Elasticity is a measure of how much response there is to a change.
There are three types of elasticity we discuss regarding the demand curve.
PED (Price Elasticity of Demand)
XED (Cross Elasticity of Demand)
YED (Income Elasticity of Demand)
Each of these is a measure of the response to a change.
PED measures the response to a change in the price of the good itself. This means that we are measuring the movement along the curve. We are measuring how much a certain percentage change in price will affect the overall percent change in the quantity demanded.
XED measures the response to a change in the price another good. This means that we are measuring the amount of movement (shift) of the whole demand curve when there is a change in the price of another good.
YED measures the response to a change in the Income of the people buying the good. This means we are measuring the amount movement (shift) of the whole demand curve in response to a change in consumers' income.
Price Elasticity of Demand (PED)
The formula for measuring PED is %Change in QD (divided by) the % change in Price of the product. We take the absolute value because the sign will always be negative due to the law of demand (a positive change in price would lead to a negative change in QD and vise versa).
PED is not a measure of the Slope of the Curve. The slope of the curve is a product of the ratio of the rise to run. If we have a straight line demand curve with a 1 to 1 ratio, then for every $1 of price change we will see a 1 unit change in QD.
However, the PED will change as we move along the demand curve.
For example, if we have a $10 price tag and we lower the price to $9 then that 1 dollar change in price is a 10% decrease in the price. If that $1 decrease in price leads from 1 unit being demanded to 2 units being demanded, then the QD doubled (or increased by 100%). If we look at the slope of the curve, we note that there was a $1 decrease in the price and 1 unit increase in the quantity demanded. Thus, a 1 to 1 ratio between price and QD. This would be the same on the other end of the demand curve when we have, say, a $2 price tag and drop the price to $1. This is still a 1 dollar change in price. However, if at a price of $2 the QD was 10 units, and at $1 the QD is at 11 units, then the cutting of the price in half only led to a 10% increase in the quantity demanded.
But when we look at the elasticity, we see that the percentage of the price change is much smaller or larger compared to the percentage change in the quantity demanded.
When the price was $10 and the QD was at 1 unit, then a relatively small change in price (a 10% decrease) led to a relatively large change in quantity demanded (100% increase).
If you think about this in terms of pure revenue, then we see why this concept is important. At a price of $10 and a QD of 1, the total revenue was $10x1unit = $10. But, when we lower the price to $9 and see the increase in QD to 2 units then the total revenue goes from $10 to $9x2units = $18.
However, if we look at the other end of the demand curve and check our revenue we see something very different. At a price tag of $2 and a demand of 10 units the total revenue is $2x10units = $20. However, when the price is lowered to $1 and the QD increases from 10 units to 11 units, the new total revenue is $1x11units = $11. This was a decrease in revenue by 9 dollars.
In fact, a more advanced economic concept regarding total revenue, shows that total revenue is always maximized where the PED = 1, which occurs at the midpoint of the straight line demand curve. Every price point above the midpoint will have an elasticity greater than 1 and is considered price elastic, and each percentage decrease in price will lead to a relatively greater percentage increase in the quantity that is demanded, and the revenue will go up. At every price point below the midpoint on a straight line demand curve, the elasticity is less than 1 and is considered price inelastic, and each percentage decrease in price will lead to a relatively smaller increase in the percentage of the quantity that is demanded, and the revenue will go down.
To summarize, every straight line demand curve has a midpoint with a PED of 1 (a midpoint with unitary elasticity) and a segment of increasing elasticity heading away from one (1) and getting closer and closer to infinity, and a segment of increasing inelasticity below one (1) (a decimal number) heading closer and closer to zero (0).
Cross Elasticity of Demand (XED)
The formula for measuring XED is the % change in Demand of of Good B (divided by) % change in the price of good A. In other words, we are looking at how much response a product has to a change the price of another product. Additionally, we are looking at how the product responds in addition to how much it responds.
Since the price of Good B is not changing the demand curve for Good B is shifting in response to the change in the price of another product which may be a substitute or a complement. In fact, there is a change in the quantity demanded of Good B at every price; thus, the whole curve moves.
In the above graph, the price of Good A was lowered from $9 to $2. This led to an increase of the quantity demanded of Good A from 2 units to 10 units. But where did these customers come from? Some where not purchasing anything as they waited for the price to drop. But some were buying a similar good, or in economic terms a substitute good, like Good B. So, as the price drops for Good A, those people buying Good B as a substitute for Good A begin to buy less of Good B at every price point. Therefore, the demand for Good B at every price decreases, represented by a shift of the whole demand curve for Good B to the left.
It is possible that another good sees an increase in the demand at every price due to the fact that people are purchasing more of the first good. This relationship is called complementary goods. Image that Good A is an iPhone. If the price of iPhones decreases and the quantity demanded of iPhones increases, then a complementary good, such as phone cases (Good C), will see an increase in sales at each and every price (a rightward shift of the curve).
Both of the the above situations are referred to as the "Substitution Effect."
XED is used to determine which way the curve will shift and to what extent the response will be.
If XED is positive then the goods are substitutes
If XED is negative then the goods are complements
The closer the XED is to zero (0), the more unrelated the two goods are.