A Tax Rate Word Problem from Ryan Lyk

I found myself reading the UMD Statesman, as I’m wont to do, when I stumbled across an opinion piece by Ryan Lyk. For those of you not familiar with Ryan, he is a self-proclaimed “Rising voice of the Republican Party.” Sounds impressive, eh? (Have I been spending too much time in Canada?)

Mr. Lyk wrote an editorial explaining that Rep. Jim Oberstar – a man who has won a House of Representatives election every two years by at least 60% going back to well before Ryan Lyk was born (with one exception where he only took 59% of the vote in 1992) – should not be reelected because he hasn’t “done anything useful for our state”. This is the opinion of a self-proclaimed “Rising voice of the Republican Party.”

Here’s another classic:

From what I’ve seen, Oberstar seems to be really out of touch with Minnesotans.

Then why do they keep electing him with supermajorities? Perhaps Lyk should look a little harder?

Moving on, the next paragraph is the highlight of Ryan Lyk’s editorial. He presents a hypothetical tax policy where, as population grows, not only does the tax base grow, but the tax rate increases exponentially. Here’s the word problem:

There is also the problem of increasing taxes every time we need money. As a population grows, more tax money is needed to take care of the population. It seems logical then that raising taxes is the best route. Well, let us look at this from a purely logical and common sense approach. As an example, let us take a country of 20 people. The government needs 1 percent of the total income to support two people so the current tax would be set at 10 percent. Say this population grows to 40 and the government needs to account for the growth so they raise their taxes to 20 percent. Soon the population hits 100 and has a tax of 50 percent. Eventually, there are 200 people in this country, and the government raises taxes to 100 percent. Does this make any sense? But how can the government account for the extra money needed if not through tax increases?

Maybe I’m reading this wrong (that’s the first challenge in word problems, eh?) but as I understand Mr. Lyk’s reasoning, he’s saying that as a population grows, a government needs additional revenue in order to support the growing population. I think most people would agree with that statement. Where Lyk loses me is when he suggests that the revenue needed to support a population grows at a rate well beyond the growth of the population. This would suggest that there are no economies of scale gained from driving on the same roads, sharing the same utility grids, scaling police forces, or maintaining jails.

I’ve tried to visualize Lyk’s word problem in the following chart where I’ve taken the four scenarios he’s presented. I used a constant of $30,000 for income along with Lyk’s population and tax rate scenarios to create this:

Ryan Lyk's Hypothetical Tax System

The gold line represents gross income, so as the community grows from 20 to 200 members, the income generated within the community increases 10X, assuming a consistent per capita income.

The interesting line here is the gray line. That’s the hypothetical income the government would collect under Lyk’s scenarios. It starts out at a 10% tax rate on the left, but for some reason, the tax rate increases at an absurdly high rate, reaching a point where every dollar earned goes directly to the government. And the population only had to reach 200 people before every dollar earned went straight to Uncle Sam.

As I look at this, I wonder if Mr. Lyk understands basic algebra. Does he understand that, as a population grows, it will naturally bring in more revenue to support itself as long as the per capita income remains the same? I’ve tried to visualize that in the following chart:

Reality Based Tax System

Here’s the difference: Under Ryan Lyk’s scenario, the cost of government services for a population of 20 is 10% of income, so assuming $30,000 per capita income * 20 people, the gross income is $600,000 and government revenue is $60,000, so the government operates on $3,000 per individual. Yet somehow, the cost of government under Lyk’s scenarios spirals out of control from there. By the time 200 people live in a community, the cost of government increases from $3,000 per individual to 10X higher: $30,000 per person.

That’s obviously absurd. I don’t know if this is a case of ignorance, bad math, or a deliberate misinterpretation of the facts by Ryan Lyk to make an unsupportable point.

