He became a lecturer at the London School of Economics (LSE) later becoming Professor of Statistics. He wrote many papers and books on mathematical economics including the paper on A Reconsideration of the Theory of Value published in Economics in 1934 with Sir John Hicks.
Other books include: Mathematical Analysis for Economists (1938), Statistics for Economists (1949), Mathematical Economics (1956), and Macroeconomic Theory (1967).
Allen was knighted in 1966 for his services to economics and became president of the Royal Statistical Society, who awarded him the Guy Medal in Gold in 1978. He was also treasurer of the British Academy of which he was a fellow (FBA).
Allen became a fellow of Sidney Sussex, Cambridge and died in 1983. He had a son, Jeremy, who was a co-founder of the consultancy International Planning and Research, and a grandson, Dion.
Publications (selection)
"The Nature of Indifference Curves", 1934, RES.
"The Concept of the Arc Elasticity of Demand", 1934, RES
"A Reconsideration of the Theory of Value", 1934, Economica, Part II 1(2), pp. 196-219. (Part I by J.R. Hicks)