for clarification: https://economics.stackexchange.com/questions/10709/is-mrs-supposed-to-have-a-minus-sign-or-not-whats-there-to-say-about-convexity
VARulle
CC BY-SA 4.0
2022-06-28T05:30:56.473Z
@VARulle "*But in the screenshot shown, Varian appears to...*" There is no contradiction with anything 1muflon1 wrote? Or am I missing something? Also, the linked question my be better as a comment under the answer. You can even initiate a duplicate vote with it.
Giskard
CC BY-SA 4.0
2022-06-28T12:15:27.280Z
@Giskard: Well, 1muflon1 wrote "MRS ... is given by $-\frac{dy}{dx}$, while Varian writes "the slope ... is known as the ... MRS". Since "the slope" is $\frac{dy}{dx}$, there is a contradiction.
VARulle
CC BY-SA 4.0
2022-06-28T12:22:10.930Z
@VARulle English is high context language but this is my understanding of Varian saying MRS is a slope means that $MRS=dy/dx$ Then Varian doesn't continue it but as long as $dy/dx = -MU_x/MU_y$ then that will be equivalent to saying its a negative slope where negative slope is given by $-dy/dx = MU_x/MU_y$ Varian doesn't mention the MU_x/MU_y part so there is some ambiguity there in a text of that undergraduate book, but since he consistently in his graduate books uses $dy/dx = -MU_x/MU_y$ I think its fair to assume thats what he means here
1muflon1
CC BY-SA 4.0
2022-06-28T23:29:19.947Z
@1muflon1, This $dy/dx=-MU_x/MU_y$ thing is a red herring. There is no discussion about those two expressions, and no one doubts this equality. The question is whether (1) $MRS=dy/dx$ or (2) $MRS=-dy/dx$. These are simply different definitions, and Varian uses (1), while Snyder/Nicholson use (2). So the answer "It is not different definition" is a bit disingenuous.
VARulle
CC BY-SA 4.0
2022-06-28T23:37:22.943Z
@VARulle it is not red herring. $MRS=dy/dx$ and $MRS=−dy/dx$ will be the same definitions if $MRS=dy/dx=−MU_x/MU_y $ and  $MRS=−dy/dx=MU_x/MU_y$ since  $MRS=−MU_x/MU_y \Leftrightarrow -MRS=MU_x/MU_y $
1muflon1
CC BY-SA 4.0
2022-06-28T23:45:28.787Z
@1muflon1, sorry, but this is ridiculous. $A=5$ and $A=-5$ are not "the same definitions" in anybody's world.
VARulle
CC BY-SA 4.0
2022-06-28T23:51:10.877Z
@VARulle but $A=-B$| $B=5$ and $A=B$ |$B=-5$ are the same definitions
1muflon1
CC BY-SA 4.0
2022-06-29T09:50:13.327Z
@1muflon1: True, but you are repeatedly arguing that $A=-B|-B=5$ and $A=B|B=-5$ are the same definitions, and that's simply wrong.
VARulle
CC BY-SA 4.0
2022-06-30T00:13:03.843Z
I have to agree with @VARulle, my question is just about the sign of the MRS. There is no doubt about How it is defined. As mentioned in another comment, at the end what we care about is the absolute value of the MRS, so everything still holds regardless of definition
Javier H
CC BY-SA 4.0
2022-06-27T15:34:03.273Z
2022-06-27T15:34:03.273Z
1muflon1
<p><a href="https://i.sstatic.net/hvPE9.png" rel="nofollow noreferrer"><img src="https://i.sstatic.net/hvPE9.png" alt="MRS According to Varian" /></a></p>
<p>Varian defines the MRS as the slope of the indifference curve.
However, Snyder/Nicholson (and apparently Wikipedia) define the MRS as the <strong>negative</strong> of the slope.
Does Varian use a different definition, or am I missing something?
Thanks.</p>

<microeconomics><utility>
Does Varian define the MRS differently/ as negative?
Javier H
# Does Varian define the MRS differently/ as negative?

(Asked by: username_0 on 2022-06-27)

[![MRS According to Varian](https://i.sstatic.net/hvPE9.png)](https://i.sstatic.net/hvPE9.png)

Varian defines the MRS as the slope of the indifference curve.
However, Snyder/Nicholson (and apparently Wikipedia) define the MRS as the **negative** of the slope.
Does Varian use a different definition, or am I missing something?
Thanks.

