Obviously, macro-economic modelling is a very complex and sophisticated topic so there's not going to be a simple YES/NO answer to your question, but even when we look at the current global market we've seen challenges in that environment which go some way to highlighting what you need to consider for your hypothetical market. There are a few more to consider beyond the global market as well, but one thing at a time...
Why we call it trade
The one thing that your diagram has is arrows in both directions to each 'zone'. (I'll call them zones as I'm assuming that Earth, Mars, et al are acting as a single market in your diagram - if not, this gets far more complex.) This is a good thing, as it's important that you not have one group entirely dependent on supply of goods, with no demand for what they can provide back. That isn't trade and would cause it to be uneconomic to sustain such a zone.
But, there must be balance
What we don't see in your diagram is how much of each commodity is being traded. If one zone needs a lot of commodity X but can only offer a little of commodity y in return, this creates challenges. Ideally, this is managed through currency exchange. Let's say Venus is buying more than it sells, then (in theory) the value of its currency goes down by comparison to other currencies, because less people need to buy it to trade for goods, and more people are trying to offload it to buy the goods of others.
If the commodity in question is not life sustaining, this pressure causes less Venusians to buy goods from other zones, and Venusian goods become more attractive because they cost less outside Venus. This creates a self-balancing effect.
Cost of shipping
On Earth, the only metrics to consider for shipping is how far away the two parties are from each other, and what's in between them. Goods are shipped by road, sea and air, and some other mechanisms besides, like pipeline. The point being that for the most part, countries don't have the complexities that you would expect of space in terms of shipping cost.
Earth and Venus (in your model) are going to cost a LOT to ship from because of the gravity well. Let's assume that spaceflight is relatively common, the energy requirement is still there (even if the cost of energy has diminished) meaning that it will cost more to get goods off those planets than it would off Mars or the Asteroid belt. This also needs to be considered in your economic model because the cost of shipping alone may well make the same commodity at the same price from (say) the Asteroid belt more attractive than it would from Earth.
The other wrinkle you have that Earth doesn't have is the essentials for life. People use the same amount of O2 (for example) whether they are on Earth or the asteroid belt. That said, the asteroid belt has far less O2 than Earth does. Same would go for (say) wheat.
Ultimately, the supply and demand curve that we see in modern economics only really works if the commodity is not seen as essential. When it is, there are other forces at work and these are often not left to a free market economy to manage because of the humanitarian factors. To be frank, we've never had a country that has needed water to be shipped to it on an ongoing basis because it has none of its own. If we did, people just wouldn't live there in the first place. In this situation though, one has to ask whether or not these 'colonies' are now independent of the powers that first invested the tremendous resources required to establish them initially. If not, then one would expect the essential commodities to be a state run supply model. If not, then these independent economic 'states' have a bargaining weakness insofar as they can't afford to risk losing such supplies meaning that unscrupulous merchants would be able to charge whatever they wanted for critical shipments, effectively bankrupting most of these states for vital supplies.
If the question is really 'is it plausible' then the answer is yes. You have supply and demand to all zones, which makes it possible. For some commodities, you have multiple sources, making for competition and generally you're looking at a larger scale and slightly more complex version of the existing global marketplace.
If you're asking 'is it viable' then there are some challenges that we face before even getting off this planet that may introduce difficulties that in your world may prove insurmountable. The issue of vital supplies for one is something that ideally would be heavily regulated because otherwise you have people entirely dependent on trade for their survival, which while it has happened for relatively short periods in history before, doesn't work economically as part of a 'chronic condition'.
Finally, if you're asking is it probable, the answer is no. The simple reason for that is that these colonies cost something to set up in the first place and the state or company that set them up is going to want a return on its investment before letting them go independent. What that means in practice is that by the time they have the opportunity to do so, these zones have lost most (if not all) of the commodities they have to trade for what they need. It's almost a joke to let them become independent at that point because they'd be entirely dependent on the supplies of others to survive.
To that end; I'd have to say that the basics are there, but in practice I can't see it being viable unless the zones in question have massive reserves of commodities that they've hidden before becoming independent. Without that, they're just not economically viable unless they have some unique manufacturing process or service which simply isn't possible in a different set of environmental conditions or within Earth's gravity well.