Elasticity (economics)/Tutorials: Difference between revisions
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Elasticity of Demand (an example of the algebra of elasticity) | |||
Supposing that Q is the quantity of a product that would be bought by consumers when its price is P, and that Q is related to P by the equation: | |||
:::<math> Q = -AP + B</math> | |||
- then the elasticity of demand, ''E'', for the product is given by: | |||
:::<math>E = (dQ/Q)/(dP/P)</math>, or | |||
:::<math>E = (dQ/dP)(P/Q)</math>, | |||
- where dQ and dP are small changes in the values of Q and P. | |||
It can be shown that, for the simplified linear example,: | |||
:::<math>dQ/dP = -A</math> so that <math> E = -A(P/Q)</math> | |||
- and E will vary in value with different values of P and Q because as P increases the fraction P/Q will increase. | |||
The terms "''elastic''" and "''inelastic''" are applied to commodities for which E is respectively ''numerically'' (ie ignoring the sign) greater or less than 1. If the elasticity of demand for a product is greater than 1, a price increase will lead to a fall in the amount PQ spent on the product, because demand Q will fall more than the rise in P. Conversely, if its elasticity is numerically less than 1, a price rise will result in a rise in the amount spent on it. | |||
Cross elasticity of demand is defined as above in algebraic terms, except that Q is the quantity of one of the products that will be bought when P is the price of the other. | |||
Latest revision as of 10:42, 2 May 2008
Elasticity of Demand (an example of the algebra of elasticity)
Supposing that Q is the quantity of a product that would be bought by consumers when its price is P, and that Q is related to P by the equation:
- then the elasticity of demand, E, for the product is given by:
- , or
- ,
- where dQ and dP are small changes in the values of Q and P.
It can be shown that, for the simplified linear example,:
- so that
- and E will vary in value with different values of P and Q because as P increases the fraction P/Q will increase.
The terms "elastic" and "inelastic" are applied to commodities for which E is respectively numerically (ie ignoring the sign) greater or less than 1. If the elasticity of demand for a product is greater than 1, a price increase will lead to a fall in the amount PQ spent on the product, because demand Q will fall more than the rise in P. Conversely, if its elasticity is numerically less than 1, a price rise will result in a rise in the amount spent on it.
Cross elasticity of demand is defined as above in algebraic terms, except that Q is the quantity of one of the products that will be bought when P is the price of the other.