Paul Samuelson and the Provision of Collective Consumption Goods: A Rejection of Competitiveness Logic

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Matthew Watson, Professor of Political Economy, University of Warwick

Matthew Watson, Professor of Political Economy, University of Warwick

Paul Samuelson pioneered the mathematical models of maximisation that today form a central part of the economics of competitiveness.  It is significant, then, that the pioneer himself deployed his method of difference equations to come to a conclusion that is wholly opposed to modern-day competitiveness mantra.  This post by Matthew Watson brings Samuelson’s argument to a wider audience as the latest instalment in our series tracing the intellectual underpinnings of contemporary competitiveness discourse.  It reviews his defence of collective provision of the public goods that enhance individual welfare and his view that the funding of public goods should be protected from race-to-the-bottom dynamics.



Paul Samuelson and the Provision of Collective Consumption Goods: A Rejection of Competitiveness Logic

Nicholas Shaxson’s recent post on the Fools’ Gold blog examines Charles Tiebout’s theory of how utility maximising citizens vote with their feet to find their preferred mix of low taxes and public services.  The post raises all sorts of important implications when trying to assess the current dominance of the idea that competitiveness concerns must be prioritised above all other economic objectives.  Viewed in its historical context, an extra interesting issue to explore is not just what, but who, Tiebout was arguing against.  Into the Fools’ Gold files on the history of competitiveness discourse we introduce Economics Nobel Laureate Paul Samuelson.

Tiebout made his name by inverting the position that Samuelson took in his 1954 paper, ‘The Pure Theory of Public Expenditure’.  Samuelson had insisted that a collective solution was required to prevent local jurisdictions from competitively undercutting one another on tax.  Tiebout, though, was having none of this, arguing that efficiency gains were there to be had in aggregate if local jurisdictions engaged competitively in this manner.  All they had to do was allow citizens to follow their preferred mix of taxation and public services by upping sticks and taking themselves to wherever this magic formula was in place.

The dispute, at heart, was over a technical detail in neoclassical economics.  By the 1950s, adherents of the neoclassical tradition treated as axiomatic the assumption that all economic activity should be modelled on the ideal of utility maximisation.  The only question was how much behavioural complexity should be allowed into the model.

Samuelson argued that utility maximising agents would under-declare their interest in contributing towards the provision of public goods which enhanced the welfare of society as a whole.  This meant that the price signals to which they would respond for public goods under-represented the true interest they held in seeing their government deliver those public goods.  Their utility was only truly maximised, said Samuelson, when the government overrode price signals to insist on delivering the welfare-enhancing services that taxpayers could not necessarily be trusted to vote for.

Tiebout’s agents, by contrast, are more straightforward.  They have no propensity to deceive themselves into voting for a solution that would put more money in their pockets to purchase goods on private markets, but would see them lose out overall as public services were bargained away.  Interests and utility maximisation lined up in simple symmetry for Tiebout.  Voters have a one-dimensional interest in paying as little tax as possible and would always vote accordingly in order to maximise their utility.

In career terms if nothing else, Tiebout chose his target wisely.  He was a young academic looking to make his name, whilst Samuelson, though less than ten years his senior, was already established as a significant authority figure within the American economics profession.  He was well on the way to cementing a reputation for being the ‘Father of Modern Economics’, and was never shy of assuming that his vision of the profession was the only one that economists should be concerned with.  This self-confidence came at an early age and was evident in his PhD thesis, in which he put the whole of the economics profession in the dock for its clumsy use of really rather elementary mathematics.  On matters of mathematical method, his certainty appears to have known no bounds that he was right and everyone else was wrong.  It was so pronounced that the legendary Joseph Schumpeter is reputed to have turned to his fellow examiners having listened to Samuelson defend his PhD thesis to ask, “Well, have we passed?”  That thesis became the basis for the 1947 book, Foundations of Economic Analysis, which set up the whole of his Nobel Prize-winning career.  It also brought him to the attention of textbook publishers, securing an invitation to write the book that enabled him to be the person who taught all of the new generations of American economists from its first edition in 1948.  If he wanted to make a name for himself, then, who better for Tiebout to take on than Samuelson?  My concern here, however, is with the fact that there was something for him to oppose in the first place: i.e., that the leading exponent of orthodox mathematical economics in the post-war period constructed a strictly orthodox utility maximising model to argue against a competitive race to the bottom on taxation.

In many ways this is classic Samuelson, revealing him to be at the peak of his powers.  For anyone who is unfamiliar with the manner in which he worked, reading the two and a half pages of ‘The Pure Theory of Public Expenditure’ can be a somewhat disorienting experience.  Perhaps most obviously, there is so little here to actually read.  Most of the analysis involves establishing a mathematical model that might be relied upon for tracing through how people could be expected to behave were it possible to strip them down to pure instantiations of maximising economic behaviour.  These are not actual people placed in real-life public policy dilemmas of how much to tax, how much to spend and how best to construct stories about competitiveness from the balance between the two.  They are merely exemplars through which a pure economic logic might be devised to shed light on public policy dilemmas.

