## Wednesday, May 13, 2015

### The "true value" of a dollar

What is the true value of a dollar?

Let's say you are moving from Noira with currency N dollars (NOD) to another country Moira. That country also has (local) M dollars (MOD), but the tax rate there is much lower. Let's say the tax rate at Noira is 40%, and in Moira 15%, but there is also a 7% or so VAT on every good you by.

As you move, you are told to take a pay-cut of 10% i.e. your current emoluments in NOD are converted to MOD, then multiplied by 0.9, and that's the yearly MOD you are paid once you make the move. Question is, should you take the job?

This calculation is a completely non-trivial undertaking. For instance, there may be things about Moira that are more of value to you in intangible terms than what Noira offers. And since life never works this way, it is unlikely that taken as a set, all attributes of one or the other country totally dominate the attributes of the other under consideration in terms of your preference. [OK, I am considering roughly comparable economies. If you were to take "the best" (by whatever arbitrary metric you choose) country that is in the so-called "developed economies", and another that is the lowest of the countries in the so called "developing world", then attribute dominance may in fact exist.]

Total attribute dominance makes answering your question easier, but the easier the question is to answer in real terms, the higher the barrier to entry, or the moat to your promised land. Not to say such barriers are insurmountable, just that it takes more to get there.

So back to the question at hand...
From a very simple economic perspective, we can classify all consumables people use to be of one of two types - either a. goods, or b. services.

In more developed countries, manufactured goods tend to be cheaper, while services are more expensive. The converse is true in developing countries - people-power tends to be more plentiful and less expensive, while finished goods cost a great deal more. For sake of argument, let's say Noira has more expensive goods than services, and Moira, more expensive services than goods. Let's also say as a long-time resident of Noira, you spend 50% on goods, 30% on services, though change in life-style when you move might mean the mix might go down to 30/50 on each. And you are habituated to saving 20% of your income each year on a monthly basis.

The model becomes slightly more involved. If the NODMOD exchange rate is x, this means you receive x MOD for 1 NOD. If your monthly pay before the move is m NOD, then you are paid: mx*0.9 MOD after.

Your take home pay in Noira is m*0.6 NOD (40% tax rate), and you save m*0.6*0.2=0.12 m NOD every month. Along the same lines, in Moira you would save mx*0.9*0.2=0.18 mx MOD

Now, what if Noira gave you the ability to put in some amount into tax-deferred 401k like savings plan but Moira had no such? What if Noira had an international tax regime for citizens and Moira didn't? What if you were a Noira citizen, and wanted to return to Noira from Moira after a few years? What if Moira had subsidized medicine, but Noira did not? When you return you want to convert your MOD back to NOD, so you want to make sure the exchange rate is in your favor (you want a very low NODMOD rate because you want as many NOD dollars as you can get for your MOD dollars you have saved while living in Moira). And of course, you also want to make certain that when your pay is first bench-marked, the exchange rate is in your favor as well (here you want a very high NODMOD rate - the highest you can manage, because you want the benchmark to give you as high a salary in MOD as you can get for your current NOD pay). All these factors play into your decision.

This is an example of a simple mathematical model. Of course, this can be made much more realistic by adding in more assumptions. And as we get more complicated, we need to start using spreadsheets. Excel is your friend as you go down that path.