Microeconomics questions exactly, vertical, horizontal

stalkey

Hi
I hope some of you can help me clear my uncertainty about the microeconomics reading.I have two questions:
(1) Interpretation of marginal rate of substitution (MRS):
- When MRS is written for example with a subscript “XY”, does that always translate into “how many units the consumer is willing to give up of Y for exactly 1 unit of X”?
- Is the last letter in the subscript (Y in this case) always the product on the vertical axis, and the first always the product on the horizontal axis (X in this case)?
- Can you provide some intuition behind this?
(2) MRS = Price ratio, why is that not maximizing utility? In the CFAI curriculum (p 77) they write “it is important to note that this equilibrium point represents the tangency between the highest indifference curve and budget constraint. At a tangency point, the two curves have the same slope, meaning that MRS(BW) must be equal to the price ratio, P(B) / P(W).” Doesn’t this mean that where the budget constraint is tangent to the highest indifference curve, ie where the utility is maximized, is the same point as where MRS = Price ratio?
In the practice problems at the end of the reading they ask “maximum utility is reached (b) at the tangency between the highest attainable indifference curve and the budget constraint or (c) when the MRS is equal to the ratio of the price of good Y to the price of good X”. Isn’t that the same thing?
I hope you can help..

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.