The first elasticity tutorial took a qualitative approach to elasticity. The idea conveyed was
Elasticity = Responsiveness
The elasticity of Q with respect to P is the responsiveness of Q to changes in P.
Q is the quantity demanded. P is the price per unit.
Elasticity has a quantitative meaning, too. Elasticity is a specific way of measuring responsiveness.
Suppose P changes, and Q changes as a result.
The elasticity of Q with respect to P is the relative change in Q divided by the corresponding relative change in P.
You can also say:
The elasticity of Q with respect to P is the percentage change in Q divided by the corresponding percentage change in P.
For example, if the price of something goes up by 1% and
sales fall by 2%, the elasticity of quantity demanded with respect to price
is -2%/1% = -2.
(Don't neglect the minus sign. For demand, the elasticity number is negative, because price and quantity move
in opposite directions.)
You can write the elasticity formula this way:
(Change in Q) / (level of Q) Elasticity = --------------------------------- (Change in P) / (level of P)The numerator of this fraction is the change in Q relative to the level of Q.
The elasticity concept can be applied to other things besides Quantity and Price. You can use the concept whenever changing one thing makes something else change. For example, some researchers have estimated the elasticity of population health status with respect to the population's medical care expenditure. This elasticity is the percentage difference in health status divided by the percentage difference in medical care expenditure. (This elasticity usually comes out small, by the way.) In this example, health status goes in the place of Q and medical care spending goes in the place of P. In the formula, you can consider Q and P as placeholders for anything that changes in response to changes in something else.
There's a shorter way to say "the elasticity of Q with respect to P." You can say "the P elasticity of Q," as in "the price elasticity of demand" or "the income elasticity of demand." Here's the formula again for the P elasticity of Q:
(Change in Q) / (level of Q) Elasticity = --------------------------------- (Change in P) / (level of P)Let's try to apply this. Suppose that a medical practice finds that when the price of a certain test is is $10, the quantity demanded is 100 tests per month, while if the price is $30, the quantity demanded is only 60 tests per month.
The first point is that, when you figure the changes in Q and P, you do both in the same direction of time. Let's call the $10 price and 100 quantity the "before" situation, and the $30 price and 60 quantity the "after" situation. To be consistent, you have to calculate all changes as "after" minus "before" or "before" minus "after." Let's calculate all changes as "after" minus "before."
What is the change in Q, "after" minus "before"?
The next point is about what numbers you should use for the "levels" in the formula. Let me ask you: What number do you think you should use for the level of Q?
(I'm leaving some space here. Scroll down after you answer.)
You have a choice of what level of Q should go into the formula. There is no one right answer. The phrase "level of Q" is ambiguous. You could use the "before" level of Q. You could use the "after" level of Q. You could use something in between.
Whichever you use, be consistent. If you use the "before" level of Q, use the "before" level of P.
If the change in Q is small relative to the levels of Q, it doesn't matter much which Q you use for the level of Q. The elasticity comes out about the same regardless.
If the change in Q is not small, it's customary to the "arc elasticity," which is halfway between "before" and "after." Let's do that.
Here's the definition of arc elasticity:
(Change in Q) / (average of Q's) Arc Elasticity = ------------------------------------ (Change in P) / (average of P's)To get the average of the Q's, add them and divide by 2. The same goes for the average of the P's.
Let's use that in the calculation.
The data again are:
If the price is $10, demanded quantity is 100 tests per month.
If the price is $30, demanded quantity is 60 tests per month.
So far, we have that the Change in Q is -40 tests per month.
What is the average of the Q's?
So, the (Change in Q) / (average of Q's) is what?
(Express as a decimal number, not as a percent.)
That's the numerator of the Arc Elasticity fraction. Next, we calculate
the denominator.
Repeating the data again:
If the price is $10, demanded quantity is 100 tests per month.
If the price changes to $30, demanded quantity is 60 tests per month.
So far, we have this for our arc elasticity fraction:
-0.5 Arc Elasticity = ------------------------------------ (Change in P) / (average of P's)Tackling the denominator, what is the change in P, "after" minus "before"?
-0.5 Arc Elasticity = ------------------------------------ 1Last step: Based on the above fraction, what is the arc elasticity?
Good! That's how you calculate an arc elasticity.
The terms "elastic" and "inelastic" can be given a precise meaning in
terms of the number that comes out of the elasticity fraction. The
divider between elastic and inelastic demand is -1.
(For elasticities where you expect a positive relationship between Q and
P, such as for elasticities of supply, the divider is +1.)
If the demand elasticity is more negative than -1, the demand is elastic.
If the demand elasticity is between -1 and 0, the demand is inelastic.
I avoided saying "higher" and "lower" in the above definition, because economists say that the elasticity of demand is "high" when it's a big negative number. They say that the elasticity of demand is "low" when it's a small negative number, meaning close to 0. The elasticity of demand for oil is low. The elasticity of demand for cubic zirconia (imitation diamond) is high.
In our example, we got a price elasticity of demand of -0.5. Is this
elastic or inelastic demand?
For demand, there's a relationship between the elasticity and what happens to total revenue from customers when you change your price:
| If demand is elastic | (if the elasticity is more negative than -1) | then if the
price goes up, the total amount customers spend goes down. |
| If demand is inelastic | (if the elasticity is between -1 and 0) | then if the
price goes up, the total amount customers spend goes up. |
| If you have unitary elasticity | (if the elasticity of demand is exactly -1) | then if the
price goes up, the total amount customers spend stays the same. |
Let's see how this works in our example. When the price is $10, you
do 100 tests per month. What is the total revenue (price times quantity)?
When the price is $30, you do 60 tests per month. Now what is the total
revenue?
So, raising the price from $10 to $30 does what to total revenue?
Our calculated elasticity was -0.5, which we called "inelastic" because
its absolute value was less than 1. Is this consistent with revenue
going up when the price goes up?
This is how elasticity relates to pricing strategy. If your demand is
inelastic, how would you change your price to bring in more money?
What if demand were elastic? How would you change your price to bring
in more money?
Elastic demand typically happens when you are a small player in a big
market, and there's a going market price. Undercut that price, and you
attract business. Whether you make a profit depends on your costs, but
that's a subject for another tutorial.
The extreme form of elastic demand is perfectly elastic demand. Perfectly elastic demand means you can sell as much as you want at the going market price. People will buy a practically unlimited amount at the current price, with no need for price cuts to get people to take more.
What is the elasticity, if demand is perfectly elastic?
In practice, demand that is nearly perfectly elastic occurs for small sellers in big markets. An individual farmer can have perfectly elastic demand. The market will take all he or she can produce at the going price.
Perfectly elastic supply would mean that producers can offer for sale a practically unlimited amount of the good or service at the current price.
That's all for now. Thanks for participating!
For more use of the elasticity of demand concept, see the tutorial on monopoly.
