The second branch of general equilibrium analysis deals with conceptual—some might even say philosophical—questions of how well markets allocate goods. That is, it asks whether market outcomes in general equilibrium are “desirable.” Defining “desirable” can be a sticky issue, however, so economists are fairly specific about the standards for well-functioning markets. In this section, we talk about what these standards are and whether markets can meet them.

One way economists often try to think about the overall desirability of market outcomes is to use a social welfare function, a mathematical function that combines the utility levels of the individuals in a society to obtain a single overall measure of an economy’s performance. That way, various market outcomes (i.e., distributions of utilities across all individuals in the economy) can be compared to one another. If one outcome has a higher value than another according to the social welfare function, the higher-valued outcome is considered more desirable.

The ranking of various market outcomes depends on the particular form of the social welfare function one chooses to use to evaluate outcomes in the first place. For example, a function that explicitly penalizes inequalities in individuals’ utility levels will rank certain market outcomes very differently than a function that ranks outcomes based only on average utility levels. Choosing a social welfare function to evaluate outcomes is therefore a bit of a philosophical exercise; it depends on one’s notion of what sort of outcomes are desirable in the first place. Thus, social welfare functions can be thought of as ways to rank economic outcomes once one has already decided what features of the outcomes (such as the amount of inequality or whether particular groups of individuals have systematically higher or lower utilities) are desirable. Social welfare functions are much less useful for deciding whether inequality is inherently bad, and how bad it is if so. The functions embody these views, but they don’t reveal their accuracy or lack thereof.

Given the subjectivity of social welfare function choice, economists have not decided on any hard-and-fast rules about the particular form a social welfare function should take. However, some versions are more commonly used than others because they’re easy to work with or because they succinctly capture elements of various philosophies about what is desirable in terms of the distribution of utilities across individuals.

The Utilitarian Social Welfare Function One common type of social welfare function adds together the utility levels u of everyone in the economy, with equal weight given to each person:

W = u₁ + u₂ + . . . + u_N

where W is the value of the social welfare function, the grand total of all utility in a society. The subscripts denote individuals; there are a total of N people in this economy. This utilitarian social welfare function says that society’s welfare is the sum total of every individual’s welfare. That seems easy enough. But, note that a utilitarian society will be one with relatively little concern about how equally utility is distributed among individuals. Raising anyone’s utility a given amount has the same total welfare effect for society regardless of how well off that person already was. In fact, a utilitarian function would say there’s no harm in driving any particular individual’s utility down to zero as long as someone else experiences an equal-sized utility gain, even if that person is already better off than everyone else in the economy.

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The Rawlsian and Egalitarian Social Welfare Functions The utilitarian social welfare function’s relative indifference to utility inequality has led people to propose the use of other social welfare functions.

One proposed function assumes that social welfare is determined literally by how the worst-off member of society does. The Rawlsian social welfare function is named for political philosopher John Rawls, who argued on social justice grounds that a society should strive to maximize the utility of its worst-off member. In mathematical terms, the Rawlsian social welfare function says that

W = min[u₁, u₂, . . . , u_N]

In words, society’s welfare W is the minimum of all the utilities in society. Only the utility of the least well-off individual matters; the utility levels of all other individuals in the society do not matter at all. The Rawlsian utility function is an extreme example of an egalitarian welfare function. In an ideal egalitarian society, every individual is equally well off, and any departures from total equality cannot increase social welfare.

The Drawbacks of Social Welfare Functions Although social welfare functions can be useful, they can be difficult to use as practical standards for evaluating market outcomes, especially because different functions may give such varied answers about what makes for desirable outcomes. For example, think about how differently a utilitarian society and an egalitarian society would think about taxing the rich to give to the poor. As we mentioned above, how one would evaluate the result of such policies is going to depend on subjective judgments about how worthwhile inequality reductions are in the first place.

Furthermore, even if everyone agreed on the type of social welfare function to use, combining individuals’ utility levels mathematically—which is the point of a social welfare function—is conceptually dicey, as we discussed in Chapter 4. A social welfare function can give different total welfare values to the same sets of consumption bundles, depending on the individual utility functions one chooses. This makes it even more difficult to compare economic outcomes.

