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Price Elasticity Measurement
Price elasticity of demand expresses the response of quantity demanded of a good to changes in ties price given the consumer income his tastes and prices of all other good. Thus price elasticity means the degree of responsiveness or sensitiveness of quantity demanded of a good to a change in its price unimportant method to measure price elasticity of demand is the percentage method which we explain below.
Percentage method, Price elasticity can be precisely measured by dividing the percentage change in quantity demanded in response to a small change in price, divided by the percentage change in price. Thus we can measure price elasticity by using the following formula:
Price elasticity = percentage change in quantity demanded / percentage change I price
Δq X 100 / q
Ep = q / Δ p / p = Δ q / q + Δq/p
= Δq/q X p/ Δq
= Δq / q X p/q
Where
Ep stands for price elasticity
Q stands for the original quantity
P stands for the original price
Δ stands for a small change
Mathematically speaking price elasticity of demand has a negative sing since the change in quantity demanded of a good is in opposite direction to the change in its price. When price falls quantity demanded rises and vice versa. But for the sake of convenience in understanding the magnitude of response of quantity demanded of a good to a change in ties price we ignore the negative sig and take into account only the numerical value of the elasticity. Thus if 2% change n price leads t a 4% change in quantity demanded of good A and 8% change in that of B, then the above formula of elasticity will give the value of price elasticity of good a equal to 2 and that of good B equal to 4. It indicates that the quantity demanded of good B changes relatively much more than that of good A in response to a given change in price. But if we had written minus signs before the numerical values of elasticity’s of the two goods, that is if we had written the elasticity as 2 and -4 respectively as strict mathematic would require us to do then since -4 is smaller than -2 we would have been misled in concluding that price elasticity of demand of B is less than that of good A. but as we have noted above response of demand for good B to the change in its price is greater than that of A it is better to ignore minus sign and draw conclusion form the absolute values of elasticity’s. Hence by convention minus sign before the value of price elasticity of demand is generally ignored in economics unless otherwise mentioned.
Midpoint method
When we calculate the price elasticity of demand we face a problem whether to use the initial price as the base of calculating percent change in price and initial quantity as the base of calculating the percent change in quantity demanded is response to a given percent change in price. For example suppose price of a commodity rises from $ 4 to $6.per unit and as a result the quantity demanded falls from 120 unties to 80 units. If we take initial price $ 4 as the base fo change in price then change in price by $ 2 amounts to 50 percent change in price (6-4/4 x 100 = - ½ x 100 = 50)
And taking initial quantity 120 units as the base for calculating percent change in quantity demanded, the there is 33.3 percent change in quantity demanded (120 – 80 / 120 x 100 = -1/3 x 100 = 33.3) thus we get price elasticity of demand as
Ep = 33 / 50 = 0.66
Let us now reverse the direction. Suppose the price of the commodity falls from $ 6. To $ 4 per unit and as a result quantity demanded increases from 80 units 120 units then now taking initial $ 6. As the base for calculating percentage change in price than there is 33 per cent change is prices (6-4/6 x 100 = 2/6 x 100 = 33) and taking 80 units as the base for calculating percentage change in quantity then the quantity demanded rises by 50 percent (120-80/ 80 x 100 = 40/80x 100 = 50). Thus we will now get 50/33 = 1.5 as the price elasticity of demand. It therefore follows that for the same absolute change in price and absolute change in price and absolute change in quantity demanded we get different values of price elasticity of demand if we use $ 4 or $6 as the base of calculating percentage change in price and 120 units or 80 units as the base for calculating percentage change in quantity demanded. To avoid this problem we use midpoint method for calculating the percentage changes in price and quantity demand. In mid –point method we calculate the parentage change in price or quantity demanded by taking midpoint of the initial and final values of price and quantity demanded respectively as the base. Thus in our above example midpoint (or in other words average) or prices of prices of $ 4 and $6 is 4+6/2 = 5 and midpoint (or average) of quantities demanded is 80 + 120 / 2 = 100 using this midpoint method the percentage change in price is 6-4/5 x 100 = 40 and percentage change in quantity demanded is 120-80/100 x 100 = 40. With these percentage changes in price and quantity demanded price of elasticity of demand will be
