Show that the share of income spent on a good x is sx 5 d ln E d ln px

, where E is total expenditure.

esponses 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. In the Cobb–Douglas case 1σ 5 12, the following relationship holds between the own-price elasticities of x and y: ex, px 1 ey, py 5 22.

b. If σ . 1, then ex, px 1 ey, py , 22, and if σ < 1, then ex, px 1 ey, py . 22. Provide an intuitive explanation for this result.

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