Technical Coefficients
MODEL LAB · LABORATORY 03
Technical
Coefficients.
Convert monetary transactions into production requirements. The technical-coefficient matrix reveals the input structure of every industry and provides the mathematical bridge from an accounting table to an economic model.
a₁₁ = z₁₁/x₁a₁₂ = z₁₂/x₂a₂₁ = z₂₁/x₁a₂₂ = z₂₂/x₂
FROM VALUES TO REQUIREMENTS
The economy’s
production recipe.
A technical coefficient measures the monetary amount of input from sector i directly required to produce one monetary unit of output in sector j.
Supplying sector
The row identifies the input being supplied to the production process.
Producing sector
The column identifies the industry whose output is the denominator.
Direct requirement
The input needed directly—not the complete upstream requirement generated through all production rounds.
DERIVE ONE COEFFICIENT
Divide the transaction
by the buyer’s output.
Agriculture sells to manufacturing
z₁₂ = €25m
The transaction belongs to row 1 and column 2.
→
Manufacturing is the buyer
x₂ = €160m
Normalize by the total output of the purchasing industry.
→
Direct agricultural requirement
a₁₂ = 25/160 = 0.156
Manufacturing directly requires €0.156 of agriculture per €1 of output.
The coefficient is a technological proportion expressed in value terms. It does not mean manufacturing buys only €0.156—it means that amount is required for each euro of manufacturing output.
A-MATRIX LABORATORY
Reveal the input
structure.
Change transactions or sectoral output. ECONORIA calculates every direct requirement, reconstructs each production column and tests whether positive value added remains.
| INPUT ↓ / OUTPUT → | Agriculture | Manufacturing |
|---|---|---|
| Agriculture input | 0.267 | 0.156 |
| Manufacturing input | 0.200 | 0.219 |
| Intermediate share | 0.467 | 0.375 |
| Value-added share | 0.533 | 0.625 |
Agriculture technology
Manufacturing technology
TECHNOLOGICAL READINGBoth production columns leave a positive share for primary inputs. Agriculture is more intermediate-input intensive than manufacturing.
WHAT THE A MATRIX ASSUMES
Powerful structure.
Explicit limitations.
Fixed proportions
Inputs are used in constant ratios; producers do not substitute among inputs inside the basic Leontief technology.
Constant returns
Doubling output doubles every intermediate requirement represented by the column.
Homogeneous output
Each industry is treated as producing a representative bundle with a common input structure.
Stable technology
Benchmark coefficients are assumed sufficiently stable over the policy horizon being analysed.
SCIENTIFIC CHECKPOINT
Which output belongs
in the denominator?
To calculate a₁₂ from transaction z₁₂, which output must be used?
Technical coefficients describe the production recipe of the column industry.