Ep = 40 / 40 = 1
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Percentage method, Price elasticity can be precisely measured by dividing the percentage change in quantity demanded in response to a small change in price, divided by the percentage change in price. Thus we can measure price elasticity by using the following formula:
Price elasticity = percentage change in quantity demanded / percentage change I price
Δq X 100 / q
Ep = q / Δ p / p = Δ q / q + Δq/p
= Δq/q X p/ Δq
= Δq / q X p/q
Where
Ep stands for price elasticity
Q stands for the original quantity
P stands for the original price
Δ stands for a small change
Mathematically speaking price elasticity of demand has a negative sing since the change in quantity demanded of a good is in opposite direction to the change in its price. When price falls quantity demanded rises and vice versa. But for the sake of convenience in understanding the magnitude of response of quantity demanded of a good to a change in ties price we ignore the negative sig and take into account only the numerical value of the elasticity. Thus if 2% change n price leads t a 4% change in quantity demanded of good A and 8% change in that of B, then the above formula of elasticity will give the value of price elasticity of good a equal to 2 and that of good B equal to 4. It indicates that the quantity demanded of good B changes relatively much more than that of good A in response to a given change in price. But if we had written minus signs before the numerical values of elasticity’s of the two goods, that is if we had written the elasticity as 2 and -4 respectively as strict mathematic would require us to do then since -4 is smaller than -2 we would have been misled in concluding that price elasticity of demand of B is less than that of good A. but as we have noted above response of demand for good B to the change in its price is greater than that of A it is better to ignore minus sign and draw conclusion form the absolute values of elasticity’s. Hence by convention minus sign before the value of price elasticity of demand is generally ignored in economics unless otherwise mentioned.
Midpoint method
When we calculate the price elasticity of demand we face a problem whether to use the initial price as the base of calculating percent change in price and initial quantity as the base of calculating the percent change in quantity demanded is response to a given percent change in price. For example suppose price of a commodity rises from $ 4 to $6.per unit and as a result the quantity demanded falls from 120 unties to 80 units. If we take initial price $ 4 as the base fo change in price then change in price by $ 2 amounts to 50 percent change in price (6-4/4 x 100 = - ½ x 100 = 50)
And taking initial quantity 120 units as the base for calculating percent change in quantity demanded, the there is 33.3 percent change in quantity demanded (120 – 80 / 120 x 100 = -1/3 x 100 = 33.3) thus we get price elasticity of demand as
Ep = 33 / 50 = 0.66
Let us now reverse the direction. Suppose the price of the commodity falls from $ 6. To $ 4 per unit and as a result quantity demanded increases from 80 units 120 units then now taking initial $ 6. As the base for calculating percentage change in price than there is 33 per cent change is prices (6-4/6 x 100 = 2/6 x 100 = 33) and taking 80 units as the base for calculating percentage change in quantity then the quantity demanded rises by 50 percent (120-80/ 80 x 100 = 40/80x 100 = 50). Thus we will now get 50/33 = 1.5 as the price elasticity of demand. It therefore follows that for the same absolute change in price and absolute change in price and absolute change in quantity demanded we get different values of price elasticity of demand if we use $ 4 or $6 as the base of calculating percentage change in price and 120 units or 80 units as the base for calculating percentage change in quantity demanded. To avoid this problem we use midpoint method for calculating the percentage changes in price and quantity demand. In mid –point method we calculate the parentage change in price or quantity demanded by taking midpoint of the initial and final values of price and quantity demanded respectively as the base. Thus in our above example midpoint (or in other words average) or prices of prices of $ 4 and $6 is 4+6/2 = 5 and midpoint (or average) of quantities demanded is 80 + 120 / 2 = 100 using this midpoint method the percentage change in price is 6-4/5 x 100 = 40 and percentage change in quantity demanded is 120-80/100 x 100 = 40. With these percentage changes in price and quantity demanded price of elasticity of demand will be
Ep = 40 / 40 = 1
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