MRS of good X for good Y

Question

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?"

Answer 1

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 $\ell$.

Answer 2

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