Why care about Pareto Efficiency/Improvement?

I recently saw this Bloomberg article which argued against deficits. The article pointed to a set of studies involving macroeconomic models where the authors argued that deficits are effectively Ponzi schemes. There is a lot discussed in these studies, however I’m going to focus on something narrow but much more prominent in the discourse. I will be discussing the usage of Pareto optimality/efficiency/improvement.

[As I write this, I’ve just read another article in the New York Times by Gregory Mankiw. He similarly comes out against Biden’s $3.5 trillion spending plan and mentions the “equality and efficiency tradeoff”. Pareto efficiency is also being used here.]

Figure 1

Pareto optimality (also known as Pareto efficiency) arises in situations involving multiple objectives. Pareto optimality is achieved when one of the objectives cannot be improved without another objective suffering. This is usually introduced in Econ 101 in the form of the “Production–possibility frontier”, as an example of the limitations due to scarcity. An economy has a finite amount of resources and thus cannot produce infinite things. Thus there will be a trade-off between producing quantities of one item and producing quantities of another. The dots on the figure 1 shows example amounts of items an economy can produce. The red dots are Pareto optimal; there are no dots both above and to the right of them (i.e. at a given red dot, there’s no other dot to chose from which will increase the quantity of one of the items without reducing the quantity of another item.)

Pareto optimality also comes up famously in the Fundamental Theorems of Welfare Economics. Instead of efficiency in terms of quantities of items, now the objectives being optimized are the utility(happiness) of people within the economy. The theorems show that market economies will reach equilibriums at Pareto optimal distributions of resources. At these Pareto optimal points the same logic as above applies; you cannot increase the happiness of one individual without decreasing the happiness of another. Thus by showing that the free market will achieve Pareto optimal distributions, the theorems seem to provide a strong foundation for free market fundamentalism and are established as representations of Adam Smith’s Invisible Hand view of the economy. It matches people’s natural intuitions about the economy; if everybody is free to choose, then people will only make choices that will best benefit them. The economy is then the aggregation of all these best choices. When people informally talk about the economy is about “trade-offs”, this is what they are referring to.

The Bloomberg article noted above follows in the same tradition(1). It mentions “Pareto improvement”; a type of improvement that will increase the happiness of one person without reducing the happiness of at least one other. This means that there are no possible Pareto improvements if you’ve already achieved Pareto optimality. The authors mention the “test of Pareto improvement”; any policy must be shown to be Pareto improving in order to be desirable.

It is with this test that the authors argue against deficit spending, among other things.

I’m going to clarify a few terms. As a non-economist, my familiarity with Pareto optimality comes from just general multi-objective optimization. So both the examples above, trade-offs between the production of items (figure 1) and trade-offs between people’s utility (Fundamental Theorems of Welfare) would both be considered “Pareto efficient/optimal”.

Economists on the other hand will differentiate between those two cases:

1. When considering the production of items, it is called “productive efficiency”.
2. When considering people’s utility it is called “Pareto efficiency”.

Obviously in the abstract these two are the same; the only thing you’re changing is what’s being optimized. Nevertheless I will follow the economists’ usage going forward and will only use Pareto efficiency/optimality when referring to the multi-optimization of people’s utility.

The distinction between these two becomes important when economists discuss the efficiency of the market.

In Mankiw’s NYT piece, he references a book by economist Arthur Okun: “Equality and Efficiency: The Big Tradeoff”. Once again employing the idea of trade-offs. This time as a bit of a meta-trade-off. Instead of possible trades between different Pareto optimal distributions of resources, Okun is discussing a trade-off between market efficiency and government interventions towards equality. (2)

This seems like a reasonable frame, after all the Fundamental Theorems of Welfare tell us that the free market will be Pareto efficient. Surely interventions will be non-efficient?

The rest of the blog will be exploring the different ways in which this frame is wrong. Here’s the outline for the remainder of the blog:

1. Market capitalism does not result in productive efficiency, only Pareto (utility)-efficiency.
2. You should not care about Pareto (utility)-efficiency.
3. Efficiency is not at odds with equality.

