Another vital relationship that is often referred to in economic analysis is the relationship between consumption expenditure andprice elasticity. From the law of demand, we know that quantity demanded of a commodity increases when its price falls. However, what happens to the total expenditure on that commodity: does it increase or fall? Relationship between price-elasticity and total consumption expenditure can be derived as follows. Suppose that total expenditure, E on a commodity Xat a given price,

P, all other prices remaining the same, is given by

E_X = Q_X · P_X ...............Eq. III

By differentiating Eq. III with respect to P, we get marginal expenditure (ME), as

ME= δE_x / δP_X = Q_X + {P_X + (δQ_X/δP_X)}

=Q_X {1+ (P_X / Q_X). δQ_X/δP_X} .................... Eq. IV

In Eq. 3, term (P_X/Q_X) x (δQ_X/δP_X) gives the price elasticity of consumer expenditure e_CE in response to change in price. Which is

(P_X/Q_X x (δQX/δP_X) =e_ce

By substitution, we get

ME = δE_X/δP_X

= Q_X (1-e_ce)

It can be inferred from Eq.IV that whether expenditure decreases, increases or remains constant depends on whether

It relies on whether