As the second chart illustrates, as income increases due to population growth, a government’s revenue will clearly increase as well if the per capita income remains the same. For example, if someone moved onto my block in Minneapolis, we wouldn’t need to build a new road to downtown for them to get to work. Or a new sewer system. Or hire another cop. There are some economies of scale at play here that Mr. Lyk may not fully understand.

To answer Mr. Lyk’s questions:

Question: Does this make any sense?

Answer: No. It doesn’t. It’s absolutely absurd to think that a government would need to scale taxes exponentially at such a ridiculous rate while the population is growing linearly.

Question: But how can the government account for the extra money needed if not through tax increases?

Answer: Algebra.

Here’s a word problem in return:

Imagine that 20 people go to an Outback Steakhouse and decide to split two Bloomin’ Onions. Those things are huge calorie bombs, so they’re each chipping in for 10% because that will still be plenty of food. Now imagine that 40 people go to Outback. Instead of ordering four Bloomin’ Onions (10% rate) they order eight Bloomin’ Onions (20% rate). While they’ll have twice as much food as they need, your scenario says that this is how the world works. Then a group of 100 shows up and orders 50 Bloomin’ Onions! Rather than having 10% or 20% of those fat laced appetizers, they’re splitting one among every two people. That’s a calorie bomb for ya. Now, imagine under your scenario what happens if 200 people show up at an Outback Steakhouse. They’d order 200 Bloomin’ Onions under your scenario, so they’d each have a deep fried Bloomin’ Onion set in front of them, making them wonder “why the heck do I need 3,000 calories of deep fried onions when groups of 20 are satisfied with 300?”

Does that make any sense? I wouldn’t imagine so. But that’s the same scenario you presented in your argument.

With all that being said, it’s possible that I’ve misread Mr. Lyk’s word problem. If that’s the case, could someone explain it to me in layman’s terms?

8 thoughts on “A Tax Rate Word Problem from Ryan Lyk”

  1. Looks like you “lyked” his ass, Ed. And yes, you type “eh” way too much now. Take off, hoser.

  2. You are misreading this horribly. The point is that taxes cannot continue to be increased. That at some point, you run out taxes to increase. Democrats continue to fight for tax increases and eventually the tax rates will be too high to be sensible. You are thinking way too far into a very simple example used to show that taxes need to remain rather constant. In fact, I say that in my piece, don’t I? I say that the system you say is stupid is stupid. And I also say that a tax rate should be able to support the population when staying constant because as the population grows, so does the economy. We seem to be in agreement for the most part.

    If not, are you actually advocating that taxes can continue to be increased without a cap? Thats what it seems to me.

    Thanks for the response, feedback is always fun!

    Take care.

  3. In response to your hypothetical situation, the exact numbers I use are not the significant part. Want me to use more reasonable numbers? Ok, a populaton of 100,000 has a 10% tax. Population grows to over 1,000,000, government needs more money, increase taxes? Alright, they are at 15-20. More reasonable? Well then they hit 300,000,000. At this point we have clearly defined classes. All of these classes have different tax rates, but the point remains that the tax needs to be reasonable, not to be increased exponentially. Base taxes should support the government because the economy should be increasing with it, no? I think that is what you are trying to say, and that is what I am trying to say.

  4. @Ryan, the hypothetical situation I presented was not mine but yours. The numbers presented – your numbers – have nothing to do with the realities of tax policy of any political party, so using them to try to make a point is pointless.

    It sounds like you’re saying that the current tax rates are as high as tax rates can go without tipping the economy into a death spiral. Or something like that. Yet you provide no explanation for why our current tax rates are at a magical inflection point. Our economy has grown at times when tax rates were both higher and lower than they are today, so I’m not sure how you can come to this conclusion (if that’s the conclusion you’re trying to make).

    The new numbers presented in your second comment make the same mistake as the first. It’s the bloomin’ onion all over again. A government’s revenue will increase at a linear – not exponential – rate as the population grows, if we assume that per capita income remains the same (which you seem to be willing to agree to in your models).

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