Economists very often use the concept of elasticity, which they prefer to the usual derivative. How did this concept arise? More importantly, when is it used?
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Demand function
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For any given product, the quantities involved are measured in a particular unit, which might be an item, a kilogram or a tonne. The demand q is the quantity purchased during an agreed reference period—which the seller hopes will be optimal. This quantity clearly depends on the good's unit selling price p, but also on other factors: the product's quality; the prices of competing, substitute or complementary goods; the consumer's income; and so on. Classical economic theory assumes that consumers behave hedonistically and rationally. They seek to derive the greatest possible satisfaction from their purchases while remaining within the budget imposed by the share of their disposable income available for spending. Here, we shall consider only the influence of the price p on the demand q. We assume that the dependence of q on p is known. Mathematically, we postulate the existence of a function f such that q = f (p), called the product's demand function. We assume that f is positive, continuous and differentiable on all positive real numbers. We also assume that it is decreasing, as is generally the case except for rather unusual goods such as luxury products: people are usually willing to order more of a product when its price falls.
Graphically, a demand function is represented by what is naturally called a demand curve. An example is plotted below from both the economist's and the mathematician's perspectives: the former plots price on the x-axis and quantity on the y-axis, while the latter does the reverse.
