In which of the economic systems are centralized governments most likely to provide basic services to citizens?

The economic system in which a centralized government is most likely to provide basic services for its citizens is a command economy.  Of course, governments in many economies that are mainly market economies provide some basic services for their citizens.  However, this does not happen in a true market economy.  In a command economy, the government always provides basic services for its people.

There are three main kinds of economic systems.  The first is a traditional economic system.  In this system, the three fundamental economic questions (what to produce, how to produce it, for whom to produce it) are answered by tradition.  Societies with this sort of economic system often do not have a central government at all.  Even if they do, it does not provide basic services.  Instead, those services are provided in whatever way they have traditionally been provided.  The second type of economy is a market economy.  In this economy, the basic economic questions are answered by market forces—by the choices made by millions of consumers.  In this sort of a system, governments do not intervene in the economy.  Therefore, the government does not provide basic services.

Finally, there is the command economy.  In this economy, the government answers the three fundamental economic questions.  It decides what gets made and who gets those things.  Therefore, it typically produces basic services and delivers them to those of its citizens who it chooses.  Of the three economic systems, then, the command economy is the one in which a centralized government is most likely to provide basic services for its people.