Dissecting Mike's great illustration.

From his comment...

Out west somewhere, in the 19th century, is a spot of desert ground where there is absolutely nothing. No one lives there, nothing grows there.

Sounds like the start of a good mars analogy.

Along comes a prospector and finds gold. Within weeks a town has spring up. There are prospectors and miners pulling spendable gold out of the ground.

As long as we don't get hung up on precious metals, I'm with you so far.

There are stores supplying their need, for mining equipment, food, clothing, liquor and entertainment. The owners of those stores mostly borrowed the capital to establish them.

Let's consider this in the context of mars. So we've got some martians that choose mining as their profession and they are successful. We've got other martians that choose to be shopkeepers and are willing to trade with the miners. Where do the shopkeepers get their inventory? There are only two sources: mars and earth. Most of their inventory they will get from other martians that choose to be ISRU manufacturers because that makes the most economic sense, but some things will have to come from earth until martian industry is up to supplying that demand. There are two ways of getting things from earth: direct import/export which is prohibitive, and trade with newly arriving colonists (those trades being initiated before those colonist leave earth, but with transactions finalized directly on mars.)

What about the borrowed capital? That could have happened before or after the shopkeeper left earth, but most lenders will only make a loan if they have collateral on earth providing security. It sucks, but that the reality of the lending business. The good news is the type of things miners need will probably all be producible locally on mars (including basic electronics.)

All those goods, which can not be manufactured on site, are being shipped in in return for the gold which is being shipped out and sold for profit.

This is where the analogy fails. mining equipment, food, clothing, liquor and entertainment will all be produced locally because they can and only that makes economic sense. Some entertainment consists of data which may be imported at a low enough cost to make economic sense. Mining equipment is mostly iron, hydraulics and some electronics all of which makes the most economic sense to produce on mars. No gold export required. The gold stays on mars.

Eventually, the local veins of ore are tapped out. This happened in many places.

Of course, then the miners have the normal economic decisions to make. Search for more minerals or find another means of employment. Since mars industry will have demand for mars minerals perhaps forever, most miners will probably continue with perhaps a focus on other minerals they may find. Almost anything they find will have some demand.

When that happened, the miners and prospectors, no longer able to produce wealth with which to buy the things they needed, moved on, leaving the storekeepers behind.

Nonsense. The single biggest advantage martian miners will have is that almost everything is in demand. Lowest on the list being martian iron which they can't even avoid finding.

The storekeepers could get by for a while, trading with each other, but their main market, and the source of the actual wealth, is gone.

Let's examine that premise a little closer. Would the shopkeepers have miners as their main or only customers? Not likely.

First the ones selling mining equipment close up, absolutely no demand for that.

Do you remember the general store from your history books? Inventory moves through the store and changes over time to reflect changing demand. It would be a really stupid shopkeeper that didn't consider future demand.

Then the others, without the spendable gold coming in, are no longer able to service their debts and obtain new credit to bring in additional goods, not that there is anyone to sell to anyway. So, one by one, they close and move out, leaving a ghost town behind.

The mistake here is the premise. Having a limited source of a high value export is not the correct analogy. Ghost towns are created because of a focused economy. They are avoided by having a diverse economy. To equate mars with any boom town is ridiculous precisely because export is so prohibitive. As the doctor says, "don't do that!"

It is every bit as empty as it was before. No one lives there, because there is absolutely nothing of value to bring people there. Well, that is Mars.

Only true if gold mining is what brought them there. It certainly will not be. That is not the reason people will go to mars precisely because it wll not work. This is known as the false choice fallacy (also a bit of strawman.)

There is absolutely nothing, no thing, that can be produced on Mars and shipped back to the earth and sold at a profit.

Let's agree. That just means that will not be the motivation.

There could be ingots of pure, refined gold just sitting there and they could not be recovered profitably.

Absolutely true with regard to exporting it to earth.

Thus, without an economic basis for its existence, the colony will ultimately devolve into people sitting around twiddling their thumbs, waiting for the next supply ship, until Earth decides not to spend any more money endlessly sending supplies and getting nothing in return.

You have not shown a lack of economic basis. Earth doesn't need to spend a penny. The colonist pay their own way if the ticket price comes down enough and there is another way if it doesn't. My plan pays $5 million per ticket at no cost to the earth or the colonists. It is paid for the way development is always paid for, by the free will of speculators.

The problem with your argument is you're right only if you make assumptions that aren't actual constraints.