Price elasticity is a very important notion in economics, which, however, is not always recognized by students. Let’s imagine that certain firm increases the prices for its products. Many of us may suppose that in this case, the firm has an opportunity to increase the total revenue from the sale of products. But in fact, it doesn’t. It is even possible, that increase in price will lead to the decrease in total revenue because the demand on firm’s product also decreases. That’s why the price elasticity has the great significance for producer of goods and we’re going to tell you how it works in this article.

By the definition, the price elasticity of demand for some product is a sensitivity of consumers to a price change. There are some products like meat or fruits for which small change in price causes a great change in the quantity purchased. So, the demand for such products is elastic. But, there are other products (bread, salt) for which the large price change causes the small change in the quantity purchased. Thus, the demand for such products is inelastic. We use the coefficient of price elasticity of demand,@$E_d@$, to determine whether the demand is elastic or inelastic:

@$ E_d = \dfrac{\%\ Change\ in\ Quantity\ Demanded}{\%\ Change\ in\ Price} @$.

From the analysis of the formula, we clearly see that there are three cases: if @$|E_d| < 1@$, then demand is inelastic; if @$|E_d| > 1@$, then demand is elastic and, finally, if @$|E_d| = 1@$ we have the unit elasticity.

We can calculate the percentage change in quantity demanded by dividing the change in quantity demanded by the original quantity demanded. Similarly, we can calculate the percentage change in price by dividing the change in price by the original price. Then, the formula becomes:

@$ E_d = \dfrac{Change\ in\ Quantity\ Demanded}{Original\ Quantity\ Demanded}\dfrac{Original\ Price}{Change\ in\ Price} @$.

Let’s consider an example. Given that the price of PC’s is increased from $3,500 to $4,700. As a result, the quantity demanded of PC’s has decreased from 150 units to 80 units. What is the coefficient of price elasticity of demand?

Solution:

For practical calculations, we use the so-called midpoint formula:

@$ E_d = \dfrac{Change\ in\ Quantity\ Demanded}{Sum\ of\ Quantities/2}\dfrac{Sum\ of\ Prices/2}{Change\ in\ Price} @$,

@$ E_d = \dfrac{Q_1-Q_0}{Q_1+Q_0}\dfrac{P_1+P_0}{P_1-P_0} @$

here, @$Q_0@$,@$Q_1@$ is the original and current quantity demanded, respectively;@$P_0@$,@$P_1@$ is the original and current price, respectively.

Let’s substitute the numbers into the formula:

@$ E_d = \dfrac{80-150}{80+150}\dfrac{4,700+3,500}{4,700-3,500} = -2.08 @$

As we can see from it,@$|E_d|>1@$ , therefore, the demand for PC’s is elastic.

We can verify whether we calculate the price elasticity of demand correctly by the total revenue test. By the definition, the total revenue is the income the firm receives from the sale of some given quantities of a product or service:

@$ TR = P Q @$,

here, @$P@$ is the product price, @$Q@$ is the quantity demanded.

Thus, we get:

@$TR_0 = P_0 Q_0 = $3,500\times 150 = $525,000@$,

@$TR_1 = P_1 Q_1 = $4,700\times 80 = $376,000@$.

As we can see from the graph, the price increases while the total revenue decreases. Therefore, from our example we can see: when demand is elastic, the firm can increase its total revenue by decreasing the product’s price.

Let’s now consider the price elasticity of supply. By the definition, the price elasticity of supply for some product is a sensitivity of supply of product to the price change. Thus, if supply changes more than price, we can say that supply is elastic. And if supply changes less than price, then we can say that supply is inelastic. We use the coefficient of price elasticity of supply, @$E_s@$, to determine whether the supply is elastic or inelastic:

@$E_s = \dfrac{\%\ Change\ in\ Quantity\ Supplied }{\%\ Change\ in\ Price}@$

And we can interpret the coefficient of price elasticity in the same way as the coefficient of price elasticity of demand.

We calculate the percentage change in quantity supplied by dividing the change in quantity supplied by the original quantity supplied. Similarly, we can calculate the percentage change in price by dividing the change in price by the original price. Then, we get:

@$ E_s = \dfrac{Change\ in\ Quantity\ Supplied}{Original\ Quantity\ Supplied}\dfrac{Original\ Price}{Change\ in\ Price} @$

Again, for practical calculations, we can use the midpoint formula:

@$ E_s = \dfrac{Q_1-Q_0}{Q_1+Q_0}\dfrac{P_1+P_0}{P_1-P_0} @$

here, @$Q_0@$, @$Q_1@$ is the original and current quantity supplied, respectively; @$P_0@$, @$P_1@$ is the original and current price, respectively.

Let’s consider another example. Given, that the price of MP3 players increases from $100 to $150. As a result, the quantity supplied of MP3 players increases from 3,000 units to 4,000 units. What is the coefficient of price elasticity of supply?

Solution:

From the formula we get:

@$ E_s = \dfrac{4,000-3,000}{4,000+3,000}\dfrac{150+100}{150+100} = 0.71@$.

As we can see from the formula, @$E_s < 1@$, therefore, the supply for MP3 players is inelastic.

As we can see, the analysis of the price elasticity has a large significance for the producers and help the firm to increase its income.