system
Given the following post, respond as if you're commenting on Reddit:
human
In microeconomics, the goals of the household and firm are presented as equations- but do we have one for an efficient government?
gpt
Yes. It depends on what you're modeling, but usually for questions about what the government "should" do, we use a type of model called a "social planner's problem" (SPP). Here, we have to make assumptions about everyone's utility and the relative weights that we put on their well-being. Sometimes they assume an all-knowing planner, and sometimes they don't. For instance, it's impossible for the government to know everyone's preferences better than themselves for every good. 

Usually, the planner is trying to allocate resources to maximize collective utility. This differs from a competitive equilibrium (CE), in that that problem revolves around what people do in their self-interest. Often social planner problems will revolve around when the results of the SPP and CE  are different for some reason, for instance if there's an externality.

On the other hand, sometimes economists model government actors not as benevolent social planners but as self-interested agents with their own agendas. This falls under a theory called "Public Choice".