#24 - When the rate of inflation exceeds the rate of return

[Adam Tyson]

It's the difference between being less profitable and becoming less profitable, Anureet . The former is about comparing this investment to another type of investment, one where the difference between the rate of return and the rate of inflation is lower. Clearly, this investment, with a bigger difference, is not doing as well as the most profitable one.

To show that this investment is becoming less profitable, we have to show that the difference between those two numbers is growing! Not just that the investment is losing money, but that the rate of loss is increasing over time. That's about comparing this investment to itself at an earlier time, and we have no information about what was happening with this investment prior to the moment being described. Maybe it was always losing money at the same rate? Maybe it used to be doing even worse than it is now, and it is currently less of a loser than it used to be? That's where answer B fails. This investment IS less profitable than another one, but that might not be changing, over time, and it could even be changing for the better.

The prephrase should be your guide, and in this case that prephrase should match answer C: this investment is doing worse than whatever the most profitable one is. Tricky, but I hope that clears it up!

[intrepidlady97]

I'm having a bit of trouble understanding some of the logic in this question explanation.

For A), D), and E): I ruled these out, but not because of the reasons outlined in the explanation. Since the stimulus says: "the difference between those two rates will be the percentage by which, at a minimum..." I inferred that A, D, and E would only be correct if the rate of decline for a given investment HAD to be the minimum (which it doesn't, since the difference value is just the minimum value it could be). Is this reasoning correct?

For C): I see how this can be correct, but it seems to me that I missed a commonsense assumption here that would've allowed me to understand this when I first read the question. Am I correct that being able to deduce that this is the correct answer depends on being able to make the commonsense assumption that profitability = the rate of return? While it makes sense that a higher rate of return would contribute to greater profitability, it seemed like a leap to me to assume that a higher rate of return MUST/ALWAYS mean greater profitability. Economics is very much NOT my field of expertise though so I've probably just missed a commonsense assumption!

For B): In my mind, this was not a contender because it seemed like an exaggerated answer (because I thought that an increase in the rate of decline COULD make an investment less profitable than it was, but didn't necessarily have to). However, the explanation posted here says that B) is not correct because it is comparing the past profitability to the current profitability of the investment, while the stimulus does not touch on the time aspect and only provides a means of comparing a given investment to the most profitable investment at a snapshot in time. This does not make sense to me given this part of the stimulus "If in such a circumstance the value of a particular investment declines by more than that percentage...", which seems like it's saying that the value is NOW (compared to previously) declining at a greater rate (and thus making the temporal comparison). I thought it would have to say "If in such a circumstance the value of a particular investment is declining by more than that percentage..." for us to rule out the temporal comparison and see that it is truly occurring at a snapshot in time.

Many thanks-- this question is such a mind-twister for me!

[katehos]

Hi intrepidlady97,

Thanks for posting your question! For your first question regarding (A), (D), and (E), was the inference you made that the rate of decline for a given investment needed to be equal to the difference between the rate of inflation and the rate of return for the most profitable investment? If it were true that the % decline of any investment had to be equivalent to the % decline of the most profitable investment, then every investment would be the most profitable, so no investment would be the most profitable. Please let me know if I am misunderstanding what you're asking! I am happy to reframe my answer to better assist.

Regarding your second question, we don't need to make any assumptions that profitability = rate of return, since the stimulus itself specified that we calculate the minimum decline using the most profitable investment. This superlative means that there are no other equivalent investments, so any investment that is not the most profitable is less profitable than the most profitable investment. Given that we are discussing a circumstance in which the value of a particular investment declines more than the minimum percentage decline - which is dictated by the most profitable investment rate of return and the rate of inflation at the time - we know the investment in question is less profitable. Of course, it may be helpful to know that rate of return is a measure of financial profitability, but it's not strictly necessary for understanding the logic here.

This question is certainly tricky, but I think getting too caught up in the numbers/terminology can pose an issue for some students. The numbers are very useful (and frankly, necessary) for illustrating how all of this works (many other instructors have posted examples with numbers, so I won't redo their work here), but at the end of the day, if the percentage decline is more than the minimum decline, we know we are not discussing the most profitable investment (otherwise, the percentage decline of the investment would be the same as the minimum decline!). Everything else is less profitable, the only thing we don't know is to what degree.

For your last question, honestly, I think you're overthinking the words a bit. Declines vs declining doesn't change the fact that you're comparing the percentage decline of one investment to the minimum percentage decline, so, regardless, we're not conducting a temporal comparison and are only looking at one investment compared to another. To me, your explanation sounds basically the same as the posted explanation. Both seem to be saying "sure, if the value declines more than the minimum decline then the specific investment might be less profitable than it previously was, but it doesn't have to be less profitable and it doesn't really matter this is the case." I might be misunderstanding what you mean by an increase in the rate of decline (I understand this to mean a greater rate of decline on one investment than the minimum rate calculated by the most profitable investment, as opposed to meaning a greater rate of decline on one investment at time 1 versus time 2), so please let me know if you mean the latter option instead.

I hope this helps 'untwist' some of the questions you posed! Lots of students struggle with this question, so don't hesitate to reach out if you're still confused after reading my explanation!
Kate

[mab9178]

Please:

What does the phrase "in such circumstance" refer to?

And why does it not refer to what came before it -- i.e. the whole scenario that was set up in the sufficient condition signaled by the structural indicator "[w]hen" at the beginning of the stimulus -- "When the rate of inflation exceeds the rate of return on the most profitable investment"?

Does refer to what came after it, i.e. "the value of a particular investment declines by more than that percentage"?

Please and thank you

[Adam Tyson]

It refers to the whole situation described in the first sentence. Inflation is more than the rate of return on the most profitable investment, and the value of investments are declining by at least the difference between the two. It would have to be declining by even more than that difference for any investment that is less profitable than the most profitable ones.

[ericsilvagomez]

Hi,

I understand why C is the correct answer choice, but some of the words confused me. What is a minimum decline? Also, you mention in some of the answer choice explanations that there was already a calculation, is that the one from the first sentence in the stimulus?

[Robert Carroll]

ericsilvagomez,

The minimum decline is the difference between inflation and the rate of return of the most profitable investment. If inflation exceeds the rate of return of the most profitable investment, then all investments are losing money. The one losing money the slowest is the most profitable investment - that is then, by definition, the minimum decline in value.

The difference between inflation and the rate of return would allow us to calculate the minimum decline in value.

Robert Carroll