A Dynamic Model of Resource Capture in Familial Dependency Relations

Resources acquired outside a family relationship can enlarge a recipient's opportunities while also becoming available to an actor who exercises control over the recipient. This paper develops a conditional account of the resulting interaction. A resource budget distinguishes retained resources from captured transfers, and a dynamic model allows invested transfers to maintain control and influence subsequent capture. Under a saturating capture technology, the model identifies a threshold above which positive control persists. On that branch, an increase in external resources can reduce stationary independent capacity even while the recipient retains a positive resource flow. The result depends on specified conversion and suppression mechanisms. A fixed-capture counterexample and an extension with background control clarify its limits. A separate increasing-returns specification establishes sufficient conditions for multiple stable equilibria and a threshold separating their basins. The analysis distinguishes these mathematical results from hypotheses about the emergence of familial control. It situates the framework within household economics, psychological control, economic abuse, and kinship sharing; develops observable implications; and separates developmental dependency from restrictions on agency. The contribution is a tractable account of resource-financed control and its evidential requirements. The model provides neither a prevalence estimate nor a general claim that external assistance reduces autonomy.