Equivalently, it is the ratio of the infinitesimal change of the logarithm of a function with respect to the infinitesimal change of the logarithm of the argument.
Rules for finding the elasticity of products and quotients are simpler than those for derivatives.
Then[2] The derivative can be expressed in terms of elasticity as Let a and b be constants.
This relationship provides an easy way of determining whether a demand curve is elastic or inelastic at a particular point.
First, suppose one follows the usual convention in mathematics of plotting the independent variable (P) horizontally and the dependent variable (Q) vertically.
The slope of a ray drawn from the origin through the point is the value of the average function.
[6] If the tangent line is extended to the horizontal axis the problem is simply a matter of comparing angles created by the lines and the horizontal axis.
If, however, one follows the convention adopted by economists and plots the independent variable P on the vertical axis and the dependent variable Q on the horizontal axis, then the opposite rules would apply.
since, An example of semi-elasticity is modified duration in bond trading.