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# Elasticity (economics)

In economics, elasticity is the ratio of the incremental percentage change in one variable with respect to an incremental percentage change in another variable. Elasticity is usually expressed as a positive number (i.e., an absolute value) when the sign is already clear from context.

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## Generalised cases

Keeping in mind the example of price elasticity of demand, these figures show x=Q horizontal and y=P vertical.

Figure 1: Illustrations of Perfect Elasticity and Perfect Inelasticity.

Generalised cases of elasticity are frequently used in discussions that characterise circumstances for which detailed information is not available and/or irrelevant to the discussion. There are five such cases of elasticity.

• E = 0 Perfectly inelastic. This special case of elasticity is represented in the figure to the right above. Any change in P will have 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 the figure to the left above. Change in P is zero, so elasticity is infinite.

## Mathematical definition

The general formula for elasticity (the "y-elasticity of x") is:

$E_{x,y} = \frac{{\rm percent\ change\ in}\ x}{{\rm percent\ change\ in}\ y}$

or, more formally,

$E_{x,y} = \frac{\partial ln(x)}{\partial ln(y)} = \frac{\partial x}{\partial y}\frac{y}{x}$

A common mistake for students of economics is to confuse elasticity with slope. Elasticity is the slope of a curve on a loglog graph only, 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 from 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).

## Importance

Elasticity is an important concept in understanding the incidence of indirect taxation , marginal concepts as they relate to the theory of the firm, wealth 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 .

The concept of Elasticity was also an important component of the Singer-Prebisch Thesis which is a central argument in Dependency Theory as it relates to Development Economics .