<p>This is partially correct, but you are mixing up things.</p>
<p>It is usually assumed that consumer preferences are monotone (&quot;more is better&quot;) and convex (&quot;averages are better than extremes&quot;). Monotonicity implies that indifference curves are downward sloping, and convexity implies that they are convex in the two-goods case. Since the MRS is defined as the negative of the slope, the MRS is always positive. (Caveat: A few older textbooks, e.g. Varian, define the MRS as the slope itself. With this definition, the MRS is always negative.)</p>
<p>However, the reason for this is not the <em>law of diminishing returns</em>, which is an assumption about production functions, but the assumption of monotonicity of preferences.</p>
<p>You might have confused the law of diminshing returns with the <em>principle of diminishing MRS</em>. This &quot;principle&quot; means that the MRS decreases if we increase the amount of some good. As explained above, it follows from the assumption of monotonicty together with convexity of preferences.</p>

CC BY-SA 4.0
2022-10-02T11:56:33.173Z
The law of diminishing returns would make a substitutive graph between two goods based on their fixed, constant capital costs of production-variable averages, *still*. The upward supply to price, or substitutive-complementary 2 good consumption-output case would diminish the same for supply as demand but for product revenue after cost (assume demand is ordinary). Two goods can complement to make it the “substitution” positively-sloped.
Nick Carducci for Carface Bank
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2022-10-02T17:21:44.433Z
@NickCarducci, I don't understand a word...
VARulle
CC BY-SA 4.0
2022-10-02T17:32:26.727Z
VARulle, (1) the marginal rate of substitution would be negative for complementary goods against budget constraints. (2) The diminishing return makes supply diminish with demand just the same but for extraordinary product revenue.
Nick Carducci for Carface Bank
CC BY-SA 4.0
2022-09-21T08:23:24.473Z
2022-09-21T09:50:35.893Z
2022-09-21T09:50:35.893Z
VARulle
<p>Concept question:Marginal rate of substitution(MRS)=<span class="math-container">$-\frac{dy}{dx}$</span> where dy is change in unit of y for one unit of x. Is it true that <span class="math-container">$\frac{dy}{dx}$</span> is always negative because of law of diminishing returns, and MRS will always be positive since we add a negative sign in front of <span class="math-container">$\frac{dy}{dx}$</span>? Thanks.</p>
<p>Please let me know if I need to provide extra information. (Just begun in Microeconomics study)</p>

<microeconomics>
Is marginal rate of substitution always positive
Twilight
# Is marginal rate of substitution always positive

(Asked by: username_0 on 2022-09-20)

Concept question:Marginal rate of substitution(MRS)=$-\frac{dy}{dx}$ where dy is change in unit of y for one unit of x. Is it true that $\frac{dy}{dx}$ is always negative because of law of diminishing returns, and MRS will always be positive since we add a negative sign in front of $\frac{dy}{dx}$? Thanks.

Please let me know if I need to provide extra information. (Just begun in Microeconomics study)

**Tags:** microeconomics


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## 1 answers

### Answer by username_1 on 2022-09-21. Score: 4 | Accepted answer

This is partially correct, but you are mixing up things.

It is usually assumed that consumer preferences are monotone ("more is better") and convex ("averages are better than extremes"). Monotonicity implies that indifference curves are downward sloping, and convexity implies that they are convex in the two-goods case. Since the MRS is defined as the negative of the slope, the MRS is always positive. (Caveat: A few older textbooks, e.g. Varian, define the MRS as the slope itself. With this definition, the MRS is always negative.)

However, the reason for this is not the *law of diminishing returns*, which is an assumption about production functions, but the assumption of monotonicity of preferences.

You might have confused the law of diminshing returns with the *principle of diminishing MRS*. This "principle" means that the MRS decreases if we increase the amount of some good. As explained above, it follows from the assumption of monotonicty together with convexity of preferences.

> **Comments:**
> **username_2**: The law of diminishing returns would make a substitutive graph between two goods based on their fixed, constant capital costs of production-variable averages, *still*. The upward supply to price, or substitutive-complementary 2 good consumption-output case would diminish the same for supply as demand but for product revenue after cost (assume demand is ordinary). Two goods can complement to make it the “substitution” positively-sloped.  
> **username_1**: @NickCarducci, I don't understand a word...  
> **username_2**: username_1, (1) the marginal rate of substitution would be negative for complementary goods against budget constraints. (2) The diminishing return makes supply diminish with demand just the same but for extraordinary product revenue.  

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