Newton Stewart is a town of two thousand people in the beautiful centre of Galloway, in the southwest of Scotland. My father came there in 1934, newly married, to be a teller in one of the six banks. In 1936 I was born, in a cottage across the river in the neighbouring village of Minnigaff. Three years later we moved to Newton Stewart proper, my brother was born, and, coincidentally, my conscious life began. Though later, about 1950, we moved to the coastal village of Port William, eighteen miles south, I went to school in Newton Stewart, travelling latterly by the school bus. While at primary school I was apparently quite quick at mental arithmetic, and also acquired glasses. If you need glasses it is hard to enjoy football (association football is the main sport in the area). Without them, I was not good at guessing where the ball was. That, and various childhood illnesses, gave me time to read, which suited me fine. To tell the truth, I would not have been very good at football anyway. I once took a catch in the annual cricket match.

To my relief, I passed the "control", the examination at age eleven to decide who could go on to the high school, the Douglas Ewart. In these days there were prizes every year. With much parental encouragement, I tried to win them, and as far as I remember was rather successful. But I must have had some sense that this drive to win is somewhat ignoble. When a friend beat me in chemistry I recollect being scolded at home for accepting defeat with equanimity. By the age of fourteen I had acquired a strange enthusiasm for mathematics, having managed to acquire a book called Teach Yourself Calculus, and done so. When he found out, the head mathematics teacher somehow gave me individual tuition during classes, and I raced ahead. At the same time the music teacher, who was also my piano teacher, provided books like Hogben's Mathematics for the Million. In the school bus, I tried to read my mathematics teacher's university books. This was much more fun than trying to come top. When asked by the Rector (the headmaster) what I wanted to do in life, I gave the obvious answer: be a professor of mathematics. Mr Geddie sounded appropriately sceptical.

In Scotland, unlike England, one does a wide range of subjects all through school, and for the final school examination: English, mathematics, science, French, Latin, history, in my case. Oddly enough this examination is taken in the penultimate year, at age sixteen, and the final school year is devoted to odds and ends, except that there were two special mathematics papers that one could do in that final year. I took them a year early, successfully, catching the attention of the inspector from the Scottish Education Department who suggested I should try for the Cambridge scholarship. No doubt we had heard of Cambridge, but none of us, teachers, friends or relatives, knew what this mysterious scholarship examination was, nor why going to Cambridge might be such a Good Thing. It emerged that Cambridge was not for young Scots, in the normal way, since the government grants provided to pay university fees and some subsistence, could not be used outside Scotland (the English, though, were allowed to come to Scottish universities, and many did). The one exception was the scholarship. If someone won a scholarship to Oxford or Cambridge in the college scholarship examinations, a supplementary grant would then be given. In Glasgow and Edinburgh there were schools that prepared some of their pupils for entrance to Oxford and Cambridge, but that was another world.

The examination was held in December. The suggestion to take it was made, I believe, in June. We were not aware that in English schools those preparing for the examinations would specialize for two or three years, doing, for example, nothing but mathematics. We, my mathematics teacher and I, got past examination papers and tried to do them. It was exciting, but even in late November I found I could not always solve all the questions in the time available. We did not know that rather less was expected. There was no immediate happy outcome. The weekend I should have gone to Cambridge to take the examination I was rushed to the nearest serious hospital, seventy miles away, with peritonitis. In 1954, I went to Edinburgh, which I did not mind then, and do not regret now.

Somehow I argued my way into starting the Edinburgh mathematics course in its second year, thus shortening the normal four-year Scottish degree to three years. Also, and I suspect this was the more remarkable achievement, I persuaded the authorities to let me take philosophy in my first year. It was regarded as morally dangerous to take philosophy at the beginning of one's university course, but I had a cousin who was doing philosophy at Glasgow (and still is); and on long country walks he had infected me with it. I did not do any other philosophy courses at university (though I went to some lectures later in Cambridge), but that remained an important basis for much of what I tried to do later in a subject that used to be part of the Moral Sciences tripos in Cambridge, economics.

