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10.9 Price Elasticity of Demand

Price elasticity of demand refers to the impact on demand when the price increases by one percent. If a price increase of one percent causes demand to fall by less than one percent, demand for the good is said to be relatively inelastic. If the demand falls by more than one percent, then demand for the good is said to be relatively elastic. Finally, if demand falls by exactly one percent for each one percent price increase, we say that demand for the good is unit elastic. We can make this calculation by dividing a percentage change in quantity demanded by a percentage change in price. Although applying the formula often generates a negative number in the result, elasticity is typically expressed by its absolute value.

We can calculate the overall price elasticity across the demand curve for Larry the Lobster by multiplying the regression coefficient (which is also the slope of our line) by P/Q. (P is the mean price, and Q is the mean quantity). However, it should be noted that even though the slope of that line never changes, the price elasticity of demand is actually very different at different points along that line. Along the smaller range of prices, small increases represent larger percentage changes, compared to the impact seen along the graph at higher price ranges.

To see this in action, let’s look at the price elasticity of demand when we go from $5.00 to $5.50 along our curve. In this scenario, the price increases by 10%: (5.50-5.00)/5.00, while the quantity decreases by 7.9%: (228-210) / 228. The percentage change in quantity demanded, divided by the percentage change in price, gives us an elasticity of |0.79|. At this point on the curve, we can say that demand is relatively inelastic.

What happens when the price goes from $8.00 to $8.50? In that scenario, we have a 6.25% increase in price. We would expect demand to fall from 119 to 101, based on our demand function shown above. This is a 15.12% drop, so the price elasticity of demand in this scenario is |2.42|. Demand is much more elastic along this point on the curve!

We can use the describe() function to get the mean values for price and quantity, as shown below.

Across the entire demand curve, our estimate of price elasticity of demand is -36.42 * (7.5/137.143) = -1.99. For each one percent increase in the price charged for Larry the Lobster stuffed animals, demand falls by nearly two percent. In between operating seasons, when Lobster Land often reviews its pricing structure for everything offered in the park, management can use this insight to help inform its projections about the likely impacts that would result from a change in price for Larry the Lobster.

While many factors can influence a good’s price elasticity of demand, five that we will explore in the table below are:

Availability of substitutes;
Timeframe;
Income share;
Luxury vs. Necessity;
Narrowness of Market

Factors that Influence Price Elasticity of Demand

	Its Impact	Extreme Example (Elasticity)	Extreme Example (Inelasticity)
Availability of substitutes	The more easily some particular product can be replaced with a similar alternative, the more quickly consumers can be expected to respond to price increases.	Imagine that you are completely indifferent between Coke and Pepsi – you, they have the exact same taste. If Coke is selling for $1 and Pepsi is $2 at the same store, you will choose Coke every time.	Imagine that you absolutely love Dr. Pepper. To your palate, no other drink hits quite the same way, with quite the same taste. For years, you have consumed exactly one 20 oz. bottle every day with lunch. If Dr. Pepper starts to charge its wholesalers 20% more, and that cost is passed on to consumers? You are likely to continue buying.
Timeframe	The more time consumers have to react to price changes, the more likely they will be able to adjust their buying habits.	Imagine that gas prices steadily ascend, year over year, at a 20 percent growth rate. When you go to make a major purchase (compact car or sport-utility vehicle), you will choose the vehicle that consumes the least gas.	Imagine taking a road trip with your friends. You are nearly out of gas, but you pull over and find a gas station just as the fuel gauge hits “E.” Since the last time you purchased gas, its price has gone up 25%. That’s frustrating, but you need gas right now! You will buy it.
Income share	All else equal, a product that takes up a smaller share of its buyers’ incomes will show less price elasticity of demand	Imagine that each year, for several years, you and your family have taken a weeklong vacation to an all-inclusive resort. Suddenly, the price jumps from $2000 to $4000. That’s a 100% increase, and it takes the vacation’s cost from ‘manageable aspect of family budget’ to ‘not possible without taking on new debt’	Imagine that each weekday, just prior to your ride home, you buy a small piece of $0.05 candy at the train station to reward yourself for a hard day’s work. If the seller bumps that price up to $0.10? That’s a 100% increase, but your consumption pattern might not even change at all – the cost is still negligible.
Luxury vs. Necessity	How vital is this product in the minds of its buyers? If people don’t perceive the product as a necessity,	Imagine that your morning ritual involves a trip down the street to your favorite coffee shop, where you buy a large iced Americano for $5. You realize that you could make the same drink at home for less money, but you enjoy the ritual, and the cost does not break your budget. What if, tomorrow, the cost suddenly jumped to $10? The make-it-at-home option might start to look more appealing!	Imagine that you need a particular prescription drug, regularly, in order to regulate a vital bodily function – and you must pay for it out of pocket. If the price doubles tomorrow? You will still find a way to buy it.
Narrowness of Market	How many sellers are out there for this product, or others like it?	Imagine if, inexplicably, one ice cream shop in town just raises its prices by 50%, overnight. Since there are three other ice cream shops within a 0.25 mile radius, customers will just “vote with their feet” and decide to shop elsewhere instead.	Imagine if the ONE ice cream shop on a resort island raises its prices by 50%, overnight. With no other ice cream shops around, consumers lack alternatives, besides simply not going out for ice cream. Demand may fall in this case, but may not fall very sharply.