The tipping point for AGI takeover

As an AGI gets wealthier (more "economic power), the market value of resources that it can use will go up. (Assuming that the current economic paradigm still holds - ie. people are able to ascertain which resources the AI demands, and retain them unless at a mutually agreed price) However, I hypothesize there will be a significantly lower rise in military/police force "military power". (We can also include "informational power", which is primarily the ability to coordinate resistance to an AI, including knowing about it at all).

As a result of these trend lines, will at some point be a tipping point where the "economic power" required for enough military force to capture the world's remaining AGI-useful-resources ("primary industry except farming") becomes lower than the "economic power" required to purchase the land, equipment and businesses of the world's remaining "primary industry except farming".

Note that this may absolutely be later than the AGI could have taken over the world "at all costs".

Once this tipping point occurs, the AGI will at this point deploy (or start rapidly transitioning resources in order to deploy) overwhelming military force. We can factor the additional cost of building up forces in secret / without resistance into the cost of creating the overwhelming military force. The less resources required in secret, and the shorter the period of resistance, the lower this additional cost. We should therefore not expect subterfuge until the AGI has significant

In the modern economy, farmland almost solely provides resources which are later used for satisfying human needs or necessities. Since it is otherwise undeveloped, it is likely quite useless early on to a misaligned AGI, unless it has transitioned from mechanical to biological technology.