Basically the two main ideologies in Extropia are Anarcho-Capitalism and Mutualism.
Although they're both considered part of the same faction, the ideologies have very different outlooks on society:
From what I've derived from Mutualism, the idea is that the price of goods and services are equal to the time and effort necessary to produce or perform the good/service. Costs 50 dollars to make something, you sell it for 50 dollars.
Anarcho-capitalist society encourages competition between providers of goods and services. In such a system, prices will not be equal and differ based on quality, the reputation of the provider/producer, and numerous other factors. Additionally, capitalism encourages profit, and many businesses want to produce their products as cheaply as possible while selling it for as much as they can within the limits of the market (too expensive, and nobody buys).
There's more differences as well, such as private property vs. personal property.
How do you think that the two groups interact? What are your thoughts on the matter?
I can Mutualists as the more "predictable" faction. They're predictable in that you know what you get. Anarcho-capitalists are competing all the time, and sometimes the price (reputation-wise) of goods and services may wildly change as competitors try to undersell each other or jack up prices if they corner the market. The Mutualists are consistent in the sense that the cost of the service/product is always the same.
Mutualists may be less stingy in regards to property, except that they have tighter restrictions on who can use it (you can't just buy land and let it sit there of use to nobody). Despite preferring the free market, many Mutualists are also critical of capitalism (specifically the practices of separating labor from ownership, the relationship between landlord/tenants and merchants/producers). I can see Anarcho-capitalists and Mutualists bitterly arguing over terraforming projects and whether or not the new ecological zones should be open to all willing to labor or restricted to property owners.
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"Liberty means responsibility. That is why most men dread it."
~George Bernard Shaw, 1856-1950