On some properties of the adjoint variable in the relations of the Pontryagin maximum principle for optimal economic growth problems

For a class of infinite horizon optimal control problems that appear in studies on economic growth processes, the properties of the adjoint variable in the relations of the Pontryagin maximum principle defined by a formula similar to the Cauchy formula for the solutions to linear differential systems are studied. It is shown that, under a dominating discount condition, the adjoint variable defined in this way satisfies both the core relations of the maximum principle (the adjoint system and the maximum condition) in the normal form and the additional stationarity condition for the Hamiltonian. In addition, a new economic interpretation of the adjoint variable based on this formula is considered.