7.10 A formal definition of what we have been calling the substitution elasticity is



 1

.

a. Interpret this as an elasticity—what variables are being changed and how do these changes (in proportional terms) reflect the curvature of indifference curves. (See also the discussion in Chapter 11 of the elasticity of substitution in the context of a production function.)

b. Apply the definition of given above to the CES utility function U(X, Y )
.

Show that
1 

1

 and that this value is constant for all values of X and Y, thereby justifying the CES function’s name.