Background of Research

James A. Mirrlees

Having a mathematical culture, He supposed he expected that at some point there would be a real idea, an inspiration, and one day in November 1961 it came. He tried to think about how the amount of uncertainty should affect the optimal rate of saving in an economy. He thought of a neat way of modeling the question. Contrary to what everyone else seemed to think then, he showed that quite commonly, greater uncertainty is a reason for saving more, not less. Then he met Paul Samuelson and Bob Solow, and gave a seminar at MIT on optimum growth under uncertainty. They spotted a mistake but were nevertheless encouraging. 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 his two examiners. He tried very hard to find the mistakes and failed. But James had still never been able to solve the main problem the thesis addressed, at least to his satisfaction. He published only one small paper on the subject, much later. The stimulus of teaching took him in some new directions, as he thought increasingly about general welfare economics, conceived as a general theory of economic policy. It was the beginning of the work on optimal taxation that Peter Diamond and James did in the next few years. That in turn led to thinking about nonlinear tax schedules, and what we still call optimal income tax theory. And that step, towards a more general conception of relationships between principal and agent in economic contracts, came after he had essentially left Cambridge. 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.