Kenneth Arrow, who has died aged 95 at his home in Palo Alto, California, on Tuesday was a towering figure in 20th century economics. In 1972, at the age of 51, he won one of the first Nobel memorial prizes in economics, the youngest winner then or since. Yet even a Nobel Prize understates Arrow’s contribution to economic theory. A brilliant mathematician, he ranged widely, breaking ground in areas that have subsequently yielded many further Nobels, including risk, innovation, health economics and economic growth.
Two achievements are particularly celebrated: his impossibility theorem about the paradoxes of social choice, and his welfare theorems, which formalised the most famous intuition in economics — Adam Smith’s idea that a market produces social good from individual selfishness.
Born in New York on August 23 1921 to immigrant parents, Kenneth Joseph Arrow had his formative experiences shaped by poverty — his businessman father “lost everything” in the Depression. But Arrow flourished at school and received an MA in mathematics from Columbia University at the age of 19. He interrupted his graduate studies to serve as a wartime weather researcher and US Army Air Corps captain.
His doctorate, published in 1951, made up for lost time. The thesis explored the problem of turning individuals’ preferences into a picture of what a society as a whole preferred. Scholars had long known that voting systems could produce perverse results but Arrow went further, showing that the very idea of “what society prefers” was incoherent. He set out four reasonable sounding requirements for building social preferences from individual ones — and proved that no system could satisfy all four of those requirements.
Arrow then turned to the familiar problem of supply and demand. In a well-functioning market for a single good such as apples, there is an efficient outcome with a price at which the number of apples supplied would equal the number of apples demanded.
But that was just one market. It was influenced by the market for pears, for agricultural land, for farm labourers and even for bank loans. Each market pushed and pulled others. What happened when one considered the interactions between every market in the world?
Working at times with the French economist Gérard Debreu, Arrow demonstrated that the intuitions from a single market could be generalised. First, there was a general equilibrium at which prices equalised supply and demand in every market at once. Second, this equilibrium was efficient. And third, any efficient allocation of resources could be reached by redistributing wealth and then letting competitive markets take over. Markets could still fail, but Arrow’s analysis explained the circumstances under which they would succeed.
Alongside such deep theoretical work, Arrow made many contributions to practical economic problems from insurance to healthcare to climate change. On occasion he took an active role on politically contentious issues, and was co-author of the 1997 “Economists’ Statement on Climate Change”, which warned of the dangers of global warming.
He was also noted for his love of gossip and his quick wit. One story tells of Arrow and a colleague waiting for an elevator to take them down, while several passed them going up. The colleague wondered aloud why everyone was going up. The immediate reply: “You’re confusing supply with demand.”
Arrow spent most of his career at Stanford University, apart from an 11-year spell at Harvard. He married Selma Schweitzer in 1947; she died in 2015. He is survived by his sons David and Andrew. He is also survived by his sister Anita, who married Robert Summers, a noted economist and brother of Nobel laureate Paul Samuelson. Her son, Arrow’s nephew, is the former US Treasury secretary Lawrence Summers.
Written for and first published in the Financial Times.
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