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Elasticity

Elasticity

Key Terms for Elasticity

Practice Problems for Elasticity

What is Elasticity?

Elasticity refers to the degree of responsiveness in supply or demand in relation to changes in price. If a curve is more elastic, then small changes in price will cause large changes in quantity consumed. If a curve is less elastic, then it will take large changes in price to effect a change in quantity consumed. Graphically, elasticity can be represented by the appearance of the supply or demand curve. A more elastic curve will be horizontal, and a less elastic curve will tilt more vertically. When talking about elasticity, the term "flat" refers to curves that are horizontal; a "flatter" elastic curve is closer to perfectly horizontal.

Figure %: Elastic and Inelastic Curves
At the extremes, a perfectly elastic curve will be horizontal, and a perfectly inelastic curve will be vertical. Hint: You can use perfectly inelastic and perfectly elastic curves to help you remember what inelastic and elastic curves look like: an Inelastic curve is more vertical, like the letter I. An Elastic curve is flatter, like the horizontal lines in the letter E.

Figure %: Perfectly Elastic and Perfectly Inelastic Curves

Price elasticity of demand, also called the elasticity of demand, refers to the degree of responsiveness in demand quantity with respect to price. Consider a case in the figure below where demand is very elastic, that is, when the curve is almost flat. You can see that if the price changes from $.75 to $1, the quantity decreases by a lot. There are many possible reasons for this phenomenon. Buyers might be able to easily substitute away from the good, so that when the price increases, they have little tolerance for the price change. Maybe the buyers don't want the good that much, so a small change in price has a large effect on their demand for the good.

Figure %: Elastic Demand

If demand is very inelastic, then large changes in price won't do very much to the quantity demanded. For instance, whereas a change of 25 cents reduced quantity by 6 units in the elastic curve in the figure above, in the inelastic curve below, a price jump of a full dollar reduces the demand by just 2 units. With inelastic curves, it takes a very big jump in price to change how much demand there is in the graph below. Possible explanations for this situation could be that the good is an essential good that is not easily substituted for by other goods. That is, for a good with an inelastic curve, customers really want or really need the good, and they can't get want that good offers from anywhere else. This means that consumers will need to buy the same amount of the good from week to week, regardless of the price.

Figure %: Inelastic Demand

Like demand, supply also has varying degrees of responsiveness to price, which we refer to as price elasticity of supply, or the elasticity of supply. An inelastic supplier (one with a steeper supply curve) will always supply the same amount of goods, regardless of the price, and an elastic supplier (one with a flatter supply curve) will change quantity supplied in response to changes in price.

How Is Elasticity Measured?

As we have noted, elasticity can be roughly compared by looking at the relative steepness or flatness of a supply or demand curve. Thus, it makes sense that the formula for calculating elasticity is similar to the formula used for calculating slope. Instead of relating the actual prices and quantities of goods, however, elasticity shows the relationship between changes in price and quantity. To calculate the coefficient for elasticity, divide the percent change in quantity by the percent change in price:

Elasticity = (% Change in Quantity)/(% Change in Price)

Remember that to find percent change itself, you divide the amount of change in a variable by the initial level of the variable:

% Change = (Amount of Change)/(Initial Level)

Another important thing to remember is that percentage changes can be positive or negative, but elasticity is always an absolute value. That is, even when an increase in price is paired with a decrease in quantity (as with most demand curves), the elasticity will be positive; remember to drop any minus signs when finding your final value for elasticity.

Let's apply this and solve for elasticity in the market for ping pong balls. When ping pong balls cost $1 each, Alice is willing to buy 10 balls, and Joe is willing to sell 10 balls. When they cost $1.50 each, Alice is willing to buy 6 balls, and Joe is willing to sell 20. First, let's solve for Alice's price elasticity of demand:

% Change in Quantity = (6-10)/10 = -0.4 = -40%
% Change in Price = (1.50-1)/1 = 0.5 = 50%
(-40%)/(50%) = -0.8
Take the absolute value to find elasticity.
Elasticity of Demand = 0.8

Now, we use the same process to find Joe's price elasticity of supply:

% Change in Quantity = (20-10)/10 = 1 = 100%
% Change in Price = (1.50-1)/1 = 0.5 = 50%
Elasticity of Supply = (100%)/(50%) = 2

Elastic vs. Inelastic?

