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Economics 1936

Quantitative Input and Output Relations in the Economic System of the United States

Wassily Leontief

Every industry's output is another's input — so map the whole economy as one grid of give-and-take, and solve it.

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In depth · the introduction

To bake a loaf you need flour; to make flour you need a mill; to build a mill you need steel — Leontief found the arithmetic that follows every one of those threads at once.

The idea, unpacked

An economy is a web in which almost everything is both a product and an ingredient. Electricity lights the steel mill; steel builds the trucks; trucks deliver the grain; grain feeds the workers who run the power station. Pull on any one thread and the whole web twitches.

Leontief's insight was that you can write this web as a single table — every industry a row and a column — and turn it into arithmetic. Tell the table how much of each final good people actually want, and it computes how much every industry must produce in total, once you count not just the obvious direct orders but all the hidden inputs behind them, and the inputs behind those.

Where it came from

Wassily Leontief was a Russian-born economist who settled in the United States and, at Harvard in the 1930s, set out to do something economists had mostly only talked about: measure the entire interlocking economy. Earlier thinkers — Quesnay in 18th-century France, Walras in the 19th — had pictured the economy as one great system of mutual dependence, but as theory on paper. Leontief made it real, painstakingly assembling the first input–output table of the American economy from scratch.

The calculations were enormous — inverting a big table by hand is punishing — and his project became one of the first serious customers for early computers. The work earned him the 1973 Nobel Prize, and the tables he pioneered are now built by governments all over the world.

Why it mattered

For the first time a planner could ask a precise question and get a number: if the country wants this many houses and this many cars next year, exactly how much steel, electricity, glass, and labour must every industry produce to deliver them? Because the method captures the indirect demands — the steel inside the car, the coal inside the steel — it sees costs a simpler tally misses. That made it indispensable for wartime production, for building national economic statistics, and, today, for measuring things like the carbon footprint hidden inside everything we buy.

A way to picture it

Think of a recipe book in which every recipe's ingredients are themselves dishes with their own recipes. To throw a dinner for ten you don't just cook ten plates — you cook the sauces those plates need, and the stocks those sauces need, down and down. Leontief's inverse is the master shopping list that adds up every ingredient at every level, so you know the true total you must produce. The tool below lets you place the order and watch the hidden layers pile up.

A three-sector economy — agriculture, manufacturing, services. Three sliders set the final demand delivered to consumers; a fourth slider walks the rounds of production. Each industry's bar splits into the part going to final demand and the part swallowed as intermediate inputs by other industries, with a dashed outline for the fully converged total. As you advance the rounds the bars climb from the bare order toward roughly three times that.

Where it sits

Leontief turned Walras's abstract general equilibrium (also in this Library) into something you could compute with real numbers, descending from Quesnay's centuries-old dream of charting the economy's circulation. His table is a cousin of other ways of finding the steady state of a system that feeds back on itself — the same spirit as Markov chains, or the link-counting behind modern web search.

The original document
Original source text
Wassily Leontief · The Review of Economics and Statistics, Vol. 18, No. 3 (Aug. 1936), pp. 105–125 · doi:10.2307/1927837
The interindustry table
The paper proposes to draw, for the modern United States, the kind of picture François Quesnay had sketched for 18th-century France: a tableau that follows goods as they pass from one industry to another. Leontief lays out a grand table of the American economy in which each industry appears as both a row — where its product goes — and a column — what it consumes — with households and other final users along the margin.
From flows to coefficients
Dividing each industry's purchases by its level of output, Leontief replaces the raw money flows with technical coefficients: fixed amounts of each input required per unit of output. He argues that these ratios can be treated as stable features of the prevailing technology rather than as accidents of a single year.
The system of equations
The accounting requirement that each industry's output equal the sum of what every other industry buys from it plus what goes to final use becomes a system of simultaneous linear equations. Solving the system gives the total output every industry must produce to satisfy any given schedule of final demand — with the indirect, supply-chain requirements automatically included.
The first American input–output table
Leontief applies the scheme to actual statistics, presenting numerical input–output tables for the United States economy of 1919 (the 1929 table follows in his later work) — the first empirical realization of a closed, solvable model of an entire national economy.
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Cambridge, Massachusetts · 1936