The general formula for elasticity (the "y-elasticity of x") is:
Ex,y = % change in x / % change in y,
or, more formally,
Ex,y = (dx/dy)(y/x).
There are five cases of elasticity. (Elasticity is almost always referred to as a positive value, i.e. the absolute value in the case of a kind of elasticity that is normally negative.)
Figure 1: Example of Perfect Elasticity and Perfect Inelasticity.
Keeping in mind the example of Price elasticity of demand we consider figures with x=Q horizontal and y=P vertical.
E = 0 Perfectly inelastic. This special case of elasticity is represented in the right figure above. Any change in P will have an no effect on Q.
E < 1 Inelastic. The proportional change in Q is less than the proportional change in P.
E = 1 Unit elasticity. The proportional change in one variable is equal to the proportional change in another variable.
E > 1 Elastic. The proportional change in Q is greater than the proportional change in P.
E = infinity Perfectly elastic. This special case of elasticity is represented in left figure above. Change in P is zero so by definition elasticity is undefined--hence infinite.
Figure 2: Example of unit elasticity for a supply line passing through the origin.
A common mistake for students of economics is to confuse elasticity with slope. Elasticity is the slope on a loglog graph[?], not on a regular graph (taking into account whether the independent variable is on the horizontal or the vertical axis). Consider the information in figure 2--this is a special case which illustrates that slope and elasticity are different. In the above example the slope of S1 is clearly different than the slope of S2, but since the rate of change of P relative to Q is always proportionate both S1 and S2 are unit elastic (i.e. E = 1).
Elasticity is an important concept in understanding the incidence of indirect taxation[?]. marginal concepts[?] as they relate to the theory of the firm[?]. Weath inequality[?] and different types of goods[?] as they relate to the theory of consumer choice[?] and the Lagrange Multiplier. Elasticity is also crucially important in any discussion of welfare distribution: in particular consumer surplus, producer surplus, or government surplus[?].
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