Elasticity measures the percentage reaction of a dependent variable to a percentage change in a independent variable. For example, elasticity of -2 means that an increase by 1% provokes a fall of 2%.
Elasticity is easy to compute both in models and in reality, but in the real world it may be difficult to single out the effect of the independent variable on the dependent one, since many variables change at the same time and - furthermore - there often exists a self-propelling dynamics in the independent one.
Just divide the percentage change in the dependent variable and the percentage change in the independent one. If the latter increases by 3% and the former by 1.5%, this means that elasticity is 0.5.
Conversely, if you know the elasticity you can forecast the change in the dependent variables for each variation in the independent one.
Elasticity of 1 means that the two variables change always by the same proportion (a 5% increase determines a 5% increase). Elasticity of -1 means that the two variables goes in opposite directions but in the same proportion.
Price elasticity
What happens when the price grows? The demanded quantity falls? By how much? To answer these questions you need to know the price elasticity. If it is -3, this means that the quantity will fall by three times the percentage increase in price (e.g. a 1% increase produces a 3% fall).
This elasticity is more precisely called own-price elasticity of demand since it refers to changes in quantities due to changes in the price of that good.
Cross-price elasticity measure the effect of changes in other goods' prices on a given good. If competitors increase their prices shall we enjoy an increase in sales of our good? Yes, if cross-price elasticity is positive, since in this case they are substitutes.
Test yourself
1. Download our free software about consumer choice and make the following experiments: a change by 10% in the price of good X. By which percentage does the quantity of X changes (to compute the own-price elasticity)? By which percentage does the quantity of Y changes (to compute the cross-price elasticity)? By which percentage does utility changes? Then change by 10% the consumer's income. By which percentage does the quantity of X changes (to compute the income elasticity of X)?
2. Download our free software about a monopoly and make this experiment: a change by 10% in the price of your good. By which percentage does the quantity of X changes in the next period? Repeat for some periods the same experiment. Does own price elasticity change over time? Why? (Answer: Yes, because of the self-propelling autonomous dynamics of demand).
Cost elasticity
What happens to costs when sales grow? Variable costs will increase by a fraction of the sales if their elasticity is lower than 1 (implying economies of scale in variable costs). Fixed costs will not change (by definition), thus their elasticity is zero and they are said to be "unelastic" to sales.
Test yourself
Download our free software about costs and make experiments
Elasticity in macroeconomic variables
By how much will GDP rise because of an increase in exports? In public expenditure? In investments? Other things equal, elasticity will be equal as the share each one of these GDP components represent on total GDP. If exports represent 20% of GDP, the elasticity of GDP to export will be 0.2, other things equal.
Test yourself
Download our free data about GDP and its components, choose a country and make the following computation: by which percentage GDP rose in 1990 with respect to 1989? By which percentage investment rose? Make the ratio of the two so to compute the elasticity of GDP to investment. Repeat this computation in other cases. Is elasticity always the same? Are you sure that GDP depends on investment only? Are you sure that investment is an independent variable? Look at what the standard IS-LM model says.
Similarly, you can experiment how the overall price level reacts to single price increase by using this spreadsheet.
In models, you can usually compute what would happen at different levels of an independent variable, everything else equal. Thus, you can make comparative statics exercises and compute immediate elasticity. But in real world it's possible that some time should elapse in order some effect on the dependent variable be noticeable.
Impulse-response analysis is used to see which is the time-dependent elasticity of one variable to another. You'll compute the change in the former in successive periods and relate them to the impulse given in the base period.
In this way, you can distiguish short run elasticity from long run elasticity.
Needless to say, the longer is the time that elapses, the less is reasonable to assume that all the other variables stayed equal and the same qualification of "independent" variable and "dependent" variable becomes less clear-cut, because of feedback processes.
To have real life examples of elastic relations, you would need to collect data about price over time and the respective quantities sold. You will soon discover that prices stay at the same level for days and weeks, but that each day the sales are different (so that price alone cannot explain sales). By taking some arbitrary average (e.g. aggregating sales for weeks) you can compare what happens during the short period of commercial promotions, where prices are temporarily cut. A large increase of sales indeed occurs (most of the times!), because people concentrate their purchases in those periods, react on the spot with larger quantities and flock to the Point of Sale (POS) where the promotion is taking place (especially if they have this piece of information, e.g. by advertising and leaflets). Sales in other POS usually fall during this period, with a positive cross-product elasticity.
There are systematic differences between elasticity as assumed in neoclassical models and in reality. First of all, elasticity is - in neoclassical models - symmetric for changes in both directions (increase and decrease), whereas in reality changes can be asymmetric (with stronger reaction to increases than to falls, for instance). Secondly, the sequence of changes (e.g. first an increase, then a fall) is assumed to be irrelevant (with final level of the dependent variable being the same), but in reality it may matter (e.g. the demand for a good which has been discounted by 30% during a temporary promotion may be not the same as the level of demand for the good if it is temporarily more expensive by 30% from reference price - even if the actual price to be paid is the same during the period). For a model in which elasticity is not simmetric see here.
Formal models Consumer theory: the neoclassical model
Price elasticity in monopoly
Elasticity to quality and advertising
Real world elasticities (144 countries) - Price elasticities and income elasticities of consumption classes (food and non-food) - Food share on household budget
Income and price elasticities of export for 53 countries
GDP and its components in 136 countries: a long term time series
Consumers microdata (income, preferences for performance and comfort, decision rules)
