<p>MRS of good1 for good2 is the rate at which you will substitute good 1 for good 2, hence it is <strong>CHANGE IN X1/CHANGE IN X2</strong></p>
<p>and <em>similarly</em></p>
<p>MRS of good 2 for good 1 is the rate at which you will substitute good 2 for good 1, i.e. <strong>CHANGE IN X2/CHANGE IN X1</strong></p>

CC BY-SA 4.0
2020-11-11T11:05:38.880Z
2020-11-11T11:05:38.880Z
Jagrati Goyal
<p>It is your second answer. From MWG:</p>

<blockquote>
  <p><span class="math-container">$$\frac{\partial u(x^*)/\partial x_\ell}{\partial u(x^*)/\partial_k}=\frac{p_\ell}{p_k}\tag{3.D.5}$$</span>
  The expression on the left of <span class="math-container">$\text{(3.D.5)}$</span> is the <em>marginal rate of substitution of good <span class="math-container">$\ell$</span> for good <span class="math-container">$k$</span> at <span class="math-container">$x^*$</span>, <span class="math-container">$MRS_{\ell k}(x^*)$</span></em>; it tells us <strong>the amount of good <span class="math-container">$k$</span> that the consumer must be given to compensate her for a one-unit marginal reduction in her consumption of good <span class="math-container">$\ell$</span></strong>.</p>
</blockquote>

CC BY-SA 4.0
2019-04-08T19:50:53.013Z
In the future, please try to post texts as texts to enhance searchability. Images of texts may not get picked up by search engines as easily as texts.
Herr K.
CC BY-SA 4.0
2019-04-08T18:46:05.767Z
2019-04-08T19:47:59.723Z
2019-04-08T19:47:59.723Z
Marcelo Gelati
<p>I'm having some confusion with using the terminology of MRS. For example, let's take up this question:</p>

<blockquote>
  <p>If good 1 is a “neutral,” what is its marginal rate of substitution for good 2?</p>
</blockquote>

<p>The answer is:</p>

<blockquote>
  <p>Zero—if you take away some of good 1, the consumer needs zero units
  of good 2 to compensate him for his loss.</p>
</blockquote>

<p>The question is asking for the MRS of good 2. The answer interprets this question as "how much of good 2 will one need to give up for a loss in good 1?". In that case, it is, of course, 0. But, you can just as easily interpret the question as: "How much of good 1 will one need to give up for a loss in good 2?" -- in which case, the answer is infinity -- the consumer would not want to give up any amount of good 1 for a loss in good 2. </p>

<p>In a different question, this was asked: "What is your marginal rate of substitution of \$1 bills for \$5 bills?". And the answer was "5". So, in this question, the good after the word "of" (\$1 bills) is what you're giving up. In other words, the answer is the answer to the question: "How many \$1 bills would you give up for a \$5 bill?" So this answer interprets the question in completely the opposite way.</p>

<p>To phrase it more clearly, when someone asks: </p>

<blockquote>
  <p>What is the MRS of good 1 for good 2?</p>
</blockquote>

<p>How should I interpret it? Is it "how much good 2 you would give up for an increase in good 1?" or "How much good 1 you would give up for an increase in good 2?"</p>

<microeconomics>
MRS of good X for good Y
WorldGov
# MRS of good X for good Y

(Asked by: username_0 on 2019-02-14)

I'm having some confusion with using the terminology of MRS. For example, let's take up this question:

> If good 1 is a “neutral,” what is its marginal rate of substitution for good 2?

The answer is:

> Zero—if you take away some of good 1, the consumer needs zero units
> of good 2 to compensate him for his loss.

The question is asking for the MRS of good 2. The answer interprets this question as "how much of good 2 will one need to give up for a loss in good 1?". In that case, it is, of course, 0. But, you can just as easily interpret the question as: "How much of good 1 will one need to give up for a loss in good 2?" -- in which case, the answer is infinity -- the consumer would not want to give up any amount of good 1 for a loss in good 2.

In a different question, this was asked: "What is your marginal rate of substitution of \$1 bills for \$5 bills?". And the answer was "5". So, in this question, the good after the word "of" (\$1 bills) is what you're giving up. In other words, the answer is the answer to the question: "How many \$1 bills would you give up for a \$5 bill?" So this answer interprets the question in completely the opposite way.

To phrase it more clearly, when someone asks:

> What is the MRS of good 1 for good 2?

How should I interpret it? Is it "how much good 2 you would give up for an increase in good 1?" or "How much good 1 you would give up for an increase in good 2?"

**Tags:** microeconomics

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## 2 answers

### Answer by username_2 on 2019-04-08. Score: 5 | Accepted answer

It is your second answer. From MWG:

> $$\frac{\partial u(x^\*)/\partial x\_\ell}{\partial u(x^\*)/\partial\_k}=\frac{p\_\ell}{p\_k}\tag{3.D.5}$$
> The expression on the left of $\text{(3.D.5)}$ is the *marginal rate of substitution of good $\ell$ for good $k$ at $x^\*$, $MRS\_{\ell k}(x^\*)$*; it tells us **the amount of good $k$ that the consumer must be given to compensate her for a one-unit marginal reduction in her consumption of good $\ell$**.

> **Comments:**
> **username_3**: In the future, please try to post texts as texts to enhance searchability. Images of texts may not get picked up by search engines as easily as texts.  

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### Answer by username_1 on 2020-11-11. Score: 0

MRS of good1 for good2 is the rate at which you will substitute good 1 for good 2, hence it is **CHANGE IN X1/CHANGE IN X2**

and *similarly*

MRS of good 2 for good 1 is the rate at which you will substitute good 2 for good 1, i.e. **CHANGE IN X2/CHANGE IN X1**


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