Benjiko

Good Day,
1) Your understanding of the marginal rate of substitution is correct. MRS = the rate at which a consumer is willing to give up one good to obtain one unit of a second good, all else being equal. MRS subscript “XY” can be thought of as the MRS of X for Y - the rate at which the consumer is willing to give up Y for one unit of X. On the indifference curve, good X (the first component of the subscript) is typically listed on the x-axis and good Y (the second component of the subscript) is listed on the y-axis. This is just a matter of convention. We could flip everything around and the relationship would still hold true.
2) Upon reviewing practice problem #5 from page 89, it looks to be that answer (c) is incorrect because it states that the MRS = the ratio of the price of good y to the price of good x. If (c) were correct, the answer would have to read MRS = the ratio of the price of good x to the price of good y. This intuition matches the example that you referenced on page 77.
I hope that this is helpful.