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Input–output

What every sector needs from the others.

A Leontief table says how much each sector must make for the others and for final demand. Cut demand for one, and the engine solves what all of them must make.

Try it liveRead the formats
A geoeconomics simulation on a globe in the CommandAGI workbench: oil flows from the Persian Gulf to China, India, Japan, South Korea, Europe and the United States drawn as arcs, each country coloured by its oil inflow, while the globe turns slowly from the Gulf toward the Pacific.
Recorded in the workbench: the geo-hormuz world on its globe. Its numbers are illustrative, not data.

The model

x = (I − A)⁻¹ f.

z is the relations between members, f the final demand, x each sector's output. A shock is a cut in final demand, f × (1 − restriction). The engine refuses a table whose spectral radius is 1 or more.

How the input–output system couples to the oil priceThe oil market's price sets the energy sector's restriction, a cut in its final demand of a quarter of the price rise. The Leontief system solves the output each of three sectors, energy, manufacturing and services, must make for the others and for final demand, re-solving only when the demand moves.The Leontief system iof × (1 − r)400 bn/d250 bn/d500 bn/dOil pricefrom the market's updateenergy.restriction0.25 × (price / 80 − 1)Energyfinal demand 350Manufacturingfinal demand 1,700Servicesfinal demand 2,400How the input–output system couples to the oil priceThe oil market's price sets the energy sector's restriction, a cut in its final demand of a quarter of the price rise. The Leontief system solves the output each of three sectors, energy, manufacturing and services, must make for the others and for final demand, re-solving only when the demand moves.The Leontief system iof × (1 − r)400 bn/d250 bn/d500 bn/dOil pricefrom the market's updateenergy.restriction0.25 × (price / 80 − 1)Energyfinal demand 350Manufacturingfinal demand 1,700Servicesfinal demand 2,400

Read the formats

Outputs, billion USD a day.

scripts/sites/case-studies.mjs hormuz stepped the shipped world at escalation 1.8. Each line is the system's solution that day.

geo-hormuz · io.<sector>.outputthe engine's numbers · simulation · 2026-11-04
day   0  price  $80.0  energy 1060.0  manufacturing 2890.0  services 3820.0
day  30  price $108.0  energy 1026.7  manufacturing 2885.8  services 3816.3
day  70  price $117.2  energy 1015.7  manufacturing 2884.4  services 3815.0
day  90  price  $91.5  energy 1046.3  manufacturing 2888.3  services 3818.5
day 120  price  $80.1  energy 1059.9  manufacturing 2890.0  services 3820.0

The ripple

Energy falls 4.2%. The others feel it less.

At the height of the crisis energy's output is 1,015.7 against 1,060.0, manufacturing's 2,884.4 against 2,890.0 (case-studies/hormuz/stats.json).

A requirements calculation. What the table computes is structural: what each sector must make. It is never a calibrated forecast. Real tables are in the Drive. BEA's input–output tables are in CommandAGI's Drive as consumes and produces relations (48 MB on dev). This world does not read them yet. Solved to 10⁻¹⁰. A Neumann series to a tolerance of 10⁻¹⁰ within 10,000 rounds. Running out of rounds is recorded, never hidden.

energy's required output at the height
−4.2%
manufacturing's
−0.2%
days solved, day 0 to day 120
121

Simulated

The energy sector's output through the crisis
The numbers
The energy sector's output through the crisis
DayEnergy output
01060
101060
201050
301030
401020
501020
601020
701020
801020
901050
1001060
1101060
1201060
ProvenanceFile cloud://global/examples/template-library/worlds/geo-hormuz/world.tsxOutput case-studies/hormuz/stats.jsonTool scripts/sites/case-studies.mjs hormuz: sim-engine.jsRan on This computer (dell-gb10-1)When

Change a coefficient. Solve it again.

Every rate is a number in the world's file.

Try it liveSee stock and flow