In those years at Edinburgh, mathematics was easy, and needed little time. Having obtained a number of individually small scholarships through various examinations, I had just a little more money than the minimum, and could afford the new Penguin books as they came out. The university library had lovely open shelves and easy access. I could afford to go to some concerts, which were cheap at that time, and the National Gallery of Scotland is a wonderful introduction to painting. There were plenty of university societies too, and being far from home I threw myself into them too, debating, philosophy, but not then much politics; and endless talk in Cowan House, a long disappeared hall of residence with, I think, selective admission. At any rate, it was a great group of people.

Although mathematics then seemed easy, I am sure I was getting careless. But as usual I was lucky, and got the Napier medal in the final examination. Earlier that year, I had, at last, taken the Cambridge scholarship examination, as had a series of other Edinburgh mathematics students, and thereby earned a further grant to go on and do yet another undergraduate degree. In 1957, at the age of twenty-one, I left Scotland, like many before and since, an excited member of the Scottish diaspora, with my birthday present, a typewriter. In the summer, I had taught myself to touch-type.

The mathematics undergraduate degree at Cambridge had three parts, or triposes. For a degree it was sufficient to do Part I and Part II: the famous "wranglers" are those who are in the first class in Part II. The best mathematicians did Part II in their second year and then Part III in their third. Those of us who came from Edinburgh (and other universities whose preparation was deemed insufficient for an immediate plunge into research) did Part II in the first year, Part III in the second. In Trinity, the College I had joined, two of us from Edinburgh enjoyed being taught together by some of the best mathematicians one could hope to find. It was exciting, and not yet too difficult. We duly became wranglers.

In Cambridge you can go to lectures in any subject, without formality. I took full advantage. In the summer I wrote a mathematical essay for a prize. The subject I chose was game theory, and I didn't make much of it. My Edinburgh friend got the prize. Then came Part III mathematics, with subjects on the borders of current research. That was hard, and there was a lot I wanted to do besides mathematics. The result was good enough to allow me to go on to research had I wanted to do so, but I did not. Social science, perhaps even sociology, beckoned. Peter Swinnerton-Dyer, in mathematics, guided me to Piero Sraffa, in economics. In any case it was indeed economics I wanted to do, because I kept discussing it with economist friends, and they didn't make sense to me; and because poverty in what were then called the underdeveloped countries, seemed to me what really mattered in the world, and that meant economics.

How could I possibly get finance for a third undergraduate degree? Fortunately Cambridge had an arrangement whereby you did a part of the final undergraduate examination in one year, called it the Diploma in Economics, and treated it as an initial year of graduate work. Still, money had to be found. All students in a Cambridge college have a Tutor, who looks after them in a general way, administratively not academically. Each Tutor has many students. Somehow mine managed to get the Department of Scientific and Industrial Research to give me a three year award to do a Ph.D. in economics. They had an interesting incentive contract: I did not have to take a Ph.D., but if I did not, then I had to write a thesis of equivalent length. I didn't enquire what the sanctions were, I just got on and did it. Somehow the examiners at the end of the first year were fooled into thinking I knew some economics. Economics takes a while to learn, even if much of it is in a way quite simple. It is simple to be wrong as well as to be right, and it is none too easy to distinguish between them.

David Champernowne, newly returned from a Chair in Oxford to a Cambridge readership and a teaching fellowship in Trinity, was my first teacher. In Oxford people did not appreciate science fiction and computers, so he had returned to what he regarded as the centre of economics. Being taught on one's own or with one other seems extraordinarily wasteful and expensive, but I have benefited immensely from it, and still enjoy doing it as a teacher. If it works, it is not usually by the simple transmission of information. David started by telling me to read Keynes's General Theory, I think because he had just been re-reading it. That may not have been the best advice, but it did no great harm, and one day I hope to finish it. Needless to say, I also relied a great deal on fellow students, who in effect taught me most generously. They were cooperative times. My reading remained haphazard, and the lectures and seminars of the notable Cambridge names, Kahn, Kaldor and Joan Robinson were highly idiosyncratic, but it was a stimulating time.

