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Demand Elasticity Essay

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Price elasticity of demand
Not to be confused with Price elasticity of supply.
PED is derived from the percentage change in quantity (%ΔQd) and percentage change in price (%ΔP).

Price elasticity of demand (PED or Ed) is a measure used in economics to show the responsiveness, or elasticity, of the quantity demanded of a good or service to a change in its price. More precisely, it gives the percentage change in quantity demanded in response to a one percent change in price (holding constant all the other determinants of demand, such as income). It was devised by Alfred Marshall.

Price elasticities are almost ...view middle of the document...

 The formula for the coefficient of price elasticity of demand for a good is:

E_d = \frac{\%\ \mbox{change in quantity demanded}}{\%\ \mbox{change in price}} = \frac{\Delta Q_d/Q_d}{\Delta P/P}

The above formula usually yields a negative value, due to the inverse nature of the relationship between price and quantity demanded, as described by the "law of demand". For example, if the price increases by 5% and quantity demanded decreases by 5%, then the elasticity at the initial price and quantity = −5%/5% = −1. The only classes of goods which have a PED of greater than 0 are Veblen and Giffen goods. Because the PED is negative for the vast majority of goods and services, however, economists often refer to price elasticity of demand as a positive value (i.e., in absolute value terms).

This measure of elasticity is sometimes referred to as the own-price elasticity of demand for a good, i.e., the elasticity of demand with respect to the good's own price, in order to distinguish it from the elasticity of demand for that good with respect to the change in the price of some other good, i.e., a complementary or substitute good. The latter type of elasticity measure is called a cross-price elasticity of demand.

As the difference between the two prices or quantities increases, the accuracy of the PED given by the formula above decreases for a combination of two reasons. First, the PED for a good is not necessarily constant; as explained below, PED can vary at different points along the demand curve, due to its percentage nature. Elasticity is not the same thing as the slope of the demand curve, which is dependent on the units used for both price and quantity. Second, percentage changes are not symmetric; instead, the percentage change between any two values depends on which one is chosen as the starting value and which as the ending value. For example, if quantity demanded increases from 10 units to 15 units, the percentage change is 50%, i.e., (15 − 10) ÷ 10 (converted to a percentage). But if quantity demanded decreases from 15 units to 10 units, the percentage change is −33.3%, i.e., (15 − 10) ÷ 15.

Two alternative elasticity measures avoid or minimise these shortcomings of the basic elasticity formula: point-price elasticity and arc elasticity.
 Point-price elasticity

One way to avoid the accuracy problem described above is to minimise the difference between the starting and ending prices and quantities. This is the approach taken in the definition of point-price elasticity, which uses differential calculus to calculate the elasticity for an infinitesimal change in price and quantity at any given point on the demand curve: 

E_d = \frac{P}{Q_d}\times\frac{dQ_d}{dP}

In other words, it is equal to the absolute value of the first derivative of quantity with respect to price (dQd/dP) multiplied by the point's price (P) divided by its quantity (Qd).

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