7.7 The “expenditure elasticity” for a good is defined as the proportional change in total expenditures on the good in response to a 1 percent change in income. That is, ePX X,I
 .

Prove that ePX  X,I
eX,I. Show also that ePX  X,PX
1 eX,PX

. Both of these results are useful for empirical work in cases where quantity measures are not available, because income and price elasticities can be derived from expenditure elasticities.