Richard Stone was my official supervisor, to guide my research, and as soon as the first year was over he involved me in the Growth Project that he was beginning, a project to simulate realistically the long-term growth of an economy, particularly the UK. The guiding star was indicative planning, a forgotten notion. Stone pointed me to Ramsey on optimal saving (an interest of David Champernowne's too) and at some point in all this I had discovered Samuelson and mathematical economics. I tried writing research papers, which were largely rubbish. Dick passed something, I forget what, to Frank Hahn, just lured to Cambridge by Kaldor. Frank somehow saw merit amid the rubbish, and was encouraging. He became another unofficial supervisor and great mentor. I ought to have been feeling lost and confused that year, but I was engaged and happy, and got married to Gill, just finishing her teacher training in Cambridge. So we set off to Scotland for a honeymoon, with my typewriter, and I set about doing a Fellowship dissertation for Trinity. Considering I had made no discoveries, it seems a daft enterprise. Oddly enough I still have a copy: Contributions to a theory of economic planning. Without looking inside, I am sure there were no contributions. It was submitted for the October competition, and was unsuccessful. I remember no disappointment, just surprise when I learned that the thesis had not been so far from success. Writing a couple of hundred pages was a great way of learning anyway. There was little mathematics in it.

I was thinking about planning, which was the main theme of Stone's Growth Project. Having a mathematical culture, I suppose I expected that at some point there would be a real idea, an inspiration, and one day in November 1961 it came. Uncertainty seemed to me unduly neglected, so I tried to think about how the amount of uncertainty should affect the optimal rate of saving in an economy. I thought of a neat way of modelling the question. Contrary to what everyone else seemed to think (then), I showed that quite commonly, greater uncertainty is a reason for saving more, not less. I started using Wiener processes and discovered the Ito calculus for myself. Of course it would have been more sensible to learn the techniques that were already known, but I didn't know where to find them.

The thesis could have been finished at the end of that academic year, but two things happened. Nicholas Kaldor wanted a research assistant to help with writing a paper on growth, a continuation of a notable series. David Champernowne put us together. Nicky was no mathematician, so I was what he needed. In the end he generously made me a co-author. The paper is a bit mixed up, but our long discussions were a wonderful experience, as he tried to make sense of economic growth, and I tried to make sense of him. For a month or so, it was full time, and the thesis languished.

Then Amartya Sen suggested and arranged that I go to India for a year, with the India Project run by Paul Rosenstein-Rodan for the MIT Center for International Studies. Rosie said I must first go to MIT for the summer "to acclimatize", and Gill and I had our only period of mild impoverishment living for three months in a basement in Somerville, Massachusetts, followed by a remarkably and inappropriately luxurious eight months in India. But it was a good summer: I met Paul Samuelson and Bob Solow, and gave a seminar at MIT on optimum growth under uncertainty. They spotted a mistake (which had not been in the thesis, I must add) but were nevertheless encouraging. Probably I am mistake-prone, but have learned to live with it. In September, we continued on our way to New Delhi.

It was never clear quite what I was supposed to be doing on the India Project, particularly after an initial period helping with a rightly abortive input-output exercise. I thought a lot, and wrote many little papers, particularly about investment appraisal, and efficiency wages. Some years later I remembered that I had worked out the theory of efficiency-wage equilibria in 1962 on our way from MIT to India, on the long, long flight from San Francisco to Tokyo, and wrote it up as a paper in the early seventies, a paper I still rather like. The work on investment appraisal, including ideas about uncertainty, led on, after a lapse of years, to work with Ian Little on criteria for cost-benefit analysis in developing countries. I fear I did not do as much for the Planning Commission as had been hoped or intended. I learned an immense amount, both from the country and from its many fine economists. In these days Jagdish Bhagwati, T. N. Srinivasan and Sukhomoy Chakravarty were all there too, and Amartya Sen was about to return.

Before I had left Cambridge, Nuffield College, Oxford offered me a research fellowship for which I had not applied. Trinity retaliated almost instantly by offering me a teaching fellowship in economics to be taken up in 1963, when Sen would be leaving to return to India. I accepted the Trinity job. It seems ridiculous, but I have never had a job I applied for. When I do apply, I don't get it, but that is a small sample. While in India, I was told I had been given a university assistant lectureship. That meant I would not have to do so much individual teaching in Trinity, and would have to give lectures.

When we got back from India, two things had to be done. It was time to write the thesis, and to have a child. We did. Catriona was born in a College flat in Trinity Street, and I cooked duck a l'orange for the only time in my life since Gill couldn't very well cook the celebratory dinner. The thesis was duly submitted in September 1963, on Optimum Accumulation Under Uncertainty. Wonderfully, Ken Arrow was visiting Cambridge that year, and was one of my two examiners. He tried very hard to find the mistakes and failed. But I have still never been able to solve the main problem the thesis addressed, at least to my satisfaction. I published only one small paper on the subject, much later.

