Optimal digital product maintenance with a continuous revenue stream

We use a control framework to analyze the profit maximization problem of digital vendors that capture market share by focusing effort on post-launch product maintenance effort. Effort influences user perception of the product and drives the revenue stream via user adoption. We show necessary and sufficient conditions for optimality, and that perceived quality declines over a product's life cycle. This corresponds with Lehman's 7th law of software evolution. Last, we illustrate control paths under possible market conditions, assuming linearized functions.