How is that going to work on mars? Well, we have to start with some assumptions.
People will get to mars by whatever means they do with whatever political baggage they carry. So there may be many groups but with all of mars to choose from they should keep themselves from causing each other too much trouble. Survival will suggest they are helpful to each other regardless of where they came from. Political baggage is unavoidable. However, we are going to assume the members of our local community are fiercely independent and have all agreed to the settlement charter which is to say strong property rights. Nobody can take anybody's property except in free trade. No eminent domain or property taxes by any name will exist. No country is going to find it worth the expense to send enforcement to mars to collect any tax and the martians will mostly ignore them were they to try. We will discuss the exception to this after we've finished with our assumptions. Land will either be owned or unowned. If unowned anybody could mine it but it is subject to claim by any newly arriving member of the charter at which time mining must stop until arrangements agreeable to the new owner are met. So it would be unwise to invest too heavily in unowned property.
We have to understand the time value of money. Which simply means future dollars have a cost which reduces their buying power. If you borrow money, expect to pay a fee.
Since we have no better numbers we will assume the Mars One lander parameters. $150m to $190m will buy you one to the surface of mars with 2500 kg of stuff. Let's use the higher number but say that includes the 9 mo. time value of money. So imports from earth will all have a $76k/kg surcharge. The buyer also owns that lander which has 18 dracos, 8 superdracos, tanks, and about 4 tons of aluminum. Aluminum is 100% recyclable. They may keep that lander as an emergency habitat or scrap it. It is their [strongly enforced by the locals] private property. It may be that none are ever purchased to be sent to mars, outside of the settlement charter contract, but that's ok as you shall see.
Contract law is the law of the land and commodities will be traded and assume whatever natural exchange rate free trade determines. Mars will have no fiat currency. They will have members that do have fiat currency and perhaps other assets on earth. We will assume that most members arrive on mars in a four person lander with personal items. That would mean 625 kg per person (including their own mass.) However, the settlement charter requires the transportation company to provide 1000 kg per person so they will deliver that extra 375 kg separately. So any colonist that severed all ties with earth and sold all their earthly assets would still arrive on mars with over 400 kg of resellable items worth a minimum of $30m. in surcharge value and claim one square kilometer with about 500 plots all of which is potential collateral at a mars bank to start any business they might choose. It should be quite common for arriving settlers to trade some of these imported items for a habitat when they arrive and sell the rest over the course of time.
This may eliminate the need for other resupply from earth essentially making martians independent in that sense quite soon. But wait, $76k/kg? Who on mars could afford that? Probably nobody, so what happens in a free market? People trade. People compete. People will compete by finding ways to make some of those imports ISRU. People will involve themselves in the local economy in individual ways, no central planning required. There are no gouging laws. If something is scarce it will be able to demand a higher price. Things that demand a higher price will look good to somebody wanting to produce and sell such items ISRU. More sellers competing brings the prices down. The laws of economics work everywhere.
How about liquidity? Money exists for a reason. You don't want to have to carry around barter items for day to day transactions. That's where banks come in. Anyone that gains the trust of the community can be a banker. Strong contract law protects everybody. Banks collect commodities (metals most likely, but anything not perishable would do) and issue bank cards that act as money. They do not produce money through fractional lending. They make their money in the commodities exchange and commercial lending to people that all have collateral. Everybody is going to have internet and card readers will be a common item for anybody in business (probably built into the cell phones everybody has.) To avoid multiple bank cards, banks may all agree to just use a personal ID card with the user choosing what bank to draw funds from for any given transaction (martians are very rational you know.) It's quite likely the protocols will be worked out early so the mars ID card (with an extra backup) is part of every arriving colonists stuff. The balance on the card may be kept in grams of silver. So in making a deposit at a bank of iron, copper, gold or whatever, banks will compete on rates to turn that into silver. Business would naturally advertise their wares in grams of silver (about 64 cents here on earth at the moment.) Bank runs should never happen as long as banks use their assets wisely. If it did happen, depositors might have to accept other than silver to cover their deposits. It's not fractional banking. They will be able to pay their depositors. They will have to make all their assets available in reports to everybody over the internet and inspections would be something for the locals to determine (you really can't get away from some politics.) They might have a bank regulations that limit how much exchange rates can change in a single day but that's not essential and something for the locals to determine for themselves. It will all be written in contracts. Caveat Emptor.
All of this economic activity on mars will create value and wealth. Companies on mars may someday go public on earth. This makes earth wealthier without importing a single gram from mars. The banks themselves might have public stock issued on earth.
With people possessing and developing land on mars, people on earth will have confidence that they could buy land as an investment knowing it will go up in value over time. Price determined by a free market. The companies transporting colonists according to the settlement charter would no doubt be able to make more money faster in other ways. But with 500,000 half acre plots to sell for every person they transport, they have a very large potential return on their money even if it takes decades to break even. I expect once people are living on mars and lots of people want to go to mars (having millions of dollars in assets the moment you arrive might be considered an incentive... at least 200,000 people want to go now even without that incentive) the value of land will appreciate rapidly and return on investment for transportation may only take months once the ball is rolling.
So now, what about those countries that do want to take the assets of some that are left on earth? Being smart (my ex-wife believe rich is the definition of smart) they know they will need to protect their assets from confiscation. They will (the rich are funny that way.) Everybody else will not have any assets on earth for them to confiscate. Really that may be the main attraction of mars... getting a fresh start without nanny looking over your shoulder. That's Galt's Gulch.
I want to talk about two more things, dust and food (but not dusty food.)
Dust blows all over mars and some quiver at the dangers. But economically that dust has value. It will be collected for the minerals in it (refined and deposited at your local bank.) They will decide for themselves how to channel that dust on their property with walls and wind breaks.
The early colonists must be provided with enough food to survive. This means they should not depend on local farming at all to start. We don't really know how local farming is going to work out except by doing in on mars, hands on. It won't be nothing. I believe a 50m Zubrin hobby farm will feed three to four. Whatever the true rate of growth per acre is they will be able to grow something. That's what the early colonists will find out for us. That will determine how fast new colonists can arrive. It's not something to wring our hands over but it would be good to know how much it will cost to keep the early colonists alive.
Water is not a problem as long as they have power. They need enough power to take care of all their needs and in addition enough power for the industry to create more means of getting power. So we should be absolutely certain that we oversupply them with power. This is not negotiable. The colony will not survive without this. If you have power and water you have air. So food is really the only issue.
They will need 2.5kg of food per person per day or about 650g if freeze dried. Let's say a combination being about 1kg or $76k per day. To keep a dozen colonists alive would cost over $300m per year. That's a lot of money. That's $650m every 26 month for food supplies or 3.25 landers. So if we don't want to spend $650m a second time they will have to learn to grow enough food before the second wave of colonists arrive. Can they?
Absolutely they will. Even if they don't start with as much variety as they eventually will have. Potatoes alone grow dense enough that nobody is going to starve, but they will have more variety. Food will have value. People will grow it not just for themselves but for others. Expect thriving farmers markets on mars.
Update: This is where I will provide some food production numbers after I've done a bit more research on the topic.