Markets would be abolished in anarchist society by simply not having them. Markets are a top down mechanism of logistical distribution. They must be built to exist in practice. Anarchist societies can abolish markets by simply not practicing market logic. They are not a natural phenomenon despite what libertarian capitalist brains say.

If you actually read the literature that calls markets “natural” or posits some kind of natural tendency for them to form, it reads very much like the idea of the WAAAAGH in WH40K Orks. Orks have a magical power which is essentially “The Secret”, by thinking something works a specific way Orks through their communal latent psychic abilities change the world to be that way. The more Orks, and the more unified and stronger their belief, the more true something is in reality around them. They are a belief society.

Markets are sold in this way in capitalist states. The idea is even if the market is not a physical place or a device, demand exists in the minds of people. That’s a really fucking silly jump in logic from “wanting things” to “commodity form” (the essence of what a market is, a widget with supply and demand that follows capitalist economic rules). Just because people want things doesn’t mean the commodity form is “natural” or “inevitable”.

Anarchist economics is about building resilient voluntary communal economic cells and trading between them based on needs. This is difficult for a couple of reasons:

1. It is “inefficient” by classic economic understandings, but that is the essential trade off of economics something can be resilient or it can be efficient but it cannot actually be both because economic resiliency is the idea that over production of certain resources is key to maintaining economic function due to disruptions in other areas of the economy.

2. Voluntarism essentially means you cannot use the power of the state to take/enforce unfair agreements (or even mild compromises) which are essential to running large markets. If a bar of Lindt chocolate sells for $20 in the states, the farmer who farms the cocoa would never voluntarily agree to only $0.25 of it’s price, they simply do because they have no other choice. This is difficult in a modern world because it essentially undercuts the treatlerism of modern life / advanced economies. Essentially you can’t have all the treats your heart desires by design unless you can repay treats in kind.

3. Trade can be built on several different ways inside economic units and between them, one commune can be a gift economy, another could simply barter, a third can use Bakunin bucks (labor vouchers), some would use actual money. Anarchists have a hard time integrating into the global trade system historically simply because they do not want to issue currency, even if they end up doing it. Maknovischinia used regional currencies and eventually had to mint it’s own for use in trade with non-anarchist countries.

4. Anarchist horrizontalism is hard, and slow. It requires time to convince people, time to develop capacity, time to develop trust and relations. The main difference between communists and anarchists in this regard is that communists have traditionally thought they can bring to heel the social inventions of the nation-state, market, industrialization, and wage-labor relations to compete with capitalism, while anarchists have typically rejected these forms unless they could be recreated in a voluntary way. Communists essentially think they can use these tools to build out a prosperous society and then in software terms “pay off the tech debt”, but historically that has yet to be proven. Anarchists build slow and mindfully in comparison because for anarchists typically the anarchist social relation is more important in the long run than material conditions, since the social relation is actually what prevents exploitation (both Marxist and non-Marxist sense).

5. Because of #3 and #4 this has knock on effects on society especially in Western Nations that people are simply ingrained in. Supermarkets and global cuisine would cease to exist, seasonal and regional cuisine would be necessary to take their place. Likewise equipment would be difficult to procure until it can be made locally. In order to develop these industrial capacities communities may opt to purchase these goods through communal savings programs.

6. Until there are anarchist communities that have not just the anarchist economic orientation but the wealth to trade on the global market, it will be tough to develop without succumbing to the temptation of using coercive social/economic forms. Some communities may be luckier than others in what they can expropriate / scavenge that already exists. The reality is that it simply depends on the goal of the communities. If it’s buying iPads being a poorer community is hard mode, but if it’s being fair to one another being a poorer community is actually easier because you have more time to build the social relations and cultural attitudes to prevent becoming richer from adversely affecting your community through individuals hoarding, jealousy, etc. Communities with abundant resources regardless of goals are hard mode because teaching people anarchist social relations and developing an anarchist culture would be extremely difficult if the people you’re working with are Western treatlers.

A good example of Anarchist societies working with global capital markets is the Zapatistas coffee/durable goods trade which can be found at https://schoolsforchiapas.org/ in their “Solidarity Store” which is pay what you want but with a price floor. You can learn more about Zapatista Coffee Coops here: https://en.wikipedia.org/wiki/Zapatista_coffee_cooperatives. They’ve been incredibly successful at their mission despite wrecking from the Mexican government over taxes which essentially closed down Mut-vitz, but Mut-vitz proved the model was a successful way to create an international anarchist trade enterprise.