AGGREGATION AND MULTIPLICATIVE PRODUCTION FUNCTIONS

Abstract

Consider a sector of the economy composed of several fully integrated industries, producing final products only. Write the sectoral production function (1) Q (t) = A(t)K(t) L(t)1- , where Q = output, K = capital input, L = labor input, t = time, and A is a technology parameter. Further, let the production function for industry i be written (2) Qi(t) = Ai(t)Ki(t) i Li(t)1- i. Now, the percentage rate of technical change -what Domar terms the "Residual" -- for the sector can be expressed (3) A = Q - K - (1- )L, A Q K L and similarly for an industry. The problem, then, is to find a method for weighting and aggregating the industry production functions which leaves the rate of technical change invariant with respect to aggregation. Professor Domar's solution is to raise both sides of (2) to the vi power, where vi= Qi and to multiply Q , industry production functions together to obtain the sector function.

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Document Details

Document Type
Technical Report
Publication Date
Feb 01, 1963
Accession Number
AD0296818

Entities

People

  • Benton F. Massell

Organizations

  • RAND Corporation

Tags

Communities of Interest

  • Materials and Manufacturing Processes

DTIC Thesaurus Topics

  • Additives (Chemicals)
  • Corporations
  • Equations
  • Government Procurement
  • Governments
  • Manufacturing
  • Procurement
  • Production
  • Productivity
  • Residuals

Readers

  • Approximation Theory.
  • Educational Psychology
  • Industrial Economics