Multipliers, factor contents, and productivity

The theory underlying indirect, multiplier effects of final consumption is detailed in this chapter. The classical example is the computation of the factors of production, first and foremost labor, embodied in final products. These embodiments are determined by taking the Leontief inverse of the matrix of direct input-output coefficients. Conditions on the input-output matrix which are both necessary and sufficient for the convergence of the multiplier effects are presented. Further multiplier effects due to household consumption are incorporated. The less labor is embodied in a product of an economy, the more productive the economy is in making that product. The relationship between input-output analysis and productivity measurement is detailed. The neoclassical approach of measuring total factor productivity by measuring input reductions using fixed prices has been criticized and alternative "effective" industry productivity growth rates have been presented in the input-output literature, but the two approaches will be demonstrated to be perfectly consistent. The analysis is also shown to encompass inefficiency measures and service productivity measures.