By David F. Heathfield (auth.)
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Additional resources for Production Functions
Example text
This is not possible with the CES function since dividing the function expressed in terms of current-valued variables by that expressed in base-period valued variables does not yield a similar function in terms of indices for each variable. The value taken by the efficiency term (y) cannot therefore be made independent of 8 or of the units of Y, K and L. The aggregation problem raised in the case ofthe Cobb-Douglas function is equally applicable here. If the CES function is used to describe the production process of a firm, thenit ought not to be used to describe the aggregate production processes of all the firms in industry.
This approach is based on the general equilibrium model of Leon Walras [58] who first published his Elements d'economie politique pure in 1874. Samuelson [49] ascribes its origins to Walras's predecessors, the physiocrats, and Quesnay's Tableau Economique. For a more contemporary exposition of the principles involved, see Sraffa [52] and Dorfman et al. [19]. Now if interest is concentrated on the flows of goods between processes, it is fairly obvious that by redefining what is a process one alters the whole structure of the production function.
E. the inverse elasticity of the supply curve for labour. If we call this EWL, we may write ae aL = W(EWL+ 1). " . ae ar For profi t maxtmlSlng, aL = aL ar aL = W(EWL+ 1). therefore From the adding-up requirement and constant returns to scale ar + ar 1'= a? aLL. e. ) Therefore l' = ar + W(EWL+ I)L. '_ ar! e. r- B= MK-B +aL-B. In this case, however, a is (~) 11 A (€WL + I) and if we write this in we have r- 9= MK-9 + (~)l/A(€WL+ I)L-8. This gives rise to two pertinent questions with regard to production functions.