If we place so much emphasis on the sign, why is it ignored?
How does it do this?
As the price increases (plus), there will be a decrease (minus) in the quantity demanded. Therefore, in the formula, there will be a minus change in quantity divided by a plus change in price (or a plus change in quantity divided by a minus change in price). A plus by a minus will always give a minus. Therefore PRICE ELASTICITY OF DEMAND for Normal Goods is always negative.
The sign is also used to differentiate between Normal Goods and Inferior Goods when we are dealing with Income Elasticity of Demand. More of a Normal Good tends to be purchased if the national level of Income rises - this gives a plus by a plus which equals a plus. Less of a Normal Good tends to be purchased if the national level of Income falls - this gives a minus by a minus, which also gives a plus. Therefore INCOME ELASTICITY OF DEMAND for Normal Goods is always positive.
In discussing Cross Elasticity of Demand, you will see that the sign will show whether the goods are Substitute or Complementary Goods. Substitute Goods will always have a positive sign, and Complementary Goods will always have a negative sign.
Two points arise from this question.
The importance of the Sign is that it will show us whether the good in question is Normal, Giffen, or Inferior.
So, why do we ignore the Sign?
The sign is ignored because we only need to know the absolute value of the number. Having established whether the goods are Normal, or Giffen, or Inferior, we know how they are going to react with respect to a price change. Therefore, the sign serves no further useful purpose and can be ignored.
What we need to know now is not the direction (up or down) of the change in quantity, but the size of the change.
The nearer the absolute number is to zero, the more inelastic it is - it will remain inelastic for as long as it is less than zero. Unity, of course, is the one-to-one relationship between price and quantity - as price increases by 1% demand will decrease by 1%. Any absolute number greater than one is treated as being elastic - a 1% increase in price will bring about a greater than 1% decrease in demand.