Input-output analysis is a quantitative technique for studying economic interdependencies among sectors, using structured matrices to represent the flow of goods and services. The Leontief production function models these relationships with a linear equation and assumes fixed input-output coefficients, no substitution, and a closed economy. This method provides a static analysis of economic interactions at a specific point in time.

1. Input – Output Analysis
 Definition:
Input-Output Analysis is a quantitative economic technique developed by
Wassily Leontief, used to study the interdependencies among different sectors
of an economy. It represents the flow of goods and services between
industries in a structured mathematical format.

2. Input-Output Table
• A matrix showing the inputs (resources) required by each sector from
others to produce outputs.
• Rows: Outputs of each sector distributed to other sectors.
• Columns: Inputs consumed by each sector from other sectors.

3. Leontief Production Function
 Leontief Production Function:
• Assumes a linear relationship between inputs and outputs: X=AX+YX = AX +
YX=AX+Y Where:
• XXX: Total output vector (n×1)
• AAA: Input-output coefficient matrix (n×n)
• YYY: Final demand vector (n×1)

4. Input-Output Coefficients

5. Core Equation

6. Assumptions
1. Linear Production Technology: Input-output relationships are fixed
(constant returns to scale).
2. No Substitution: Inputs are used in fixed proportions.
3. Closed Economy: Initially assumes no external trade (can be extended to
include imports and exports).
4. Static Analysis: Focuses on a snapshot in time rather than dynamic
changes.