5.10 Aggregation of elasticities for many goods The three aggregation relationships presented in this chapter can be generalised to any number of goods.

This problem asks you to do so. We assume that there are n goods and that the share of income devoted to good i is denoted by si. We also define the following elasticities:

ei, I = �xi

�I

· I xi

, ei, j = �xi

�pj

· pj xi

.

a.

b.

c.

Homogeneity: an j=1

= ei, j + ei, I = 0.

Engel aggregation: an i=1

= si ei, I = 1.

Cournot aggregation: an i=1 si ei, j = −sj

.