I am a bit confused about the term “Ramsey problem”. When I learned economic growth theory, Ramsey problem is to solve a centralized equilibrium in a model without firms and households. The Ramsey planner allocates consumption-saving and production problems at the same time.
When I learned monetary economics, Ramsey problem describes the Ramsey planner that chooses endogenous variables subjects to the decentralized equilibrium conditions.
I want to know if there is any precise terminology to separate these two concepts? Is there any paper discuss the difference between the two models?