1. Market capitalism does not result in productive efficiency, only Pareto efficiency.

Mankiw’s NYT article use the well-worn pie metaphor when talking about the efficiency-equality trade-off. He states:

According to Mr. Okun, policymakers want to maximize the economic pie while slicing it equally. But these goals often conflict. As policymakers attempt to rectify the market’s outcome by equalizing the slices, the pie tends to shrink.

The implication here is that the pie represents the items produced and distributed by the economy. Efficiency means the pie is as big as it can be, but the equality-efficiency trade-off means that fairer distributions of the pie will result in a smaller pie. That is, a fairer distributions of things means less things to go around overall.

Okun makes it seem as if it were mathematically unavoidable, and goes on to say that even minor improvements towards equality will come at too large a cost of efficiency.

But precisely because it would operate within the constraints of preserving these rights, the collectivized system would, in my judgment, achieve only a small improvement in equality at the expense of a significant worsening of efficiency. (p. 60 of Equality and Efficiency)

This is where the pie metaphor becomes a bit deceptive. It implies the maximization of things produced; i.e. productive efficiency. But the fundamental theorems of welfare do not guarantee anything about productive efficiency in market economies. Sure, productive efficiency and Pareto (utility)-efficiency are related; people get more utility(happiness) if there’s more things to go around. But the connection is not 1-to-1; historically there have been many times when market mechanisms have led to unproductive economies. I will return to this point in part 3 (“Efficiency is not at odds with equality”).

You might object and say that Okun and Mankiw’s metaphorical pie doesn’t refer production, it refers to utility. So the size of the pie roughly corresponds to the “size” of people’s happiness. If that’s the case, then we need to take a closer look at what it means to be Pareto efficient.

2. You should not care about Pareto efficiency.

Now that we’ve shown that the market does not guarantee productive efficiency, let’s take a look at Pareto efficiency, which is achieved by the market. Since Pareto (utility)-efficiency is optimizing utility, surely it’s the correct objective focus on. This is true, but Pareto is different from other forms of efficiency that you may be used to. It is not just “one good number”, as you would have for the efficiency of a vehicle’s fuel consumption. It is not a “size” of a pie.

As shown in figure 1 above, Pareto efficient refers to a large set of possibilities. The question becomes how disparate can these possibilities look?

I think there is a good way to illustrate the uselessness of Pareto optimality. It is somewhat topical as Kanye is in the news again with his release of Donda.

A few years back Kanye made headlines when he went to the TMZ offices and went on an incoherent rant, and said slavery was a choice:

When you hear about slavery for 400 years … For 400 years? That sounds like a choice.

This garnered some well earned backlash, though I think there was a fixation on the usage of “choice”. Some commenters argued that slavery didn’t involve choice since attempts to flee slavery would lead to death.

I think this tendency comes from an idealized view of choice, one emphasized by free market fundamentalism and neoliberalism, where any and all choices are uncoerced.

I think it is more useful to understand that “choice” is not inherently good, and choices can be coerced; it is then a question of degree. Slavery then becomes the most extreme example of coerced choice and once that’s covered, we can move on to less extreme examples.

Back to the Kanye quote and why I think the slavery example might be useful: because slave states are Pareto optimal.

We can check this fairly easily by just considering a mini slave economy involving a slave and slave owner. Consider the options available to the slave: they could continue being a slave, or they could attempt to flee and be killed. For the slave owner: they keep the slave or set the slave free and lose out on free labor. Clearly the favored option for the slave is continue to be alive as a slave, and for the slave owner to continue to own slaves. There is no action one or both of them can make which will benefit one without detriment to the other.

Now lets consider the policy of abolishing slavery. This will increase the happiness for the slave. But, since the slave owner loses out on free labor, their happiness/utility decreases. Thus the abolishment of slavery is not Pareto Improving.

This is the heart of Pareto efficiency. To imply that economic efficiency means “one good number”, as economists do, is being willfully misleading. Economists are imagining a world without coercion. Pareto optimums are just the result of choice and exchange. It is important to understand what these choices look like.

