Elasticity

A measure of the degree of responsiveness of one variable to changes in another. For example, the price elasticity of demand for a particular good is the relative degree of responsiveness of the quantity demanded to relatively small changes in its price. On a supply-demand graph drawn as normally presented in textbooks, elasticity of demand can be very roughly assessed simply by eyeballing the steepness of the slope of the demand curve: a very steeply sloping demand curve (that is, almost straight up and down) indicates that a given percentage increase in price will induce only a comparatively smaller percentage decrease in the quantity of the commodity that potential consumers wish to buy ("relatively inelastic demand"); while a very gently sloping demand curve shows that a given percentage increase in price will produce a still larger percentage decrease in quantity demanded ("relatively elastic demand").

Similarly, price elasticity of supply measures the degree of proportionality with which the quantity of a commodity offered for sale on the market changes in response to a given change in the going price; income elasticity of demand measures the responsiveness of consumer demand for a commodity to changes in consumer incomes; and so on. Presumably the term "elasticity" was originally adopted because it enables us to compare how much several dependent variables "stretch" in response to the same degree of "pulling force" from the same independent variable.

When a numerical estimate is required for a precise prediction of the consequences of a particular price change for the quantity of a good likely to be traded, elasticity is usually defined by the percentage change in the dependent variable (for example, quantity demanded) divided by the associated percentage change in the independent variable (for example, price). Ignoring the plus or minus sign, an elasticity greater than 1 is referred to as relatively elastic and an elasticity less than 1 is referred to as relatively inelastic. (An elasticity precisely equal to 1 is termed unit elasticity.) For relatively small changes, this is practically equivalent to the calculus expression below that includes the slope of the curve and the values of the independent and dependent variables at the point on the curve in question where elasticity is being assessed:

`elasticity = (dY/dX) * X/Y`

where X is the independent variable (price, income, etc.) and Y is the dependent variable (quantity demanded, quantity supplied, etc). (Notice that the presence of X and Y as well as dX and dY in the expression makes the elasticity vary based not only on the general slope of the curve but also based on the particular part of the curve that is under consideration -- the elasticity is not generally identical for each and every segment of a given demand or supply curve.)

As we try to illustrate throughout this course, a surprising amount of detail about the general direction of the economic consequences of particular kinds of events or changes in public policy can be predicted by deduction from very broad generalizations like the laws of supply and demand. But when much more precise numerical predictions of consequences are desired, more detailed information is needed about the exact parameters defining the supply and demand schedules in the particular markets concerned at the relevant time. Statistical techniques for estimating numerical values for particular real world supply and demand functions (and other economic relationships) and especially for measuring their long-term and short-term elasticities are at the heart of most applied economic research done by both government economists and economists employed by business firms in the private sector.

To illustrate the practical importance of the elasticity concept, consider the following example:

If the Alabama legislature is considering a ten cents per liter increase in the tax on liquor, many members of the legislature might want to know the answers to one or more of the following questions before casting their votes:

1. How much will raising the tax diminish Alabamians' purchases of the demerit good "demon rum"?
2. How much additional revenue will the tax increase bring in?
3. How will the economic burden of the tax increase be divided up between the purchasers of liquor (who have a lot of votes) and the liquor industry (who do not have a lot of votes but who often make sizable campaign contributions)?

Answering any of these questions depends upon making good estimates of the price elasticities of supply and demand for liquor in Alabama over the relevant time periods.

1. The lower the price elasticities of supply and of demand for liquor turn out to be (in other words, the more inelastic the supply and demand), then the smaller the decrease in the amount of liquor sold in Alabama will be. Inelastic demand or inelastic supply is bad news for the Baptist clergy, because if either one (or both) is relatively inelastic, the decline in liquor sales after the tax increase will be rather small.

2. The revenue increase for the state will be equal to \$.10 times the total number of liters of liquor sold minus the old tax rate times the decrease in liters sold. So it will be very good news for the Alabama Treasurer if either the demand or the supply schedule (or both) is relatively inelastic for liquor. The more inelastic the price elasticities of demand or supply for liquor, the greater the amount of the liquor taxmoney that will be flowing into the state's coffers. (By the same logic, if both demand and supply are relatively elastic, total liquor tax revenues will actually be less than before the tax rate increase, because the decline in sales will be more than big enough to cancel out the increase in the rate of tax per bottle!)

3. The division of the new tax's financial burden between the liquor industry (how much will come out of lowering wages and profits?) and liquor consumers (how much will come from higher costs for their drinking habits?) turns out to depend entirely on the ratio between the price elasticity of demand and the price elasticity of supply. The lower the elasticity of demand and the higher the elasticity of supply, the larger will be the proportionate share of the new tax burden that will be shouldered by the consumers and the lower will be the share of the burden extracted from the liquor industry's owners and employees. (It turns out not to matter at all for the division of the real burden of the tax whether the tax law officially levies an excise tax on the buyer or on the seller of the good.)

Some generalizations about what seems to determine price-elasticities: Goods that are less urgently or specifically desired by consumers (often because there are very many other close substitutes readily available on the market) generally would be expected to display higher price elasticity of demand -- such as, for example, different types of breakfast cereals. "Items of necessity" that are used constantly in normal daily life and which have only very imperfect substitutes tend to display less price- elasticity of demand -- for example, salt, matches, or soap in our society. "Luxury" items, by definition, are goods that people do not believe they really have to have "at any price," and the price elasticity of demand for such goods therefore tends to be quite high -- making it difficult to "soak the rich" very effectively by means of luxury taxes. Heroin, cocaine, alcohol, tobacco, gambling devices and other addictive or quasi-addictive products would be extreme examples of goods for which we would expect the demand to be very price-inelastic (which is one of the reasons why "sin taxes" are so often very lucrative for governments to impose -- people are generally very determined to keep right on sinning at almost any price!). "Big ticket" items whose prices represent a hefty share of most customers' monthly incomes (such as automobiles, motorboats, washing machines or TV sets) very often display relatively high price elasticity of demand because even a relatively small percentage increase in price still means "big bucks" and may put purchase beyond the financial reach of significant numbers of potential customers.

It should also be kept in mind that the length of the time period under consideration nearly always makes a big difference in the degree of elasticity exhibited by buyers and sellers -- that is, people (and business organizations) often have serious practical difficulties or psychological rigidities in adjusting their buying or selling behavior to price changes on very short notice, but then as time goes on, more and more extensive adaptation to the new situation is likely to take place. As a result, the elasticities of long-term supply and long-term demand curves are nearly always much greater than the elasticity of short-term supply and demand curves for the same goods and services.