Anthony Zhou

Psychology, Economics, Programming, or anything interesting.

The Invisible Hand Theorem

Do free markets work? Economic theory has some answers.

The early 20th century was a time of great ambition — perhaps hubris — in the design of modern societies. The triumphs of industrialism and modern science, coupled with the horrors of urban poverty and warfare, prompted many to wonder if society could be redesigned using rational principles. Hayek, Keynes, Schumpeter, and Marx set the terms for an ideological battleground that we inhabit to this day.

For a moment, Keynes and Marx seemed to be winning. In the 1950s, the Soviet Union and China were charging ahead with central planning, while the US was adopting a Keynesian approach characterized by big government spending. In response to Keynesianism, Hayek had started the Mount Pelerin society in 1947 to form an alternative based on laissez faire policies, which for most of the 50s and 60s remained on the edges of policy discourse. Seemingly out of nowhere, a young Mount Pelerin member named Milton Friedman burst onto the public scene arguing against the Keynesian orthodoxy of the 1960s. With the economic crisis of the early 1970s seen as a failure of Keynesian economics, the neoliberals seized the opportunity, and pushed their policies through politicians like Ronald Reagan and Margaret Thatcher.

Beginning with Reagan, free trade, privatization, and deregulation became the new orthodoxy. As Adam Smith puts it in The Wealth of Nations, for the selfish merchant, “by pursuing his own interest he frequently promotes that of the society more effectually than when he really intends to promote it.” This notion — of altruistic actions guided by selfish motives — became immortalized as the Invisible Hand.

Since 2008, the laissez-faire ethos of neoliberal economics has once again fallen out of fashion. So it bears asking, under what conditions does laissez-faire genuinely work?

It turns out that there is a theorem — the First Fundamental Theorem of Welfare Economics — that tells us exactly when we should expect laissez-faire policies to work. It states that, as long as certain assumptions hold, you cannot get more efficient than a free market by reallocating the resources in any other way. In other words, a free-market system will result in maximum economic output.

The First Fundamental Theorem of Welfare Economics

From Wikipedia:

In economic equilibrium, a set of complete markets, with complete information, and in perfect competition, will be Pareto optimal (in the sense that no further exchange would make one person better off without making another worse off).

Pareto optimality is defined by its efficiency: to think of efficiency simply, imagine the case of a zero-sum game, like splitting a pie. Assuming everyone wants as much pie as possible, any outcome that uses the whole pie is considered Pareto efficient. Even if there are three people involved, and two people split the pie between themselves — leaving nothing for the third person — the outcome is still Pareto efficient.

Designing an economy is a lot like splitting a pie for pie lovers. While you may not achieve an even split, you'd be silly not to use the whole pie. Thus, a system that guarantees Pareto optimality seems like a reasonable starting point for a welfare-maximizing economy.

There are three big (and well-recognized) cases where this theorem fails to apply. First, the theorem's assumptions — complete information, complete markets, and perfect competition — often do not apply in practice. Second, it makes no statements about equity, which many rightfully believe is an important aspect of society. Third, its goal of Pareto optimality doesn't reflect true welfare value, especially if people's preferences are in some way perverse.

1. Issues with the assumptions — AKA market failure

Market Power. Monopolies are one clear example of market power. For instance, when people complain about the sky-high prices of drugs, they are really complaining about the monopolistic state of the market, which allows pharmaceutical companies with patents to charge prices that far exceed the cost of production. A more subtle form of market power is monopsony, in which a single customer dominates a market. In The Walmart Effect, Charles Fishman documents how Wal-Mart partnered with Vlasic pickles to sell a gallon jar of pickles for just $2.97, which meant at most a cent or two of profit per jar. Vlasic's gallon jars were so popular that they cannibalized its other pickle sales, leaving the company with 25% less profits.

Incomplete Information. Imagine you are buying a used car. Used cars often have flaws you might not notice unless you drive them for a while. To account for such unknown issues, you probably expect a significant discount compared to a car that is guaranteed to work. On the other hand, someone with a working used car would not want to sell their car for such a low price, which is below the theoretical going rate for a functioning used car. Because used cars involve information that buyers lack access to, only sellers with secret issues would list their cars for your risk-adjusted and cheaper offer. This was the key insight of George Akerlof's paper "The Market for Lemons," and it explains why both used cars and health insurance have issues forming markets in a laissez-faire system.

