The concept of social welfare is hardly "social" at all. Once again the market takes center stage; and we are left wondering whether any social institutions could possibly exist in the bizarre world that Mankiw is painting for his readers. Yes, of course the model he sets up is meant to idealize in order to get to the core issues. But as we will see, Mankiw discusses the model in a way that leaves the student without any methodological framework for actually understanding those tools, except at a superficially wrong level.
We arrive at Chapter 7.
Behind this question is the following general idea: suppose we were to find some way of measuring the maximum amount of social welfare derived from an individual's consumption of a particular commodity. In equilibrium, the commodity will be sold at a stable price and with a stable quantity. Now, we know that when you consume more of a particular good, the additional satisfaction you get from consuming it diminishes. Thus, if you buy 5 apples at $1, that first apple was worth a lot to you, the second not so much, and so on. Mankiw wants to find some way of measuring exactly how much that first apple was worth to you, plus how much that second apple was worth to you, ... and so on. We know that the last apple, the 5th, is worth $1 to you because we assumed that to be the equilibrium price: you consume apples up to the point where the benefits of an additional apple equal the cost (or price) of an additional apple. So, what is the sum of all the positive values in between?
That is the concept of consumer surplus, or "CS" as we will call it for the remainder of the post.
Question: That seems easy enough to understand. But how does "society" fit in here? We were told by you in a previous post that society has no actual agency in the market, that it's really all about market mechanisms. But now you're telling us that Mankiw wants to judge whether the price of the good is "just" according to society. How does that leap take place?
Answer: The key lies in a concept that is not developed in Mankiw's presentation, thereby leading to the confusion. The key to clearing up your confusion is in coming up with a definition of "social welfare". That is, we need to define social welfare in an economy in order to say that markets maximize "social welfare"! The point is simple, and yet extremely crucial, at the same time.
Question: That seems like a simple problem to solve, though. We can measure the CS of any one individual by figuring out how much that individual values each apple. We just survey him or her (theoretically speaking) and come up with a number in money terms. Why don't we just do that for all consumers in the economy? Since everything is measured in money terms, we have a common unit of measurement. So we just add everything up! What's wrong with that?
Answer: There's nothing wrong with that, by any objective standard of right or wrong. But I do think that you need to realize what implicitly you are doing when you propose that measure of social welfare.
Recall first something that was mentioned at the beginning of this chapter of Mankiw: i.e. that we are now in the normative world of economics: what ought to be. Therefore, in your answer to me, you are implicitly saying that society ought to define social welfare as the equally weighted sum of all individually-summed CS's. That's a very big task you've taken on there!
First of all, you're arguing that your weighting scheme: " 1*(CS of consumer A) + 1*(CS of consumer B) + 1*(CS of consumer ...) + 1*(CS) + ... = SW" is not arrived at democratically or socially in any sane sense of the term. Rather, you're positing that that weighting mechanism is just how you think we should add things up to determine welfare.
Second of all, it's pretty arbitrary, don't you think? We've said that each person is unique in society. For example, some people are poor, and constrained much more by their budgets than other people. So, might there be a social welfare function that captures this fact more accurately? Think of person A and B: person A spends 90% of her income on food and other necessities (like turkey) while person B spends only 40%. How will a change in the price of turkey affect these two people? Most likely, it will affect them wildly differently.
Therefore, when you say "Competitive markets maximize social welfare" You are really saying "competitive markets maximize social welfare according to my definition of social welfare". That's not very "social".
Question: OK, let's step back here. Where does this leave Mankiw's original claim about society? All you're telling me is that society is arbitrary, or biased against people who are income-constrained. But "society" can't please everyone. Doesn't this at least give us a baseline?
Answer: No. In a text that purports to be scientific and based on measurement before theory, Mankiw 100% fails. There is nothing "scientific" about choosing an arbitrary weighting scheme and defining it as social welfare. There is also nothing "social" about it, since we are assigning this weighting scheme insulated from democratic processes which modern market economies are supposed to be all about.
We leave, for a separate post, the treatment of the social planner by Mankiw. To give the brief bottom line: it is a wild ride that involves a lot of intellectual thrashing about in the dark, making little sense and certainly not "enlightening" the student to anything regarding market processes or the significance of public policy in the real world.