The hallmark of a Samuelsonian model is the use of mathematics to search for the most general result possible. This is why he restricted the people who populate his models to holding a very simple set of ideas consistent with the demonstration of pure economic logic.  If they are cleansed of all other behavioural impulses then the preferences they reveal can be assumed to hold in the general case.  In this instance, Samuelson followed the argument of the Swedish economist, Knut Wicksell, to say that when taking each individual alone, we must expect them to issue false signals through the price system about how much they value the collective consumption activity that ensues from the payment of taxes.  The general case, then, is that price signals should not be trusted if the overall price of a good depends not on whether one person will be prepared to pay their share but on whether they can rely on everyone else to pay their shares.  For instance, the ability to continue meeting the costs of a UK National Health Service which is free at the point of need depends, ultimately, not on me alone paying my taxes but on every UK taxpayer meeting their collective responsibility.

At the time that Samuelson was writing, economists were seriously flirting with the idea that a system of market pricing was sufficient on its own to allow people to signal their true desires.  As one example, this was the central premise of Hayekian economics, which was beginning to gain a foothold in the 1950s as a source of opposition to the post-war development of the welfare state.  Trust in market prices, Hayek said, and they will act as signals for how individuals will express their choices if they are given the freedom to do as they please.

Samuelson’s article shows that he thought very similarly when it comes to markets for private consumption goods. However, the significance of ‘The Pure Theory of Public Expenditure’ for us at Fools’ Gold can be found in those moments in which he parted company with Hayekian economics.  Samuelson disagreed most vociferously with the proposition that there was a direct analogy between markets for private consumption goods and markets for collective consumption goods.  The most important observation in the article in this regard is that “no decentralized pricing system can serve to determine optimally these levels of collective consumption”.  He even placed this sentence in italics, just so its significance could not be missed.

There are some aspects of the text that non-Samuelson aficionados will find unfathomable.  There is a nod towards the “monotonic stretching of the utility index”, for instance; there is the assertion of “a maximal (ordinal) utility frontier representing the Pareto optimal points” (“of which”, we are told, “there are an (s-1)fold infinity”); and there is an unshakeable faith that the solution of a system of difference equations will always yield “optimal conditions”.  But this is merely Samuelson’s way of setting up an economically meaningful mathematical relationship.

He does so to pick out the special characteristics of goods that display what he calls “jointness of demand”.  The hospital example is a useful one once again.  Each of us is likely to assume that we will be in need of hospital care at some stage in our lives, but it falls to nobody to know exactly which illness they will be confronted with.  It therefore makes sense for us to club together to ensure that the healthcare system can act upon many more illnesses than anyone will have the bad luck to befall them personally.  The whole essence of collective healthcare is that most people will over-pay for the medical attention they ultimately receive.  But nobody knows before-the-fact whether they will be part of the over-paying majority or will need access to extra treatment.  This lack of knowledge of what the future holds is what gives rise to the ‘jointness of demand’.  According to Samuelson, the fact that such demand is “intrinsic to the very concept of collective goods and governmental activities makes it impossible for the grand ensemble of optimizing equations to have that special pattern of zeroes [as demanded by difference equations] which makes laissez-faire competition even theoretically possible”.

Samuelson’s model thus comes to the clear-cut conclusion that the modern-day competitiveness agenda is destructive of the utility-maximising individual’s true interest.  However, there is one final irony to consider here. Unlike so many other luminaries of American economics, Samuelson generally resisted the temptation of public office.  When various Presidential Administrations dangled high-profile Washington posts in front of him, ‘thanks, but no thanks’ tended to be his response.  He thought that the best way he could influence the state of the world was not through helping to formulate individual policies but through being the person who taught economics to the opinion formers.  He famously said: “I don’t care who writes a nation’s laws – or crafts its advanced treaties – if I can write its economics textbooks”.

Samuelson did, indeed, author the best-selling textbook that set the context for how generations of economics students learnt the subject field.  It was called simply Economics, without any qualification in the title about what sort of economics it stood for.  This was a characteristically bold move, staking a clear claim on the right to determine the content of what others should understand as the subject field in its entirety.  It was here that maximisation models were successfully popularised as the means of envisioning all economic problems. Samuelson extolled the privileges that this brought him: “Contact with hundreds of thousands of minds … is an experience like no other that a scholar will ever meet”.

Yet his success as a textbook writer cannot be seen as total.  Had he accepted the lure of Washington he would have been able to ensure that Samuelsonian models of maximising agents would always have been used to support the welfare-enhancing public expenditures he endorsed.  But he didn’t.  He was therefore powerless to head off challenges to his argument that the government should continue to supply public goods of this nature even if the representative taxpayer could not be persuaded that they had an interest in continuing to contribute towards their maintenance.  As the subsequent work of Tiebout demonstrates only too well, the same category of economic model could be used to derive the exact opposite political result.

Samuelson the economic methodologist was thus ultimately far more successful in overseeing the adoption of formal models of maximising behaviour than was Samuelson the political economist in maintaining control of the political content of those models.  The grip which the modern-day competitiveness discourse exerts on the political imagination is compelling evidence of this ‘two Samuelsons’ phenomenon.  Samuelson the political economist argued consistently for the introduction of political safeguards against the race-to-the-bottom dynamics of allowing jurisdictions to compete against one another on the basis of taxation.  Samuelson the economic methodologist, however, paved the way for Tiebout-style feet-voting maximisation models through which these political safeguards have been sacrificed.

Matthew Watson is Professor of Political Economy in the Department of Politics and International Studies at the University of Warwick and an Economic and Social Research Council Professorial Fellow.



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