When a fall in price of a commodity reduces total expenditure and a ri

When a fall in price of a commodity reduces total expenditure and a rise in price increases it, price elasticity of demand will be :

= 1
> 1
Infinity
This question was previously asked in
UPSC CAPF – 2014
The relationship between a change in price and the resulting change in total expenditure (Price * Quantity) reveals the price elasticity of demand.
If a fall in price reduces total expenditure (P↓, TE↓), it means the increase in quantity demanded (Q↑) was proportionally smaller than the decrease in price (ΔQ% < |ΔP%|). This is the characteristic of inelastic demand. If a rise in price increases total expenditure (P↑, TE↑), it means the decrease in quantity demanded (Q↓) was proportionally smaller than the increase in price (ΔQ% < |ΔP%|). This is also the characteristic of inelastic demand. In both cases, the price elasticity of demand (|Ed|) is less than 1.
For inelastic demand (|Ed| < 1), price and total expenditure move in the same direction: if price increases, total expenditure increases; if price decreases, total expenditure decreases.
Conversely, for elastic demand (|Ed| > 1), price and total expenditure move in opposite directions: if price increases, total expenditure decreases; if price decreases, total expenditure increases. For unit elastic demand (|Ed| = 1), total expenditure remains unchanged with a change in price.