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Total revenue, the product price times the quantity of the product demanded, can be represented at an initial point by a rectangle with corners at the following four points on the demand graph: price (P 1), quantity demanded (Q 1), point A on the demand curve, and the origin (the intersection of the price axis and the quantity axis).
A good with an elasticity of −2 has elastic demand because quantity demanded falls twice as much as the price increase; an elasticity of −0.5 has inelastic demand because the change in quantity demanded change is half of the price increase. [2] At an elasticity of 0 consumption would not change at all, in spite of any price increases.
Profit maximization means that the derivative of with respect to Q is set equal to 0: ′ + ′ = where P'(Q) = the derivative of the inverse demand function. C'(Q) = marginal cost–the derivative of total cost with respect to output. This yields:
If income elasticity of demand is lower than unity, it is a necessity good. [3] This observation for food, known as Engel's law , states that as income rises, the proportion of income spent on food falls, even if absolute expenditure on food rises.
In economics, elasticity measures the responsiveness of one economic variable to a change in another. [1] For example, if the price elasticity of the demand of a good is −2, then a 10% increase in price will cause the quantity demanded to fall by 20%.
Curves which cut through the positive part of the quantity axis and have positive quantity supplied (Q = a) even if the price is zero have a > 0 and hence always have inelastic supply. Curves which go through the origin have a = 0 and hence have an elasticity of 1. When looking at the price elasticity of supply, there are five types.
The index varies from zero (when demand is infinitely elastic (a perfectly competitive market) to 1 (when demand has an elasticity of −1). The closer the index value is to 1, the greater is the difference between price and marginal cost. The Lerner index increases as demand becomes less elastic. [34]
The concept of the elasticity of substitution was developed by two different economists, each with their own focus. One of these economists was John Hicks, who defined elasticity of substitution as the change in percentage in the relative number of factors of production used, given a particular change in percentage in relative prices or marginal products.