10.11 The elasticity of substitution and input demand elasticities The definition of the (Morishima) elasticity of substitution sij in Equation 10.54 can be recast in terms of input demand elasticities. This illustrates the basic asymmetry in the definition.

a. Show that if only wj changes, sij ¼ ex c i ,wj # ex c j ,wj

:

b. Show that if only wi changes, sji ¼ ex c j ,wi # ex c i ,wi

:

c. Show that if the production function takes the general CES form q ¼ P n xq i

& '1=q for r 6¼ 0, then all of the Morishima elasticities are the same: sij ¼ 1/(1 # r) ¼ s. This is the only case in which the Morishima definition is symmetric.