Input-Output Models

Abstract

Consider an economy that consists of three sectors: agriculture, machinery, and construction. Let the domestic output of each of these three sectors be denoted x₁, X₂ and X₃, respectively. Let the final demand in each sector be denoted y_i: final demand is typically broken down to private consumption, government consumption (say for defense), investment and foreign trade (exports less imports). For given final demand, say machines, we write

$$ {a_{21}}{\kern 1pt} {x_1}{\kern 1pt} + {\kern 1pt} {a_{22}}{\kern 1pt} {x_2}{\kern 1pt} + {\kern 1pt} {a_{23}}{\kern 1pt} {x_3}{\kern 1pt} + {\kern 1pt} [\frac{{\$ mach}}{{\$ Agr.}}]{\kern 1pt} [\$ Agr.][\frac{{\$ mach}}{{\$ mach}}][\$ mach][\frac{{\$ mach}}{{\$ Const}}][\$ Const]{y_2} = {x_2} \times {\kern 1pt} [Final{\kern 1pt} Demand{\kern 1pt} for{\kern 1pt} machines][Gross{\kern 1pt} output{\kern 1pt} of{\kern 1pt} machine{\kern 1pt} sector] $$

((6.1))