When it comes to a welfare state, many people get concerned about the type of incentives that it creates. They worry that people who receive welfare will become lazy. They worry that welfare won’t fix problems of equality – it will only worsen them.

But even if some of those concerns are valid

We should try to take some bias out of that viewpoint. And nothing does that like some maths. So let me try and give you some numbers.

Consider two women:

• Francesca; and
• Betty.

Here’s the deal:

• Francesca earns double what Betty does each month ($2,000 vs $1,000);
• Both of them spend 85% of their salaries, and save the other 15%.

At this point, I think we can say that they are fairly equal in terms of their attitudes, right? They have similar saving and spending habits – even if they have different incomes.

Now here is the twist:

• Life is uncertain, and full of unexpected out-of-pocket expenses.
• Many of those problems are medical.
• An assumption:
  • Every year, both will have at least one minor medical emergency (sickness/car accident/etc); and
  • Every five years, both will have at least one major medical emergency (serious illness/etc).
• At this point, we’ll also assume:
  • Francesca’s minor emergencies cost her $1,000; and
  • Francesca’s major emergencies cost her $10,000.
  • And just as Betty earns half Francesca’s income, so her emergency costs are about half of Francesca’s.
• These are paid for from savings – and if there are not enough savings, then the ladies will have to borrow some money.

For transparency (in case anyone wants to replicate my numbers). other factors:

• Salaries increase at 4% per year (in real terms);
• Any savings earn 4% per year as well (in real terms); and
• Credit card interest rates run at 7% (in real terms).

The ‘Equality’ Model

So if we follow all that, then here’s a picture of their relative net savings (over a 15 year period):

And that can be considered fairly equal, because if you look at their net savings positions as a percentage of their monthly salaries:

They’re on par with each other.

The Equality Problem

If you go back to my assumptions list about the ’emergencies’, I apparently decided that the cost of those emergencies should be proportional to income.

In the real world, we know that this is not how it works. Without public healthcare or regulated private insurance, medical costs would be roughly the same for both of them. Betty might be able to shop around for an affordable doctor – but Francesca would also shop around for an affordable doctor. There may be some price differentials between what the rich person pays for, and what the less-rich person pays for, but those costs are going to be within range of each other.

So let me shift that assumption a bit, and say that Betty’s unexpected emergencies are only 25% cheaper than Francesca’s.

What happens:

And the relative savings-to-salary graph:

It’s an issue, right? The minute you start hitting emergency costs that are unrelated to income levels, then the world start to fill with people that ‘can’t seem to catch a break’.

And it gets worse

As time goes on, Francesca’s nest egg grows. This means that she can afford to pay more for good healthcare, while Betty is already spiralling into debt.

This has dynamic consequences:

• The price of healthcare goes up, as the better doctors that service the rich ‘re-base’ the fees in their profession;
• Betty starts to leave even the minor medical emergencies untreated; and
• Because health can be a cumulative thing, her ‘major’ medical emergencies start to get even more major (and more frequent).

How society solves for this lack of equality

If all these emergencies are medical ones, then there are two common solutions:

1. Subsidized healthcare (the welfare state); or
2. Regulated private health insurance.

Both of those options allow the ‘medical emergency’ cost to be re-based according to income. And you get back to the first version of the ‘equality’ model.

But when you strip out either the subsidized welfare, or the regulation part of the private health insurance, then you’re back to the second model.

The trouble is:

1. Not all emergencies are medical; and
2. Even medical emergencies in a welfare state will come with uncovered costs (lost income, out-of-hospital expenses, potentially some high deductibles, often a job loss, etc).

Both of which make equality seem hypothetical, at best.

But more importantly

We need to be better about assuming that people who can’t catch a break are lazy. In order for Betty to ‘catch’ her break, she’d need to save 20% of her salary (instead of the earlier 15%). That is: she’d need to save proportionally more than Francesca in order to avoid going into debt.

And it does seem unfair to expect the person that earns less to save more, right?

But now I’m verging into a different kind of argument.

So I’ll just leave it there.

Rolling Alpha posts opinions on finance, economics, and sometimes things that are only loosely related. Follow me on Twitter @RollingAlpha, and on Facebook at www.facebook.com/rollingalpha. Also, check out the RA podcast on iTunes: The Story of Money.