This Demonstration considers elasticity, which is one of the central concepts in theoretical and empirical economics. Elasticity is indispensable because it shows relative (per cent) change of a given variable due to relative (per cent) change in another variable. We use a smooth non-negative function to demonstrate some useful properties of elasticity analysis. Visualization of different ratios, which are usually treated analytically, can be instructive for better understanding of elasticity and related economic concepts—for example, elasticity of demand function.

Change the "shape" slider to vary . The "special case" button returns the point where slopes of average and tangent curves are equal, so elasticity is effectively equal to one. Switch the checkboxes on and off to better study the interplay between functions.

Elasticity is a function that can be built from an arbitrary function . Elasticity at a certain point is usually calculated as

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We have chosen , as it has two inflection points (local minimum and local maximum), and also sections that slope up and down. As long as we have four terms on the right-hand side of the above expression, elasticity can be expressed in many forms. One interesting form, from an economic viewpoint, is the ratio of slopes of tangent and average curves that are shown on the upper plot:

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The bottom plot reflects all three functions: average , tangent and elasticity itself for a given . For each , the elasticity function defines elasticity values for each point of . Notice that the average line in our example is always non-negative. At inflection points the tangent is zero, as is the elasticity. Elasticity is negative for the downward-sloping section of .