An elasticity of 1 is the established borderline between elastic and inelastic goods. A curve with an elasticity of 1 is called unit elastic; an elasticity of 1 indicates perfect responsiveness of quantity to price; that is, in a unit elastic supply curve, a 10% increase in price yields a 10% increase in quantity; a unit elastic demand curve will have a decrease in quantity of 10% with a price decrease of 10%.

If the elasticity of demand is greater than or equal to 1, meaning that the percent change in quantity is great than the percent change in price, then the curve will be relatively flat and elastic: small price changes will have large effects on demand. If the elasticity of the demand curve is less than 1, meaning the percent change in quantity is less then the percent change in price, then the curve will be steep and inelastic: it will take a big change in price to affect demand.

Similarly, if the elasticity of supply is greater than or equal to 1, the curve will be elastic: relatively flat, with quantity supplied very responsive to changes in price. If the elasticity of the supply curve is less than 1, it will be inelastic: the curve will be flatter and quantity supplied will be less responsive to changes in price.

Remember that elasticity is an absolute value; it doesn't indicate an increase in quantity with an increase in price when you are dealing with downward-sloping curves.

Except for curves with an elasticity of 1, elasticity on straight-line curves is not constant. Why is this? As you move along the curve, the slope stays constant, so that each movement yields the same amount of increase or decrease. But as a curve shifts out, these increases or decreases make up a different percentage of the base amount, and the resulting percentage changes are therefore different at different points on the curve. Thus, unless elasticity is specifically stated to be constant on a curve, it usually changes from point to point, and so we usually only study the elasticity of demand or supply at a specific point (usually at the equilibrium point).

Note: One solution to studying elasticity over a curve, rather than at a specific point, is to calculate elasticity using the following formula:

Elasticity = (Change in quantity/Average quantity) / (Change in price/Average price)
Elasticity = ((Q1 - Q2) / (Q1 + Q2)/2 )) / ((P1 - P2)/( (P1 + P2)/2))
This formula will give you an approximation of the elasticity over a range, instead of a point-specific elasticity, but as the range gets larger, the result becomes less and less accurate, which is why many economists prefer to use the traditional measure of elasticity.

It is a little difficult to visualize why elasticity is not constant on a straight-line graph without looking at a diagram. In , the slope of this hypothetical straight-line supply curve is constant (slope = 2), but the elasticity changes as you move along the graph. Let's assume that the price of this good is initially $3, and then increases to $5. In this case, the elasticity for the good can be calculated as follows:

Elasticity = (% Change in Quantity) / (% Change in Price)
Elasticity = [(2 - 1)/1] / [(5 - 3)/3] = 3/2
If the price increases from $5 to $7 however, the elasticity is calculated as follows:
Elasticity = (% Change in Quantity) / (% Change in Price)
Elasticity = [(3 - 2)/2] / [(7 - 5)/5] = 5/4
Figure %: Changes in Elasticity Over a Straight Line Graph
The lesson? Be careful when dealing with elasticity. Don't assume that elasticity will be constant, just because you're dealing with a straight line.

The Effects of Elasticity on Equilibrium Price and Quantity

As we already know, equilibrium price and equilibrium quantity in a given market are determined by the intersection of the supply and demand curves. Depending on the elasticities of supply and demand, the equilibrium price and quantity can behave differently with shifts in supply and demand. We can see one example of how this works if we imagine a supply curve shifting in and out along a single demand curve. If demand is very elastic, then shifts in the supply curve will result in large changes in quantity demanded and small changes in price at the equilibrium point.

Figure %: Shifts in Supply with Elastic Demand
If demand is very inelastic, however, then shifts in the supply curve will result in large changes in price and small changes in quantity at the equilibrium point.
Figure %: Shifts in Supply with Inelastic Demand

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