Externalities. Many transactions affect third parties in a way that is not priced into the purchase. Consider air pollution — air pollution kills about 10 million people a year, which inflicts untold economic costs (say, on the order of $10 billion a year, assuming rather callously that each life is worth about $1000 a year in economic value). Almost none of this damage is priced in to the cost of driving a car or burning a wood stove, resulting in a clearly inefficient outcome. The same logic applies to depleting the stock of a fishery. In a free market, fishermen would overfish a fishery until the population utterly collapses — the market does not price in the cost of resource depletion.

Because of market power, incomplete information, and externalities, real economies often stray from the assumptions of the First Fundamental Theorem. Indeed, Friedman himself, in Capitalism and Freedom, gave many examples where the government might need to intervene, such as education and the environment. On the other hand, many industries — such as consumer goods — fit the assumptions quite well.

2. Pareto optimality isn't always equitable

To address the second concern — that Pareto optimal outcomes are not necessarily equitable, economists have also devised the Second Fundamental Theorem of Welfare Economics, which states that any Pareto-optimal (i.e. efficient) outcome can be achieved by some free market system with some lump-sum transfers of wealth.

In other words, you could technically make an equitable and efficient economy by redistributing money to give certain people or groups a head start. Lump sum transfers are better than after-the-fact taxation because they don't change the incentives of the people involved. In practice, however, it is often infeasible to determine the appropriate targets of such transfers because it requires a deep understanding of people's preferences. Still, subsidies and tax incentives are the government's current best approximations to the lump-sum transfers that the theorem demands.

3. Prices don't directly measure welfare

Pareto optimality is only a useful notion to the extent that people's willingness to pay a price reflects how "valuable" that good is to them. In some cases — say, cigarettes — people pay for a product that actively hurts them. More generally, as behavioral economics argues, people do not tend to behave rationally in selecting prices for goods (e.g. loss aversion, anchoring, framing, and so on).

With advertising dollars reaching all-time highs, we are forced to wonder how much consumer behavior reflects any sense of "true" preference, and how much it reflects people being persuaded into buying the hot new thing. In the extreme case, if every purchase we made was wholly decided by the advertising we consumed, then economic efficiency would not be tied to any socially beneficial outcomes, and would instead fuel a never-ending advertising arms race.

Another issue occurs when people have preferences that affect other people. Economist Amartya Sen proposed a paradox in which the principle of individual liberty contradicts the Pareto optimal outcome. His example involved two people named Prude and Lewd, and the decision of whether to allow a salacious book. Their preferences would be as follows:

| Lewd | Prude | | ------------ | ------------ | | Both read | No one reads | | Prude reads | Prude reads | | Lewd reads | No one reads | | No one reads | Lewd reads |

Notice how both Lewd and Prude consider "Prude reads" to be the second best option. For Lewd, he would rather force Prude to read then to read it himself. For Prude, he would prefer that he himself read it, lest Lewd read it and enjoy it.

Here, the Pareto-optimal outcome would be for Prude to read the book. However, the principle of individual liberty — in which individuals get to make decisions about their own lives — would observe simply that Prude places "No one reads" above "Prude reads" and Lewd places "Lewd reads" above "No one reads". Thus, they would give the book to Lewd, resulting in a Pareto-suboptimal outcome.

In general, Pareto-efficient outcomes (in this case, "Prude reads") might reflect the expression of perverse preferences. This is why it should illegal for someone to agree to get hit by a brick for money. In these cases, the government paternalistically decides that there shouldn't be a price for everything. Sometimes, issues like liberty, health, and human rights take precedence over economic efficiency.

Conclusion

Only by systematizing the assumptions of a theorem can we explore (as we did here) the cases in which it breaks down. While the First Fundamental Theorem comes with many issues — including market failures, lack of attention to equity, and the conflation of price with welfare value — it remains a useful framework for understanding the Invisible Hand.

People who continue to criticize economics as overly neoliberal — without making specific critiques — should recognize that most of the above limitations were pointed out by economists themselves. In many cases, the theorem's assumptions are quite reasonable, or can be achieved with some pragmatic policy changes like carbon pricing.

To me, the biggest theoretical blind spot left by this model is the way that prices may not even represent the welfare value that products provide to consumers. Ten years ago, native advertising was raising outrage (as in this John Oliver segment). Now, however, products are placed seamlessly into all manner of TikTok and Instagram content, making it increasingly difficult for people to distinguish between their honest preferences and those shaped by an advertising algorithm.

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