*Economic Journal*in 1927 and 1928, and also as a story of a genius who died at age 26. Cheryl Misak has written the first full biography of Ramsey:

*Frank Ramsey: A Sheer Excess of Powers*, which I have not yet read. But I ran across the review/overview of the book by Anthony Gottlieb in the

*New Yorker*(May 4, 2020), titled and subtitled \”The Man Who Thought Too Fast: Frank Ramsey—a philosopher, economist, and mathematician—was one of the greatest minds of the last century. Have we caught up with him yet?\”

Dons at Cambridge had known for a while that there was a sort of marvel in their midst: Ramsey made his mark soon after his arrival as an undergraduate at Newton’s old college, Trinity, in 1920. He was picked at the age of eighteen to produce the English translation of Ludwig Wittgenstein’s “Tractatus Logico-Philosophicus,” the most talked-about philosophy book of the time; two years later, he published a critique of it in the leading philosophy journal in English, Mind. G. E. Moore, the journal’s editor, who had been lecturing at Cambridge for a decade before Ramsey turned up, confessed that he was “distinctly nervous” when this first-year student was in the audience, because he was “very much cleverer than I was.” . …

His contribution to pure mathematics was tucked away inside a paper on something else. It consisted of two theorems that he used to investigate the procedures for determining the validity of logical formulas. More than forty years after they were published, these two tools became the basis of a branch of mathematics known as Ramsey theory, which analyzes order and disorder. (As an Oxford mathematician, Martin Gould, has explained, Ramsey theory tells us, for instance, that among any six users of Facebook there will always be either a trio of mutual friends or a trio in which none are friends.) …

In 1926, Ramsey composed a long paper about truth and probability which looked at the effects of what he called “partial beliefs”—that is, of people’s judgments of probability. This may have been his most influential work. It ingeniously used the bets one would make in hypothetical situations to measure how firmly one believes a proposition and how much one wants something, and thus laid the foundations of what are now known as decision theory and the subjective theory of probability. …

Economists now study Ramsey pricing; mathematicians ponder Ramsey numbers. Philosophers talk about Ramsey sentences, Ramseyfication, and the Ramsey test.

*Economic Journal*, 1927, 37: 145, pp. 47–61) and “A Mathematical Theory of Saving,”

*Economic Journal*, 1928, 38:4 pp. 543–559. John Maynard Keynes was editor of the

*EJ*, and as Gottleib notes: \”John Maynard Keynes was one of several Cambridge economists who deferred to the undergraduate Ramsey’s judgment and intellectual prowess.\”

*Economic Journal*on its 125th anniversary published as series of essays reflecting back on the most prominent papers that had appeared in the history of the journal, and two of the 13 papers deemed worthy of remembrance were by Ramsey.

Frank Ramsey\’s brilliant 1927 paper, modestly entitled, ‘A contribution to the theory of taxation’, is a landmark in the economics of public finance. Nearly a half century later, through the work of Diamond and Mirrlees (1971) and Mirrlees (1971), his paper can be thought of as launching the field of optimal taxation and revolutionising public finance. … Here, he addresses a question which he says was posed to him by A. C. Pigou: given that commodity taxes are distortionary, what is the best way of raising revenues, i.e. what is the set of taxes to raise a given revenue which maximises utility. The answer is now commonly referred to as Ramsey taxes. …

Ramsey showed that efficient taxation required imposing a complete array of taxes – not just a single tax. A large number of small distortions, carefully constructed, is better than a single large distortion. And he showed precisely what these market interventions would look like. (He even explains that the optimal intervention might require subsidies – what he calls bounties – for some commodities. …

In particular, when there are a set of commodities with fixed taxes (including commodities that cannot be taxed at all), he shows that there should be an equi‐proportionate reduction in the goods for which taxes can be freely set. In the case of linear and separable demand and supply curves (quadratic utility functions) and small taxes, he shows that optimal taxes are inversely related to the compensated elasticity of demand and supply. … Ramsey, however, went beyond this into an exploration of third best economics. He asked, what happens if there are some commodities that cannot be taxed, or whose tax rates are fixed. He argues that the same result (on the equi‐proportionate reduction in consumption) holds for the set of goods that can be freely taxed. …

To boil this down a bit, there is a common intuition that the \”best\” commodity tax will be a tax of the same rate across most or all goods. Ramsey instead emphasizes that if the goal of a tax is to collect money while having that tax distort other behavior as little as possible, then you need to think about demand and supply for each commodity and how they will be affected by a tax. This way of thinking about \”optimal taxation\” has turned out to have very broad applicability.

Ramsey\’s basic model was not looking at issues of inequality, but his basic framework can readily be adapted to do so. Stiglitz describes how \”at the centre of modern optimal tax theory and the work growing out of Ramsey lies a balancing of distributional and efficiency concerns.\” Nor was Ramsey\’s model looking at problems with markets like issues of pollution externalities, which his adviser A.C. Pigou was already discussing at that time, but the idea of thinking about how taxes on goods can be adapted to address externalities flows naturally from Ramsey\’s framework. If there is a concern that taxes on labor might encourage some people to shift away from taxed labor to untaxed leisure, one can build on Ramsey\’s approach to advocate taxing goods that are associated with leisure. It turns out hat when a government is thinking about how to regulate the prices charged by a public utility, Ramsey taxes become an important part of thinking about how to balance costs and benefits.

In 1928, Frank Ramsey, a British mathematician and philosopher, at the time aged only 25, published an article (Ramsey, 1928) whose content was utterly innovative and sowed the seeds of many subsequent developments. … The article sets out to answer an interesting and important question: ‘how much of its income should a nation save?’.

The basic tradeoff here is that more consumption in the present leads to less saving and investment in future growth. Over long periods of time, or successive generations, one wants to think about a rate of saving that makes sense from the standpoint of each generation. Moreover, Ramsey brings into the picture issues like technical progress, population growth, capital wearing out or being destroyed, and so on. He discusses what we know call an \”overlapping generations\” model, where even if individuals only care about their own lifetimes, the overlap of successive generations keeps propelling us forwad with concerns about the future. As Attanasio points out, a number of later prominent ideas in economics are a reworking and extension of ideas from Ramsey\’s 1928 article. Here are some examples he mentions:

The most obvious anticipation in the article is its central theme and result: the optimal growth model, as formulated by Ramsey, is very similar to what has become a basic workhorse of modern macroeconomics. In a 1998 interview Cass (1998) recounts that he read Ramsey\’s paper after writing the first chapter of his PhD dissertation in 1963, which eventually became the review of economic studies article (Cass, 1965). Talking about his celebrated 1965 article Cass (1998) says: ‘In fact I always have been kind of embarrassed because that paper is always cited although now I think of it as an exercise, almost re‐creating and going a little beyond the Ramsey model’ (p. 534). …

When considering the optimal saving problem, Ramsey uses as a first building block an intertemporal consumption problem which essentially defines the permanent income model. … These intuitions and this way of modelling were written 30 years before the publication of Friedman\’s (1957) book and Modigliani and Brumberg\’s (1954) seminal paper on the life cycle model of consumption.

Analogously, the brief description on an economy populated by individuals with ‘different birthdays’ and how their individual savings aggregates into the supply of capital is essentially a description of the overlapping generation model which was Samuelson (1958) developed 30 years later5 and subsequently enriched and studied by Diamond (1965).

Ramsey developed an abdominal infection, underwent surgery, but died in the hospital. He was an avid swimmer, and one possibility is that he picked up a liver infection from swimming in the river. His early death is one of the biggest intellectual what-if stories of the twentieth century.