Controllability of a Nonholonomic Macroeconomic System

This paper studies optimal control problems and sub‐Riemannian geometry on a nonholonomic macroeconomic system. The main results show that a nonholonomic macroeconomic system is controllable either by trajectories of a single‐time driftless control system (single‐time bang–bang controls), or by nonholonomic geodesics or by sheets of a two‐time driftless control system (two‐time bang–bang controls). They are strongly connected to the possibility of describing a nonholonomic macroeconomic system via a Gibbs–Pfaff equation or by four associated vector fields, based on a contact structure of the state space and our isomorphism between thermodynamics and macroeconomics that praises three laws of a nonholonomic macroeconomic system.