Another use of a mathematical demand function is measuring how sensitive demand is to changes in the level of one of the determinants. Suppose we would like to assess whether the demand for broadband service will change much in response to a change in its price. One indicator of the level of response to a price change is the coefficient of the price term in the demand function equation, –800 P. The interpretation of the coefficient –800 is that for each increase of $1 in the monthly subscriber price, the number of monthly subscribers will decrease by 800 subscribers.

This observation provides some insight, particularly if the broadband firm is considering a price change and would like to know the impact on the number of subscribers. However, for someone who measures price in terms of a different currency, say Japanese yen, a conversion to U.S. dollars would be needed to appreciate whether the demand change implied by the coefficient value is large or modest. Another limitation of this approach to measuring the responsiveness of demand to a determinant of demand is that the observation may not apply readily to other communities that may have a larger or smaller population of potential customers.

An alternative approach to measuring the sensitivity of demand to its determinant factors is to assess the ratio of percentage change in demand to the percentage change in its determinant factor. This type of measurement is called an **elasticity of demand**.

Assessing the elasticity of demand relative to changes in the price of the good or service being consumed is called the *own-price elasticity* or usually just the **price elasticity**. As an illustration of this, suppose we want to measure the sensitivity of demand for broadband services corresponding to a modest change in its price. First, to determine the price elasticity, you need to clearly understand the settings for all the determinant factors because elasticity changes if you look at a different configuration of factor levels. Suppose we decide to find the price elasticity when P = $30, A = $5000, CP = $25, and DIPC = $33,000. Earlier we determined that the demand quantity at this setting was Q = 40,000 monthly subscribers.

If we let the price increase by 10% from $30 to $33 and repeat the calculation of Q in the demand function, the value of Q will decline to 37,600 subscribers, which is a decline of 2400 customers. As a percentage of 40,000 monthly customers, this would be a 6% decrease. So the price elasticity here would be

\[\text{Price elasticity} = \dfrac{–6\%}{10\%} = –0.6. \nonumber\]

Since the law of demand states that quantity demanded will drop when its price increases and quantity demanded will increase when its price decreases, price elasticities are usually negative numbers (other than special cases like Giffen goods, described earlier in this chapter).

Goods and services are categorized as being **price elastic** whenever the price elasticity is more negative than –1. In this category, the percentage change in quantity will be greater than the percentage change in price if you ignore the negative sign.

When the computed price elasticity is between 0 and –1, the good or service is considered to be **price inelastic**. This does not mean that demand does not respond to changes in price, but only that the response on a percentage basis is lower than the percentage change in price when the negative sign is ignored.

In those rare instances where price elasticities are positive, the product violates the law of demand. Again, these are similar to the Giffen goods discussed earlier.

By assessing sensitivity to changes on a percentage basis, it does not matter what units are used in the variable measurements. We could have constructed our demand function with a price measurement in cents or euros, and the price elasticity would have been the same. Also, if we wanted to compare the price elasticity of broadband service in this community with the price elasticity of broadband service in a larger community, we could compare the price elasticities directly without any need for further adjustment.

Another important class of elasticities is the response of demand to changes in income, or the **income elasticity**. For our broadband example, if we were to calculate the income elasticity at the same point where we calculated the price elasticity, we would have found an elasticity of 0.33. The interpretation of this value is as follows: For an increase of 1% in income levels, demand for broadband will increase by 0.33%.

When income elasticity of a product is greater than one, we call the product a **cyclic good**. The adjective “cyclic” suggests that this demand is sensitive to changes in the business cycle and will generally change more on a percentage basis than income levels. Luxury goods that customers can do without in hard economic times often fall in this category.

When income elasticity is between zero and one, we call the product a **noncyclic good**. Our broadband service falls in this category. The demand for noncyclic goods tends to move up and down with income levels, but not as strongly on a percentage basis. Most of the staple goods and services we need are noncyclic.

Normally we would expect demand for a good or service to increase when incomes increase and decrease when incomes decrease, other things being equal. However, there are arguably some exceptions that do not behave this way. Low-cost liquor, which might see increased use in hard economic times, is one of these possible exceptions. When income elasticity is negative, we call the product a **countercyclic good**.

When elasticities are calculated to measure the response of demand to price changes for a different good or service, say either a substitute product or complementary product, we call the calculated value a **cross-price elasticity**. Cross-price elasticities tend to be positive for substitute goods and negative for complementary goods. In our example, the competitor’s service is a substitute good. If we calculate the cross-price elasticity for changes in the competitor’s price on demand for broadband service at the point examined earlier, the result is 0.125.

Elasticities can be calculated for any factor on demand that can be expressed quantitatively. In our example, we could also calculate an advertising elasticity, which has a value of 0.5 at the given settings for the four factors in our demand function. This value indicates that an increase of 1% in our monthly advertising will result in a 0.5% increase in subscribers.

In interpreting and comparing elasticities, it is important to be clear whether the elasticity applies to a single business in a market or to all sellers in a market. Some elasticities, like price elasticities and advertising elasticities, tend to reflect greater sensitivity to changes in the factor when an elasticity is calculated for a single business than when assessed for the total demand for all sellers in a market. For example, we noted earlier that consumers will be unable to decrease gasoline consumption much, at least immediately, even if gasoline prices climb dramatically. This implies that gasoline is very price inelastic. However, this observation really applies to the gasoline industry as a whole. Suppose there was a street intersection in a city that has a gasoline station on every corner selling effectively the same product at about the same price, until one station increases its price dramatically (believing gasoline was highly inelastic to changes in price, so why not), but the other three stations leave their price where it was. If prices were clearly displayed, most customers would avoid the station that tried to increase the price and that station would see nearly all of its business disappear. In this situation where the competitors’ goods are highly substitutable, the price elasticity for a single gasoline station would be very price elastic.