Price elasticity refers to the extent of change in consumer's demand for slight differences in prices of goods; on a normal day, demand increases when price reduces, and it reduces when the price is on the increase.
The price elasticity of demand will be inelastic if consumers know that there are few substitutes to a commodity. Price elasticity is basically all about substitutes. If the price of a commodity increases and the commodity has many close substitutes or it is easy to find its replacements, then the demand will be elastic.
However, if there are few close substitutes for a product whose price just got hiked or it is hard to find the substitutes, the price elasticity would be less elastic. The demand would have a unitary elasticity if the change in price results in an equal change in demand, while it is zero plasticity if a change in price does not cause any change in demand.
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