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8 - From input-output coefficients to the Cobb–Douglas function

Published online by Cambridge University Press:  18 December 2009

Thijs ten Raa
Affiliation:
Universiteit van Tilburg, The Netherlands
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Summary

Introduction

The macroeconomic production function of an economy summarizes the maximum level of net output that is possible for any combination of factor inputs. It is customary to consider two factor inputs, capital and labor (Solow 1957). The disaggregation and extension to more factor inputs is conceptually straightforward (Johansen, 1972). The macroeconomic concept of a level of net output is more problematic. The net output of an economy is a commodity vector and the measurement of a “level” requires a price system. But which price system? This problem of value has puzzled economists for centuries. Classical economists consider capital a produced commodity and labor the ultimate factor input. For each commodity they calculate the labor costs. In chapter 5 we saw that the consequent price system is invariant with respect to the composition of final demand. It could be used to measure the level of net output. If there are two factor inputs, the situation is more complicated. The PPF is no longer straight, but curved. A simple example may be used to illuminate the issue. Consider an economy with two commodities but no material inputs. For commodity 1 we need one unit of labor plus one unit of capital. For commodity 2 we need two units of labor plus one unit of capital. Let the economy be endowed with three units of labor and two units of capital. The production possibilities are plotted in figure 8.1.

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Publisher: Cambridge University Press
Print publication year: 2006

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References

Hildenbrand, W. (1981). “Short-Run Production Functions Based on Microdata,” Econometrica 49 (5), 1095–1125CrossRefGoogle Scholar
Houthakker, H. S. (1956). “The Pareto-Distribution and the Cobb–Douglas Production Function in Activity Analysis,” Review of Economic Studies 23, 27–31CrossRefGoogle Scholar
Johansen, L. (1972). Production Functions, Amsterdam, North-HollandGoogle Scholar
Solow, R. M. (1957). “Technical Change and the Aggregate Production Function,” Review of Economics and Statistics 39 (3), 312–20CrossRefGoogle Scholar

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