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The standard CES production function permits one to obtain an elasticity of substitution between inputs different from 1, as dictated by the Cobb-Douglas production function. However, the CES elasticity of substitution must be constant for all pairs of inputs. The generalized CES production function permits varying elasticities of substitution among pairs of inputs.

B1. Generalized CES Production Function

where L = labour, K = capital, M = materials and supplies, and q = product.

If rho = rhoL = rhoK = rhoM, we get the standard CES production function. If also, rho = 0, ie sigma = 1/(1+rho) = 1, we get the Cobb-Douglas production function.

Set the parameters below to re-run with your own Generalized CES parameters.

The restrictions ensure that the least-cost problems can be solved to obtain the underlying Generalized CES cost functions, using the parameters as specified.

Intermediate (and other) values of the parameters also work.