Other Elasticities

a single monopolist dominates an industry or product line. Other things being equal, the monopolist’s demand is less elastic (since it is the sole producer) than the demand facing a particular firm in a multifirm industry.

A third determinant of price elasticity is the proportion of income a consumer spends on the good in question. The issue here is the cost of searching for suitable alternatives to the good. It takes time and money to compare substitute products. If an individual spends a significant portion of income on a good, he or she will find it worthwhile to search for and compare the prices of other goods. Thus, the consumer is price sensitive. If spending on the good represents only a small portion of total income, however, the search for substitutes will not be worth the time, effort, and expense. Thus, other things being equal, the demand for small-ticket items tends to be relatively inelastic.

Finally, time of adjustment is an important influence on elasticity. When the price of gasoline dramatically increased in the last five years, consumers initially had little recourse but to pay higher prices at the pump. Much of the population continued to drive to work in large, gas-guzzling cars. As time passed, however, consumers began to make adjustments. Some commuters have now switched from automobiles to buses or other means of public transit. Gas guzzlers have been replaced by smaller, more fuel-efficient cars including hybrids. Some workers have moved closer to their jobs, and when jobs turn over, workers have found new jobs closer to their homes. Thus, in the short run, the demand for gasoline is relatively inelastic. But in the long run, demand appears to be much more elastic as people are able to cut back consumption by a surprising amount. Thus, the time of adjustment is crucial. As a general rule, demand is more elastic in the long run than in the short run.

The elasticity concept can be applied to any explanatory variable that affects sales. Many of these variables—income, the prices of substitutes and complements, and changes in population or preferences—have already been mentioned. (An additional important variable affecting sales is the firm’s spending on advertising and promotion.) To illustrate, consider the elasticity of demand with respect to income (Y). This is defined as

in a manner exactly analogous to the earlier price elasticity definition.9 Income elasticity links percentage changes in sales to changes in income, all other

EY % change in Q % change in Y ¢Q/Q ¢Y/Y

9If an infinitesimal change is considered, the corresponding elasticity expression is EY (dQ/Q)/(dY/Y). In addition, when multiple factors affect demand, the “partial derivative” notation emphasizes the separate effect of income changes on demand, all other factors held constant. In this case, we write EY ( Q/Q)/( Y/Y).

factors held constant. For example, the income elasticity of demand for spending on groceries is about.25; that is, a 10 percent increase in income results in only about a 2.5 percent increase in spending in this category. In other words, a household’s consumption of groceries is relatively insensitive to changes in income. In contrast, restaurant expenditures are highly sensitive to income changes. The income elasticity for this type of spending is about 3.0.

A main impact on the sales outlook for an industry, a firm, or a particular good or service is the overall strength of the economy. When the economy grows strongly, so do personal income, business profits, and government income. Gains in these income categories generate increased spending on a wide variety of goods and services. Conversely, when income falls during a recession, so do sales across the economy. Income elasticity thus provides an important measure of the sensitivity of sales for a given product to swings in the economy. For instance, if EY 1, sales move exactly in step with changes in income. If EY 1, sales are highly cyclical, that is, sensitive to income. For an inferior good, sales are countercyclical, that is, move in the opposite direction of income and EY 0.

CROSS-PRICE ELASTICITIES A final, commonly used elasticity links changes in a good’s sales to changes in the prices of related goods. Cross-price elasticity is defined as

EP ¢Q/Q ¢P /P

where P denotes the price of a related good or service. If the goods in question are substitutes, the cross-elasticity will be positive. For instance, if a 5 percent cut in a competitor’s intercity fare is expected to reduce the airline’s ticket sales by 2 percent, we find EP ( 2%)/( 5%) .4. The magnitude of EP provides a useful measure of the substitutability of the two goods.10 For example, if EP .05, sales of the two goods are almost unrelated. If EP is very large, however, the two goods are nearly perfect substitutes. Finally, if a pair of goods are complements, the cross-elasticity is negative. An increase in the complementary good’s price will adversely affect sales.

Table 3.1 provides estimated price and income elasticities for selected goods and services.

10We could also examine the effect of a change in the airline’s fare on the competitor’s ticket sales. Note that the two cross-price elasticities may be very different in magnitude. For instance, in our example the airline flies only half as many flights as its competitor. Given its smaller market share and presence, one would predict that changes in the airline’s price would have a much smaller impact on the sales of its larger rival than vice versa.