5.9 More on elasticities Part

(e) of Problem 5.9 has a number of useful applications because it shows how price responses depend ultimately on the underlying parameters of the utility function.

Specifically, use that result together with the Slutsky equation in elasticity terms to show:

a.

b.

c.

In the Cobb–Douglas case (σ = 1), the following relationship holds between the own-price elasticities of x and y

:

ex, px

+ ey, py

= −2.

If σ > 1 then ex, px

+ ey, py

< −2, and if σ < 1 then ex, px

+ ey, pv

> −2. Provide an intuitive explanation for this result.

How would you generalise this result to cases of more than two goods? Discuss whether such a generalisation would be especially meaningful.