# Does Varian define the MRS differently/ as negative?

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.

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.

• 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. Jun 30, 2022 at 0:11

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:

$$-\frac{dy}{dx} = \frac{MU_x}{MU_y}$$

• But in the screenshot shown, Varian appears to define MRS $= \frac{dy}{dx}$. I think the answer to this question is useful for clarification: economics.stackexchange.com/questions/10709/… Jun 27, 2022 at 19:13
• @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. Jun 28, 2022 at 5:30
• @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. Jun 28, 2022 at 12:15
• @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
Jun 28, 2022 at 12:22
• 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 Jun 30, 2022 at 0:13