In Praise of Kenneth Arrow

Does winning the Nobel Prize in economics cause longevity? We might be forgiven for thinking so. Thomas Schelling died last year aged 95. The author of the famous textbook, Paul Samuelson, passed away at 94, whilst his colleague, Bob Solow, is still going strong at 92. The British Laureate Ronald Coase reached the age of 102. Kenneth Arrow was a mere whippersnapper in comparison, dying a couple of weeks ago at 95.

The metropolitan liberal elite in America represent an aristocracy every bit as interwoven by family connections as the grandees of 18^th century England. Forget the Clintons and their daughter. Arrow was Samuelson’s brother in law. He was the uncle of Larry Summers, former Treasury Secretary and President of Harvard.

In terms of his contribution to science, Arrow was possibly the most important economist of the second half of the 20^th century. But he is essentially unknown to the general public, spending his career in the sheltered groves of American Ivy League universities.

This illustrates a fundamental feature of economics. In the media, it appears to be solely about the big features of an economy, the macro variables in the jargon, such as GDP, unemployment and inflation. In the public perception, economists seem to spend most of their time having furious arguments with each other.

But this is just the tip of the iceberg, the bit that is seen. Where Arrow worked, under the surface, is where most economics is done. And it is where economists are far more often in agreement than in dispute. It is the territory of micro economics, the study of how individuals behave and take decisions.

Arrow made a massive contribution to the crown jewel of this world, so-called general equilibrium theory. The idea that markets are a Good Thing goes back at least as far as Adam Smith, as does the insight that supply and demand can be brought into balance by changes in the price of the product.

The role of price in any particular market is easy to understand. For many decades economists wrestled with a problem which is straightforward to state but fiendishly difficult to solve. Price can equalise demand and supply in a single market. How can we establish whether a complete set of prices can exist which ensures that all markets clear in this way, so that supply is the same as demand?

An analogy with quadratic equations might help. Most readers will recall struggling to solve these at school. But there is a formula which guarantees to find the solutions to any such equation. Simply plug in the relevant numbers, and the answer pops out. Arrow’s mathematical work was not to find a set of prices for any particular economy. It was to establish the conditions, to find the formula, under which a solution could be found for any economy.

This may sound, and indeed it is, highly esoteric. But general equilibrium models, thanks to Arrow, are now, for better or for worse, part of the everyday practical tool kit of modern day economists.