The abolishment of slavery did not eradicate exploitation. Freed slaves still needed food and shelter to survive. So their choice became to earn a wage from an employer, or die.

There is a quote from Frederick Douglass, abolitionist and former slave, that is insightful:

experience demonstrates that there may be a slavery of wages only a little less galling and crushing in its effects than chattel slavery, and that this slavery of wages must go down with the other

Slavery gave way to wage slavery. Though you could choose whether or not to take a job, your choice was coerced much as it was during chattel slavery. Absolute dependence on the wage to survive meant the economy was rife with exploitation. The Industrial Revolution was well underway, and the inhumane labor conditions eventually necessitated many of the labor protections we have today.

Economists then tend to excoriate the Gilded Age at the end of the 19th century, but then somewhere between then and now we’re supposed to believe that exploitation has disappeared and that the free market will somehow result in a big pie instead of behaving more like our slavery example.

3. Efficiency is not at odds with equality.

Now that we’ve taken a good look at Pareto efficiency we can take apart Okun and Mankiw’s argument. Recall that Okun explicitly said that government policies targeting equality will invariably lead to greater reductions in efficiency. This kind of statement becomes nonsensical once you understand Pareto optimality.

In fact we have historical examples where efficiency and equality clearly weren’t being traded-off.

Slavery may be Pareto efficient, but I doubt any modern economist would argue that it’s desirable. Slave states contain few of the elements economists would find desirable in an economy: freedom (non-coercion), competition, etc. The Pareto optimums achieved by slavery involve slave owners benefiting most through the ownership of slaves. They would work slaves to the bone, but otherwise the drivers of a productive economy (such as competition) factored in very little compared benefits of ownership.

The same faults are present in the modern economy, albeit to a lesser degree. When workers are dependent on wages to survive with little alternative, then you’re going to get exploitation. Employers then will benefit from having money when people need it, and this may sometimes be in conflict with the drivers of a productive economy.

This is the heart of Keynesian economics which emphasized government spending. Market economies may exhibit characteristics just like the feudal/slave state example described above, they will achieve Pareto optimums which are clearly undesirable. Laborers are dependent on the spending of the capitalists. If the capitalists decide not to spend (e.g. it’s more profitable to be a landlord than to engage productive capital), then the economy will just not produce much. That’s why it’s more useful to have the public sector involved in the economy in these cases.

Most famously the United States recovered from the Great Depression through Franklin D Roosevelt’s New Deal policies. Though they preceded Keynes, these policies were specifically designed to uplift the poor and also involved much government intervention; regulations to the financial sector as well the creation of public works projects. Efficiency and equality are clearly not being traded off.

Economists objected to the New Deal then, just as they object to government spending now. Mankiw’s NYT piece was literally 4 days ago. The Bloomberg piece arguing against deficit spending (on the grounds that it’s not Pareto improving) was 2 months ago. Countless others have been published since the beginning of the Covid pandemic.

It might be true that massive government spending does end up doing more harm than good, but hopefully my blog was useful in clarifying why justifying these arguments with Pareto efficiency/improvement is pointless.

Footnotes:

1— Seems there’s also a few other measures used in economics which are derived from Pareto optimality, e.g. dynamic efficiency.

2— I should note that Okun doesn’t specifically reference the fundamental theorems of welfare economics. Rather he points to Adam Smith’s “invisible hand” (Ch. 2 — “The Case for the Market”, p. 51):

THE RECORD OF EFFICIENCY

The case for the efficiency of capitalism rests on the theory of the “invisible hand,” which Adam Smith first set forth two centuries ago.

It’s understandable that he wouldn’t reference the fundamental welfare theorems in a non-technical book. The fundamental theorems are probably as close as you’re going to get to a mathematical representation of the “invisible hand”, but there is always the possibility that Smith and Okun are referring to some other (non-Pareto) form of efficiency. If they are, it has not been formally theoretically established or widely accepted.