If we can observe how much quantity demanded changes when price changes, we can calculate the elasticity. The precise definition of price elasticity, Eo. is the percentage change in quantity demanded divided by the percentage change in price. For convenience, we drop the minus signs, so elasticities are all positive.

We can calculate the coefficient of price elasticity numerically according to the following formula.

Price elasticity of demand = ED
= Percentage change in quantity demanded
. percentage change in price

Now we can be more precise about the different categories of price elasticity:

When a I percent change ‘in price calls forth more than a I percent change in quantity demanded, the good has price-elastic demand. For example, if a 1 percent increase in price yields a 5 percent decrease in quantity demanded, the commodity has a highly price-elastic demand.

When a 1 percent change in price produces I’ than a 1 percent change in quantity demand the good has Price-inelastic demand. This case occurs, for instance, when a I percent increase ‘ ‘price yields only a 0.2 percent decrease in demand.

One important special case is unit-elastic demand, which occurs when the percentage’ change in quantity is exactly the same as the percentage change in price. In this case, a I percent increase in price yields a 1 percent decrease in demand. We will see later that this condition implies that total expenditures on the commodity (which equal P X CD stay the same even when the price changes.

To illustrate the calculation of elasticity. let us examine the simple case of the response of purchases to the price increase which is shown in Figure 4-1. In the original situation. price was 90 and quantity. demanded was 240 units. A price increase to 110 led . consumers to reduce their purchases to 160 units. In Figure 4-1. consumers were originally at point A but moved along their demand schedule to point B when  the price rose.

Table 4·1 shows how we calculate price elasticity The price increase is 20 percent, with the resulting quantity decrease being 40 percent. The price elasticity of demand is evidently ED = 40/20 = 2 . The price elasticity is greater than 1, and this good there- fore has price-elastic demand in the region from to B

 

Market equilibrium is originally at point A. In response to a 20 percent price increase. quantity demanded declines .40 percent, 10 point B. Price elasticity is EP =40/20 =2.Demand is therefore elastic in the region from A to B.

Case A: Price = 90 and quantity = 240
Case B: Price = 110 and quantity = 160
Percentage Price change = P/p = 20/100 = 20%
Percentage Price change = Q/Q = -80/200 = -40%
price elasticity = ED = 40/20 = 2

TABLE 4·1. Example of Good with Elastic Demand .Consider the situation where price is raised from 90 to 110.According to the demand curve, quantity demanded falls from 240 to 160. Price elasticity is the ratio of percentage change in quantity divided by percentage change in price. We drop the minus signs from the numbers so that all elasticity are positive.

In practice, calculating elasticity is somewhat tricky, and we emphasize three key steps where you have to be especially careful. First, recall that we drop the minus signs from the numbers, thereby treating all percentage changes as positive. That means all elasticity are written as positive numbers, even though prices and quantities demanded move in opposite

directions for downward-sloping demand curves.

Second, note that the definition of elasticity uses percentage changes in price and demand rather than absolute changes. That means that a change in the units of measurement does’ not affect the elasticity. So whether we measure price in pennies or dollars, the price elasticity stays the same.

A third point concerns the exact procedure for calculating percentage changes in price and quantity. The formula for a percentage change is 4P/P. The value of 4P in Table 4-1 is clearly 20 = 110 – 90. But it’s not immediately clear what value we should use for P in the denominator. Is it the’ original value of 90, the final value of 110, or something in between?
For very small percentage changes, such as from 100 to 99, it doesn’t much matter whether we use 99 or 100 as the denominator. But for larger changes. the difference is significant. To avoid ambiguity, we will take the average price to be the base price for calculating price changes. In Table 4-1, we used the average of the two prices [P = (90 + llO;/2 = 100)
as the base or denominator in the elasticity formula . Similarly, we used the average quantity [Q = (160 + 240)/2 = 200] as the base for measuring the percentage change in quantity. The exact formula for calculating elasticity is therefore.

 

where PI and Cb represent the original price and quantity and P2 and Cb stand for the new price and quantity.

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