Input-Output Analysis

Origin. Wassily Leontief (1930s, Nobel 1973); extensively used in Soviet planning under the name "balance of the national economy."

Mechanism. The economy is represented as a matrix of inter-industry flows: each industry uses outputs of other industries as inputs. The input-output table shows how much of each industry's output goes to each other industry and to final demand. Given a desired final output, compute the total production required from each industry, accounting for all the intermediate inputs required.

Procedure. Construct the input-output table: rows are producing industries, columns are consuming industries, entries are flows. Compute the technical coefficients: what fraction of industry j's output comes from industry i? Given a final demand vector, solve (I - A)x = d, where A is the technical coefficient matrix, x is total output, and d is final demand. The solution gives the total output each industry must produce to meet final demand including all intermediate requirements.

Applies to. Economic planning, supply chain analysis, impact analysis (how does a change in one sector ripple through the economy), environmental accounting (tracking resource flows).

Limitations. Assumes fixed technical coefficients: no substitution, no technological change, no economies of scale. The coefficients are derived from historical data and become stale. Large shocks that change the production structure invalidate the matrix. Also: aggregation matters; aggregating heterogeneous industries obscures substitution possibilities.