Economists use formulae like "elasticity" to measure the responsiveness of quantity demanded (and other things) to various influences.
Remember, the demand curve itself can shift, predictably. For example, an increase in consumer income can shift the demand for any good the consumer buys. In most cases, but not all, the increase in income increases demand -- shifts it to the right. To measure this response, we have the income elasticity of demand,
For example, suppose income in the country as a whole increases by 10% over a decade. We might observe that the demand for beer increases by 2.5% over the same time, even with no change in the price of beer. Then we would conclude that the income elasticity of demand for beer is 2.5/10 = 0.25. (According to the statistics I have, that's about right).
If the income elasticity is greater than one, we say that demand is income-elastic. It means that demand increases more than proportionately with income. If the income-elasticity is less than one, we say that demand is income-inelastic. Then demand increases less than proportionately to income. We might even observe that the income elasticity of demand is less than one, for some goods. That would mean that the good is an "inferior good." Recall, an "inferior good" is a good for which demand decreases as income goes up -- hamburgers, for example. Then the change in income and the change in quantity will have opposite signs. The quotient (and so the elasticity) is negative.
Looking back at the beer example above, we see that the demand for beer is income-inelastic, but beer is not an inferior good. For some consumers, beer may be an inferior good, but there are enough beer-drinkers who increase their consumption when their income is higher, so that on the average, beer consumption rises with income. But not by much -- 0.25 is a quite small elasticity of demand.
Since we now have two kinds of elasticity, from here on we will say "price elasticity" when we mean the elasticity with respect to price, and there might be any ambiguity. We will always say "income elasticity," when that is what we mean. Just "elasticity," by itself, always means the price elasticity.