**Tags:** microeconomics, utility


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## 2 answers

### Answer by username_1 on 2022-06-28. Score: 1 | Accepted answer

You are right, Varian defines $MRS=dy/dx$, while Wikipedia and Snyder/Nicholson (or Pindyck/Rubinfeld, Mas-Colell/Whinston/Green and almost all others) define $MRS=-dy/dx$. There are pros and cons to both variants, but the latter one is the de facto standard nowadays, maybe just because it is easier to work with positive numbers.

> **Comments:**
> **username_0**: Thanks! I suppose everything stays the same when we compare the absolute value of the MRS, so at the end there is no big difference. I just wanted to know if I was missing something since in my lectures the MRS is the slope, and the book I am self studying with gives a different definition.  

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### Answer by username_2 on 2022-06-27. Score: 0

It is not different definition. MRS between x and y is given by:

$$-\frac{dy}{dx} = \frac{MU\_x}{MU\_y} \Leftrightarrow \frac{dy}{dx} = -\frac{MU\_x}{MU\_y} $$

Varian in his textbooks likes to use (see Varian Microeconomic Analysis pp 97):

$$\frac{dy}{dx} = -\frac{MU\_x}{MU\_y},$$ but that is not different definition from Wikipedia's definition:

$$-\frac{dy}{dx} = \frac{MU\_x}{MU\_y} $$

> **Comments:**
> **username_1**: But in the screenshot shown, Varian appears to define MRS $= \frac{dy}{dx}$. I think the answer to this question is useful for clarification: https://economics.stackexchange.com/questions/10709/is-mrs-supposed-to-have-a-minus-sign-or-not-whats-there-to-say-about-convexity  
> **username_3**: @username_1 "*But in the screenshot shown, Varian appears to...*" There is no contradiction with anything username_2 wrote? Or am I missing something? Also, the linked question my be better as a comment under the answer. You can even initiate a duplicate vote with it.  
> **username_1**: @username_3: Well, username_2 wrote "MRS ... is given by $-\frac{dy}{dx}$, while Varian writes "the slope ... is known as the ... MRS". Since "the slope" is $\frac{dy}{dx}$, there is a contradiction.  
> **username_2**: @username_1 English is high context language but this is my understanding of Varian saying MRS is a slope means that $MRS=dy/dx$ Then Varian doesn't continue it but as long as $dy/dx = -MU_x/MU_y$ then that will be equivalent to saying its a negative slope where negative slope is given by $-dy/dx = MU_x/MU_y$ Varian doesn't mention the MU_x/MU_y part so there is some ambiguity there in a text of that undergraduate book, but since he consistently in his graduate books uses $dy/dx = -MU_x/MU_y$ I think its fair to assume thats what he means here  
> **username_1**: @username_2, This $dy/dx=-MU_x/MU_y$ thing is a red herring. There is no discussion about those two expressions, and no one doubts this equality. The question is whether (1) $MRS=dy/dx$ or (2) $MRS=-dy/dx$. These are simply different definitions, and Varian uses (1), while Snyder/Nicholson use (2). So the answer "It is not different definition" is a bit disingenuous.  
> **username_2**: @username_1 it is not red herring. $MRS=dy/dx$ and $MRS=−dy/dx$ will be the same definitions if $MRS=dy/dx=−MU_x/MU_y $ and  $MRS=−dy/dx=MU_x/MU_y$ since  $MRS=−MU_x/MU_y \Leftrightarrow -MRS=MU_x/MU_y $  
> **username_1**: @username_2, sorry, but this is ridiculous. $A=5$ and $A=-5$ are not "the same definitions" in anybody's world.  
> **username_2**: @username_1 but $A=-B$| $B=5$ and $A=B$ |$B=-5$ are the same definitions  
> **username_1**: @username_2: True, but you are repeatedly arguing that $A=-B|-B=5$ and $A=B|B=-5$ are the same definitions, and that's simply wrong.  
> **username_0**: I have to agree with @username_1, my question is just about the sign of the MRS. There is no doubt about How it is defined. As mentioned in another comment, at the end what we care about is the absolute value of the MRS, so everything still holds regardless of definition  

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