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The elasticity at a point is the limit of the arc elasticity between two points as the separation between those two points approaches zero. The concept of elasticity is widely used in economics and metabolic control analysis (MCA); see elasticity (economics) and elasticity coefficient respectively for details.
The y arc elasticity of x is defined as: , = % % where the percentage change in going from point 1 to point 2 is usually calculated relative to the midpoint: % = (+) /; % = (+) /. The use of the midpoint arc elasticity formula (with the midpoint used for the base of the change, rather than the initial point (x 1, y 1) which is used in almost all other contexts for calculating percentages) was ...
An example in microeconomics is the constant elasticity demand function, in which p is the price of a product and D(p) is the resulting quantity demanded by consumers.For most goods the elasticity r (the responsiveness of quantity demanded to price) is negative, so it can be convenient to write the constant elasticity demand function with a negative sign on the exponent, in order for the ...
It gives the contact stress as a function of the normal contact force, the radii of curvature of both bodies and the modulus of elasticity of both bodies. Hertzian contact stress forms the foundation for the equations for load bearing capabilities and fatigue life in bearings, gears, and any other bodies where two surfaces are in contact.
In continuum mechanics, the Michell solution is a general solution to the elasticity equations in polar coordinates (,) developed by John Henry Michell in 1899. [1] The solution is such that the stress components are in the form of a Fourier series in .
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Arc Elasticity is a second solution to the asymmetry problem of having an elasticity dependent on which of the two given points on a demand curve is chosen as the "original" point will and which as the "new" one is to compute the percentage change in P and Q relative to the average of the two prices and the average of the two quantities, rather ...