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The difficulties with trying to use social welfare functions to evaluate how well markets are working have led economists to use a different criterion that everyone can understand and agree on: Pareto efficiency.

Pareto efficiency holds in an economy if no one can be made better off without making someone else worse off. As an example, say that in one small economy, Larry has a laptop, Moe has a TV, and Curly has a used Buick Enclave. If there is no way to reshuffle the goods among the three guys that makes no one worse off and at least one person better off, then the economy is Pareto-efficient. If a reshuffling of the goods could make one or more better off without making anyone worse off, then the economy isn’t Pareto-efficient. So, for example, if Larry would happily swap his laptop for Curly’s Buick and Curly would also like to make this swap, then the initial allocation of goods wasn’t Pareto-efficient. These sorts of trades are not possible in a Pareto-efficient allocation because one person will not be willing to participate. Under Pareto efficiency, someone would be made worse off by any rearrangement of goods, whether it’s a simple two-person, two-good swap, or something a lot more complicated.7

What this means for general equilibrium is that a Pareto-efficient economy should not have a lot of something for nothing—what economists call “free lunches” or “$20 bills lying on the sidewalk” (figuratively or literally). In this way, Pareto efficiency is a fairly intuitive concept of efficiency.

Another important feature of Pareto efficiency is that it doesn’t have to be fair or equitable, or to maximize some social welfare function. Pareto-efficient allocations can exist even with large differences in individuals’ utility levels. In fact, as long as marginal utilities are positive, giving one person everything in the economy and everyone else nothing is Pareto-efficient! Any rearrangement of goods from this allocation requires taking something away from the person with everything. Because marginal utilities are positive, this reallocation makes that person worse off, violating the Pareto efficiency condition.

That’s why it is important to remember that Pareto efficiency is a weak standard to hold markets to. We might find a Pareto-efficient outcome (sometimes called a Pareto equilibrium) that is unappealing from the perspective of equality. Still, it is a useful benchmark, because we are interested in knowing whether voluntary trade in markets can somehow eliminate any free lunches that might exist in an initial distribution of resources.

Now that we’ve defined Pareto efficiency as a standard to measure market outcomes, let’s see how market outcomes compare to Pareto-efficient outcomes. This is an extremely important question to economists: Markets are the most common way for the world to allocate billions of goods to billions of people. We would like to know, for lack of a better phrase, whether markets are any good at it. But to answer that question, we need to compare market equilibria to standards such as Pareto efficiency.

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We start by giving away the ending: Under a certain set of assumptions about the market environment, market outcomes are Pareto-efficient. Economists have speculated about this possibility for as long as there have been economists. Adam Smith’s famous notion of an invisible hand (the unseen force in markets that tends to create socially beneficial results even though market participants act only in their individual best interests) essentially made the point that market outcomes can be efficient. It wasn’t until the mid-twentieth century, however, that the Pareto efficiency result was proven mathematically. (The highly technical proof is beyond the scope of this chapter and won the two people who proved the result—Ken Arrow and Gerard Debreu—the Nobel Prize in Economics. We will cover the economic intuition behind it in a moment.)

The market efficiency result is a big reason why economists tend to look favorably on markets: Markets have a natural tendency to arrive at efficient outcomes under a certain set of assumptions. (You are already familiar with some of these assumptions, such as perfect competition and price-taking behavior among suppliers and consumers.) The chances that all of these assumptions actually hold in any real-world market are small, however, so real markets may not be completely Pareto-efficient.

If real markets aren’t completely efficient, why do economists still seem to favor market solutions, probably much more often than the general public? It’s because the market efficiency proof shows exactly what must hold for markets to be efficient. That is, whatever makes markets work or fail isn’t mysterious. We know what things gum up the works and often this suggests what kinds of policies would remove the gum.

Therefore, economists of most political orientations tend to think that markets have the potential to create the greatest amount of benefits for the greatest number of people. What they are more likely to disagree on is how much intervention (such as government actions to reduce market power) is necessary to make markets run smoothly.

Now it’s time to look at the details of what must be true if markets are operating efficiently. Three basic conditions must all hold for an efficient economy:

We study each of these three conditions separately, in detail, below, and then show how they are interrelated in an efficient general equilibrium.

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