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
EX = QX · PX ...............Eq. III
By differentiating Eq. III with respect to P, we get marginal expenditure (ME), as
ME= δEx / δPX = QX + {PX + (δQX/δPX)}
=QX {1+ (PX / QX). δQX/δPX} .................... Eq. IV
In Eq. 3, term (PX/QX) x (δQX/δPX) gives the price elasticity of consumer expenditure eCE in response to change in price. Which is
(PX/QX x (δQX/δPX) =ece
By substitution, we get
ME = δEX/δPX
= QX (1-ece)
It can be inferred from Eq.IV that whether expenditure decreases, increases or remains constant depends on whether
It relies on whether
