#11 - Raising the tax rate on essential goods – a

[khmacdowell]

Even with this and other threads, I can't convince myself than any of the answer choices are remotely correct, but more than that, am still convinced (A) and (C) are identical (and therefore neither can be correct), and (B) is better anyway.

I'm usually good at LR; in the last 51 timed PTs I've taken, I've averaged -1.15686 per LR section, to be pointlessly specific. But no amount of time or reading has convinced me on this one, and the nerves on test day make the possibility I get routinely tripped up much higher. So I'm trying to at least feel confident in the belief I am capable of understanding every LR question, given unlimited time.

Alright, thanks for coming to my TED talk, now here's my issue, and I'm hoping you can help me out:

Three quantities are required to calculate government revenue from a sales tax: (1) the rate of the tax, (2) the price that the tax is calculated from (the price of the good), and (3) the quantity sold of the good.

(A) gives you a very rough estimate of (1), i.e., it will answer whether the tax rate is greater, or else lesser, than the tax rate on the current goods. (C) gives you an equally rough estimate of (3), i.e., it is either lower, or else not lower than the current quantity sold.

Either of these in isolation, barring some predictive model about consumer behavior tells you absolutely nothing about the relative size of the tax revenue, and whether or not it is significant.

Let's say the quantity remains the same. Well, if the tax is negligible in size, the revenue raised will not be significant, and, for the quantity to remain the same, the tax is likely negligible in size.

Let's say the quantity decreases (the obvious alternative). Well, if the tax is large enough that the revenue is still "significant," then the government official is correct even though the answer seems to discredit his assertion.

For exactly the same reason, the answer to (A) is equally devoid of useful information. The rate is either higher, or lower, than another rate. But without knowing the quantity, we can't know if the revenue raised is significant. The answer choices are logically equivalent in that they each tell you a necessarily dependent part of the information needed to assess the proposal, let alone that they both leave out the third necessary component: the price of the good (since rates are rates).

So, the only one that could possibly actually reveal useful information is (B), because at least if the answer is "yes," then it is sure that the assertion is correct. If it is "no," then at least one of the essentially infinite possible outcomes that confirms the assertion has been ruled out, making it infinitesimally less likely that the assertion is true.

The only interpretation that could seemingly justify either (A) or (C) (and it's the same interpretation, because they're logically equivalent) is that, rather than a "yes" or "no" answer, you are given a specific number, in which case you could at least make some judgment if either number were especially unreasonable.

But under this assumption, B is still the better answer, and by an even larger margin. Because if you're given an actual number, you can be certain whether or not the assertion about the proposal is, in fact, correct.

There is one situation that justifies C that I have concocted out of desperation, but it involves making inferences about the world outside the stimulus, and that is: you could look up the content of the bill, and therefore, knowing the rate is automatically possible. But I fail to see any reason why you couldn't then argue you could use a predictive model based on knowing the rate (A) to calculate the likely quantity and again, get the same information, albeit very, very slightly less certainly, since the latter involves a prediction.

Edit: Actually, I should note, the answer to (A) can only tell you higher/not higher, while (C) can only tell you equal/not equal, which is actually worse. Neither can give you any of the three possibilities (higher/lower/same). But at least in (A), the numeric range of the possibilities is smaller.

Others have brought in economic theory, so you could argue luxury goods have elastic demand, or just appeal to the fact that this happened in real life and failed and is taught in every econ 101 class. But perhaps the proposal is enumerating mutually independent possibilities, so just jewels are taxed, and those don't involve domestic labor to mine, and only rich jewelers handle them once they reach the country in question, so the blue collar shipbuilder argument is moot then also. In fact, since luxury goods in general are mentioned, ones not even on the list might be taxed as well.

Irregardless of all of the above, the question seems to come down to which answer is (100 - ε)% wrong, and which one is 100% wrong.

[KelseyWoods]

Hi KH!

You've done a very thorough analysis of this question! I'll try to address your major points/concerns. I think one problem you might be having is that you list 3 quantities that are required to calculate government revenue from a sales tax: I agree that those 3 things are necessary if we want to calculate the amount of revenue--but for this argument, we don't need to actually know what the revenue amount is. The conclusion is that the luxury tax will increase revenues. So all we need to know is whether or not the luxury tax will result in more revenue than the government currently has. Meaning that we don't actually need to know the 3 things required to calculate actual revenue. We simply need to know if raising the tax rate on luxury goods will increase overall revenue.

Answer choice (C) asks the question we need. Will the sales of luxury items remain the same? If the same amount of luxury items are sold and the tax rate on luxury items increases, then, yes, that overall revenue will increase. If the tax increase deters people from buying luxury items and the number of sales goes down, then the overall revenue won't necessarily increase.

Answer choice (A) asks if the luxury goods will be taxed at a higher rate than the current tax on essential goods but this matter is irrelevant. Whether the tax rate is higher or not, it's still an additional tax. So if all other things remained equal (like the amount of goods sold) it would increase revenue no matter what the rate is.

Answer choice (B) is also irrelevant because it's essentially asking if we'll be making the same additional revenues with the new tax that we currently make on the essential goods tax. But we don't have to make the same revenue on the essential goods as we make with the new luxury goods tax of overall tax revenue to increase. Even if the luxury goods tax is making half of what the essential goods tax is making, the new luxury goods tax + the essential goods tax will still be higher than the essential goods tax alone.

Again, we're not getting rid of the essential goods tax. We're simply adding an additional tax on luxury goods. So we need a question that really gets to the heart of whether or not this additional tax will actually raise revenue. For it to raise revenue, we need to be selling enough luxury goods so that the prior tax on luxury goods combined with the additional tax on luxury goods will generate higher revenue than the revenue generated by just the previous tax on luxury goods alone.

If you're mathematically inclined, think of the conclusion like this:

(new tax + old tax)*(new # of luxury goods sold) > (old tax)*(old # of luxury goods sold)

We already know that the new tax + the old tax will be higher than the old tax. What we need to know is about the new vs the old # of luxury goods sold.

Hope this helps!

Best,
Kelsey