Ken Arrow had already been thinking about investment choices under uncertainty, and I found that what I had worked out in India had already been done better. Bob Solow was there that year too. Growth and capital were the main subjects of discussion. I wrote up, and greatly improved, the easy part of the thesis, without uncertainty, at much the same time that Cass, Koopmans and others were developing optimum growth theory beyond the Ramsey level. Now writing slowed to a crawl, whether because of the demands of teaching, or rising standards; and because I could not prove what I guessed about the uncertainty case. Speaking of crawl, Fiona was born in 1966. Fortunately the stimulus of teaching took me in some new directions, as I thought increasingly about general welfare economics, conceived as a general theory of economic policy. An examination question about optimal taxes caused immense trouble among the examiners, since Joan Robinson would not believe the result. It should not have been in an examination paper, of course, but it was the beginning, on my side, of the work on optimal taxation that Peter Diamond and I did in the next few years, after he came on a six-month visit to Cambridge. I followed the main principle for academic success: get a good co-author (and also the second: get another). The still-continuing collaboration with Peter has been at the centre of the work, his influence on the sole-authored papers immense too.

That in turn led to thinking about nonlinear tax schedules, and what we still call optimal income tax theory, which I discuss in the Prize Lecture. But that step, towards a more general conception of relationships between principal and agent in economic contracts, came after I had essentially left Cambridge. Oxford had a professorship of economics, which had to be in mathematical economics or in econometrics. David Champernowne had held it. Now it was vacant and proving hard to fill. They decided that some baby-snatching was in order, and offered it to me in 1968. At that time, thirty-two seemed quite young for a professor. Cambridge was still a place to be, with James Meade and Dick Stone, and good new people, often recruited by Dick; but Frank Hahn had already left, and Cambridge was increasingly suffering from shrill doctrinal, almost religious, squabbles (mainly then with the rest of the economic world) . It was time to go. I briefly toyed with MIT and LSE, both standing higher than Oxford, but we were small-town people. At that time, Ian Little, at Nuffield, had already got me to do a manual on Cost Benefit Analysis with him. Paradoxically, the Oxford choice probably meant I would not specialize too severely in mathematical economics. It also meant that I would deal entirely with graduate students. It was immensely helpful to have that simplification in what had become a too complex academic life.

In the intervening sabbatical term at MIT, between Cambridge and Oxford, work on nonlinear incentive relationships began. That year, or the next, the first version of the optimum income tax paper went round, but mathematical justifications took another year and too many pages. In the end much of the rigorous justification was published only many years later. I never learned not to publish in a book: it can take a very long time to appear. Of course it can be quick too. The mimeoed version kept vanishing from the Nuffield library, so at least it was being read, or looked at.

Already several superb PhD students had come to me as supervisor, for example, Azizur Rahman Khan and Partha Dasgupta, and I had taught David Newbery as an undergraduate. From that time on I found myself almost invariably with at least one, often several research students of the highest class. The Oxford environment seemed to make that happen. I have always supervised research much more diverse than what I do myself, and by no means all of them worked in the principal/agent or welfare economics field. Some became colleagues. It was only quite loosely a school of optimal taxes and welfare and incentives. I am proud that in due course industrial economics and game theory flourished in Oxford. Even they are not unconnected with incentive and contract theory, but there is no doctrinal connection, no common catechism. I have long lost count of the number of my students who hold full professorships, but I like to think they are numerous as well as able.

There came a time when it seemed best to make a last change, to seek new stimulus. In November 1993, Gill died, five years after cancer was first diagnosed. Catriona and Fiona had grown, married, and gone. A Cambridge Chair was offered, and in 1995 I moved, and moved into Trinity. There is still work to be done.

When that curious English publication, Who's Who, first asked me for an entry, my normal inclination to brighten up dark corners led me to list as my recreations "playing the piano, reading detective stories and other forms of mathematics, travelling, listening". I did not suppose that anyone would have much reason to read it, but in these last two months it seems many have, and, looking at it again, I find no reason to change it, though I should now add other reading and computer programming. Everything is to be interpreted there in the broadest sense, as at least those (few) who have heard me play the piano may agree.

From Les Prix Nobel 1996.