Best way to pay for college puzzle

In a society, everyone goes to college and everyone has 3 children(one parent family). College is also very expensive. There are two ways that this society could pay for college. Let's say college costs $$X$$ amount. Either:

1. Everyone pays for their own college. So everyone pays $$X$$ dollars.
2. Everyone pays for their children's college. So everyone pays $$3X$$ dollars, but then they do not have to pay for their own college since their parent paid for theirs.

Question

Why does 2 cost more than 1 even though they are equivalent in outcome?

• Are they one-parent families in your society? Commented Mar 23, 2019 at 18:46
• @WeatherVane Yes. For simplicity Commented Mar 23, 2019 at 18:46
• No no no. If the kids each pay their own fee, they will each inherit the fee that I didn't have to pay for them. So their education is free ;) Commented Mar 23, 2019 at 19:00
• @WeatherVane I am not sure that I understand what you mean Commented Mar 23, 2019 at 19:05
• It doesn't matter that your own college was paid by your parents, you still have to pay 3X for your own kids, not 2X. If you also paid for your own college then you would need to pay 4X. Commented Mar 23, 2019 at 19:18

Here's why:

Imagine the family tree of such a population. It might look something like this

a                 <------Generation A - one person
b   b   b
ccc ccc ccc       <------Generation C - nine people


The solution to the paradox is that

The population is constantly growing. Having the older generation pay for the next generation concentrates the cost. Having the younger generation pay for its own education spreads out the cost.

By shifting the burden by one generation back,

There are less people in that generation to pay the same cost.

Also, it is important to consider the following

Imagine generations a, b, and c have each paid the required money in this society.

If they are paying for their children's education, then

Paying results in $$3+9+27=39$$ paid educations.

If they are paying for their own education, then

Paying results in $$1+3+9=13$$ educations paid for.

They are accomplishing two different tasks, because the burden is shifted.

@Brandon’s answer covers pretty much everything, but another way to think of it is:

Imagine we have situation 2.
Then, consider - not a single parent, but the group of the parent and their kids.
In situation 2, the parent pays 3X. The children pay nothing, so the total cost is 3X.
In situation 1, the parent pays nothing. The children each pay X, so the total cost is 3X.
We see that the cost of college is the same either way, it is just more disperse in 1.

• In situation 1 doesn't the parent pay for their own education making it 4X? Commented Mar 25, 2019 at 2:35
• @JacFrall Yes, but we are considering only the children's education. Commented Mar 25, 2019 at 7:24

Another way to think of this:

It is more expensive because it includes a storage of extra money.

Consider this scenario:

The world changes and finds college to be useless.

In option 1:

Nothing happens. They just live with no expectation of going to college.

But in option 2:

Every person in the youngest generation finds themselves with X as bonus spending money that has been saved up for them!! Woo hoo!!

Therefore:

The additional cost of scenario 2 is funding the rolling global piggy bank that is passed down each generation.

• +1 for lateral thinking Commented Mar 25, 2019 at 16:56

A couple of assumptions would be in place here:

1. Everyone gets to go to college (wow!)
2. Everyone can afford to pay for their own college which is very expensive (or even 3 times of it, depending on which side of the debate we are on)
3. Whether for one college education or three, the payment needs to come from one's earnings and not from any kind of inheritance (leave alone from the parent) or unexpected windfall/benefit (lottery, prize, or the like) or government benefit or scholarship/grant

Now to the question in question:

The outcome is not the same!
In the first case, one pays for their own college (current generation's college). So, everyone's got to work to earn their own college education.
The second case is about being born with a guaranteed, fully paid-for college education and they don't need to work to earn it. Of course, they still need to earn three times as much (plus inflation-adjustment) later by the time the kids are ready for college but that is not quite the same; it is about paying it forward.