The Productivity Paradox of AI-Assisted Software Development: Empirical Evidence, Longitudinal Quality Degradation, and a Formal Cost-Benefit Model

Large language model (LLM)-based coding assistants have achieved adoption rates unprecedented in the history of developer tooling, with over 62% of professional developers reporting active use as of 2024. The dominant narrative frames these tools as straightforward productivity multipliers, citing controlled task completion speedups of 55.8% in the most widely cited study. This paper examines whether that narrative survives contact with longitudinal production evidence and formal mathematical analysis. We present a cost-benefit model that captures both the velocity gain and the quality degradation trajectory of AI-assisted development, deriving a formal break-even expression that predicts when accumulated technical debt erases productivity gains. We then conduct a structured secondary analysis of three published industry cases — a longitudinal code quality study spanning 153 million lines of production code, a large-scale security evaluation of 1,692 AI-generated programs, and enterprise adoption survey evidence from over 2,000 professional developers — to validate the model's predictions against real data. Across all three cases we identify a consistent pattern: measurable short-term velocity gains accompanied by elevated code churn, increased duplication, and reproducible security vulnerability classes specific to LLM-generated code. We term this the AI-assisted productivity paradox and propose a formal governance framework for responsible tool integration. Our central finding is that the productivity case for LLM coding assistants is real but incomplete — standard metrics capture the benefit on a timescale of days to weeks while costs accumulate over months, creating a systematic measurement blind spot in most current adoption programs.