Taxes: a scenario inspired by physics

Everyone hates taxes.  I know I certainly do.  And it irritates me that the government can misspend my tax dollars and get away with it but the same isn’t true for the taxpayers.  Nevertheless, taxes are a necessary evil.  That leaves two questions: how much should the tax rate be and how should the taxes be levied on the populace.  Setting aside the former question, let’s explore the latter using a simplified model.  In essence, I’m going to use the basic philosophy behind physics – break it all down into the most simple “toy model” and build back up from there.  I make no claims about the accuracy of the model.  I simply think it is an instructive exercise.

So our “toy model” consists of a small country that we’re going to call “Toydonia.”  Toydonia has five residents: Alice, Bob, Charlie, Dave, and Eve.  Toydonia’s currency is called the “toy.”  Toydonia needs a road.  The road will cost 5000 toys and must be built or the country has no access to neighboring countries.  Each resident needs a bare minimum of 1000 toys to live on.  For the moment let’s not consider what would happen if they had less than that (in the words of the late, great Dennis Hopper, “bad things, man, bad things!”).  Now, Alice has 5000 toys, Bob has 2750 toys, Charlie has 2000 toys, Dave has 1500 toys, and Eve has 1000 toys.  We also won’t consider what they each did to get their money (or lose it, as the case may be).  So, here are some scenarios that are roughly analogous to various tax plans:

  1. Graduated tax – wealthy pay more: Eve can’t pay anything and live so we’ll consider her “under the poverty line” and thus exempt.  For simplicity, let’s suppose there are then two other tax brackets – those with 2500 toys or more and those with less.  For the sake of argument let’s say the upper tax bracket consists of those with more than 2500 toys.  This bracket pays 50% tax while the lower bracket pays 33%.  This scenario leaves Alice with 2500 toys, Bob with 1375 toys, Charlie with 1340 toys, Dave with 1005 toys, and Eve with her 1000.
  2. Graduated tax – wealthy pay less: Can we lower the upper bracket by 10% to 40%?  In fact we can’t even lower it to 45% if we want our road to get built.  We could lower it to 47% while raising the lower one to 42% (still assuming Eve can’t pay).  That leaves Alice with 2650, Bob with 1457.50, Charlie with 1180, Dave with 885 (!), and Eve with her 1000.  Doesn’t seem fair to Dave, but that’s life.  We could include Eve, but then she also won’t make ends meet, though we might get Dave back up above the line.  Either way, we can’t do much without someone being under the 1000 minimum.
  3. Flat tax with poverty exemption: We could flat tax everyone but Eve at 45% and have just enough to build our road.  That would leave Alice with 2750, Bob with 1512.50, Charlie with 1100, Dave with 825, and Eve with 1000.  Once again Dave gets screwed.
  4. Flat tax with no poverty exemption: Fair’s fair.  Let’s just charge everyone – including Eve – some dough for this.  That would allow us to lower the tax rate to 41% across the board leaving Alice with 2950, Bob with 1622.50, Charlie with 1180, Dave with 885, and Eve with 590.  But it now leaves us with two people without enough money to make a living.
  5. Use tax: Only people actually using the road get charged for it.  Suppose Eve walks to work.  She doesn’t need the road.  Conversely Alice owns a helicopter so she doesn’t need the road either.  So the people who would get squeezed the most are the folks in the middle who are required to use the road to get to work – Bob, Charlie, and Dave.  However you divide it up, they would end up paying way more than in any other scenario (remember Bob, Charlie, and Dave only have a total of 6250 toys).

Let’s introduce some complexities.  The first complexity we’ll introduce has to do with that 1000 threshold for making a living.  What happens to people that drop below that threshold?  Let’s take a look.  But first let’s create a “toy” economy.  Alice owns Corporation X (XCorp).  XCorp. provides most of the goods and services for Toydonia.  Eve and Dave work at XCorp’s plant.  Charlie is the sole government official for Toydonia.  Bob is the plant manager.  Everyone buys everything from XCorp. (so Alice essentially pays herself but also makes her money off of Bob, Charlie, Dave, and Eve).

  1. The first scenario above leaves Bob, Charlie, and Dave with 4720 toys of disposal money to spend on some of the more frivolous XCorp. products (we don’t count Alice since she owns the company and we don’t count Eve since she has no disposable income – recall there is no road so no trade and no immigration).
  2. The second scenario above leaves Bob, Charlie, and Dave with 4487.50 of disposable income.
  3. The third scenario above leaves Bob and Charlie with 2612.50 of disposable income.  Dave no longer has any – in fact he runs a deficit.  This means either he either has to go on welfare (which costs more toys) or he gets ignored until he goes away.  But if he goes away he needs to be replaced.  Once the road got built he could always be replaced by an immigrant (or, rather, Eve could be promoted and an immigrant from a neighboring country would fill her position) but then, unless the tax code is changed, the same thing will have to Eve.  Pretty soon Bob is having to train someone constantly for Eve’s and Dave’s positions because there’s now a high turnover.
  4. The fourth scenario leaves Bob and Charlie with 2802.50 of disposable income, but now not only is Dave lost immediately but so is Eve.  So instead of training people on a cyclic basis as in scenario 3, Bob is constantly training two people since neither can stick around very long.
  5. The fifth scenario would clearly leave less than any of the others since you’re pulling 5000 toys out of a total of 6250 available from the users of the road and Eve still has none.  This basically means the “middle class” (Bob, Charlie, and Dave) are constantly turning over.

I could go on like this, but I’ve been writing for quite awhile.  At any rate, it seems that the first two scenarios – a graduated tax – puts more disposable income back into the economy.  While it appears that Alice has less of her own in scenario 1 than in scenario 2, it’s important to remember that the disposable income of everyone else is getting spent on Alice’s goods and services.  If you assume that, under both plans, the cost of doing business is the same (say 100 toys), Alice ends up making 2120 toys in scenario 1 and only 1737.50 in scenario 2.  We could additionally assume that XCorp. pays no corporate taxes due to loopholes to simplify things and it becomes clear that Alice ends up with the most money via scenario 1.

In short, it would seem that one would want to maximize disposable income in the classes that do the majority of the spending.

Of course, the world is more complicated, but not that much more…

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