Just in case I ever decide to come back to the notion I figured I'd list a bit of a grab bag of the situations that I had in mind for my focus on transactions.
The first is the long run importance of powerful commercial groups in controlling distribution channels for long distance trade. This goes back to the middle ages and the fair system etc. and the importance of a few key merchants who had access to particular goods or finances. These merchants seemed to have an outsize impact on which fairs were successful and on how business was conducted.
The second was the importance of control of actual mediums of exchange or capital accumulation. Mostly the importance of changes from early exchange systems (which could be very complex), to money, the introduction of bank notes, the importance of relationships between banking groups (and the ability to choose to introduce someone into these circles) before the state took over the role of banker, and various attempts at concentrating early capital, such as stock systems in Genoa or Venice or shared space on ships in Southeast Asia.
Another aspect is the off noticed tendency for certain sectors of the economy to have effects on the overall system that are far larger than their size. This has been observed regarding the spice trade, the textile trade, steam engines and rail roads, and a few other sectors across history. These fields have been pioneering ones using new forms of social organization and contract to get the resources they need (sometimes this takes place with labor, sometimes with unusually large fixed capital, sometimes with new corporate organization).
Where this differs from economic history accounts is that I am downplaying the absolute size and instead focusing on which agents have the power to set the "menu" (for lack of a better word) of choices available to others. This can be early merchants who formed fairly exclusive cliques who would trade amongst themselves balancing accounts at various fairs, the great mercantile companies which introduced new trading practices in Africa and Asia, early industrialists who were able to introduce new labor contracts to fill their factories, tensions between wage labor in agriculture and other forms of tenancy, states which could favor or disfavor various forms of economic activity through taxation and other policies, modern issues involving intellectual property rights or digital infrastructure, etc.
This is all of course to some extent covered within other perspectives. What I'm mostly suggesting is that the power to shape social outcomes lies with whoever sets the menu. Who gets to decide if family businesses will dominate or if more impersonal corporate structures (and what rules will govern them) will proliferate? Can I trade my labor directly for goods or services or am I only allowed to use money? Can I trade my raise for a constant salary with less hours? Is production centralized as a matter of course, or is household production a possibility? What are the standard contracts involving loans? Simple things, like bundling of television channels so that I have no option to subscribe to Showtime to view the shows I want to watch online without owning a TV.
In this perspective, power lies with whoever makes these decisions (even if not consciously, this is a matter of socioeconomic change and small changes can lead to large effects and path dependency over time). It is not necessarily the government, nor is it necessarily those that control wealth. Rather it is whoever is able to influence how contracts are constructed or what the standard methods of exchange are. Power can lie with a corporation if it is able to control the set of contracts available* or it can lie with the government if the state gets a say over contracts. Power isn't necessarily purely a function of wealth, a marginal example would be subsistence populations with only limited contact with the market, they will frequently work for some wages in addition to their subsistence production but ultimately can impose their schedules on producers since production for the market is secondary. Wealthy and profitable business interests with high levels of fixed cost and a reliance on a skilled labor force may loom large economically but be so dependent on current conditions that they have little scope to change any existing relationships (on the other hand, if the society lets wealth get translated into the political process this business will gain the ability to exercise power). Alternately, a not so profitable industry with low fixed capital costs but many low wage, low skill jobs may have outsize power because it can shape behavior by making a credible threat to move, it's power to upset existing means of trading labor grant it power out of relation to its economic size. Alternately, a high tech sector may have outsize socioeconomic impact by being able to pioneer new forms of conducting transactions (whether by moving things online or by allowing for a more decentralized labor system that could bring back household production).
Anyway, this is a grab bag of things for me to come back to later if I decide there's something to this that isn't adequately covered elsewhere. I think there are some real gaps in economic development, especially the outsize impact on society of a small handful of sectors at various points in history or small shifts in government policy, but there may be good existing perspectives on this I'm as yet unaware of or this perspective may be too difficult to problematize to be truly effective. After this post I intend to set it aside for some time and get back to reviewing the deficit commission proposals and moving on to social security.
*This is most obvious right now with intellectual property rights. Patent holders can make innovation more difficult, or ease it. Various types of content holders can control the means of distribution, despite consumer demand, through their market clout (I have the record companies, film distributers, publishers, and such in mind here, while other options exist you need to go through them to reach a mass audience. Admittedly, there is a dimension of state support through regulatory capture but some of this is simply due to the nature of the industry).
[Update: The more I think about this, the more I think this is just a slightly different way of defining power that avoids the common confusion of too much focus on state power and instead defines it as being distributed throughout multiple levels of society. There are other conceptions of power that already do this so I'm unsure I'm adding anything.]