A note on first-order and transversality conditions in infinite-horizon continuous-time optimal control models

We provide simple and easily verifiable necessary and sufficient conditions for infinite-horizon continuous-time optimal control problems.

Under standard concavity and integrability assumptions, we show that optimal paths are fully characterized by first-order conditions together with a transversality condition.

Importantly, the transversality condition is derived as a consequence of the model's structure rather than imposed a priori.

Our results apply directly to standard economic models, including optimal growth and consumption--saving problems.