15.1 The Social Planner's Problem
Any economic model of equilibrium, such as the partial equilibrium model we analyzed in the last chapter, makes some assumptions about what motivates agents to engage in some economic behavior; posits an economic environment in which they interact; and finally, posits an equilibrium outcome to which the system converges.
When evaluating such a model, we may ask ourselves whether the outcome it describes represents a “good” outcome. There are plenty of economic models with “bad” outcomes; for example, one famous game theoretic model is called the “Prisoners’ Dilemma,” and illustrates that in certain circumstances, agents maximizing their own individual payoffs actually do worse than if they could coordinate with one another.
To answer the question of whether the outcome of a model is “good,” we often invoke the thought experiment of a disinterested, benevolent “social planner.” By disinterested we mean that this is someone who is not one of the agents in the model, and so has no personal stake in the outcome. (This is different from, say, an auctioneer who is designing a system to maximize their own revenue.) By benevolent we mean that this “social planner” is seeking to maximize the total social welfare in an economy.
How would such a “social planner” answer the fundamental economic questions of how much of a good to produce, how to produce it, and who should consume it? We might posit some criteria:
- We want the quantity of the good to produce, $Q^*$, to maximize the total “welfare” — that is, the total benefit to people minus the total cost of production.
- We want to produce this quantity $Q^*$ in the lowest-cost way possible.
- We want to distribute this quantity $Q^*$ to the people who value it the most.
Let’s approach the first question first, by analyzing a simple model in which there is just one consumer and one firm. We’ll then move on to a model of multiple consumers and multiple firms to address the other two questions.
Let’s start by analyzing the last point: how much to produce to maximize total surplus.