TITLE:
A Nonparametric Formula Relating the Elasticity of a Factor Demand to the Elasticity of Substitution
AUTHORS:
James Feigenbaum
KEYWORDS:
Elasticity of Substitution, Elasticity of Labor Demand, Output Share
JOURNAL NAME:
Theoretical Economics Letters,
Vol.9 No.1,
February
20,
2019
ABSTRACT: It is well known for a Cobb-Douglas production
function that the elasticity of a factor demand is the inverse of the share of
output going to the other factors. Since Cobb-Douglas has a unit elasticity of
substitution, the demand elasticity trivially equals the ratio of the
elasticity of substitution to the share of output going to the other factor. I
show here that this result can be generalized to any constant returns to scale
production function. As a result, if a factor is known to be a substitute for
(complement of) other factors, the inverse of the share of output going to
other factors will be a lower (upper) bound for the factor’s elasticity of
demand.