A Primer on Demand Elasticity

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Economists are empirical. We like to study things that can be measured. One crucial question we often need to answer is, “How does quantity demanded change in response to a price change?” We use price elasticity of demand to measure the responsiveness. Since that’s all we’re going to discuss here, I’ll just call it elasticity.[1]   This is a primer on demand elasticity.

This is also a companion piece for my article about the proposed energy efficiency standards for ceiling fans. If you arrived here via that post, click here to get back. Also, there is a pdf version of this article just after the endnotes.

What Determines Elasticity?[1]

  1. Availability of substitutes. The greater the number of substitutes and how closely they resemble the original product are, the more elastic demand will be. There are no close substitutes for coffee.  We expect demand to be price inelastic.  And, as we saw earlier, it is.
  2. The importance of being unimportant. When the amount you spend on a product is a small part of your budget, demand will be less elastic. Consider salt.  It costs about $1.30 a pound.  One box may last a year or more.  Nobody searches for coupons or deals on salt.
  3. Luxuries versus necessities. The demand for Tesla’s Model S is likely to be price elastic.  As we just saw, it is.  Products you need to keep you alive (such as food) are likely to have inelastic demand.
  4. Consider oil.  Short-run price elasticity is about 0.2.  But, starting with the OPEC embargoes in the 1970s, firms have been searching for substitutes.  One is cars that have higher gas mileage per gallon.  Another (supply) is improved methods of oil extraction (“fracking”). Long run demand tends to be more elastic than short-run demand.

I’ll add a fifth item to this list: the degree of market aggregation.  The demand for food is likely to be pretty inelastic.  The demand for fruit will be more elastic.  The demand for apples will be even more elastic.  And the demand for Fuji apples might very well be elastic.

Calculating Elasticity

Price elasticity of demand is the percentage change in quantity demanded divided by the percentage change in price.[2] This measures the change in quantity demanded per one percentage point increase in price. For small changes in price (p) and quantity (Q), we can calculate elasticity

Fig01 A Primer on Elasticity

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Here’s an important point: price elasticity of demand is always negative. Demand curves slope downward. Their slope is negative. An increase in price (positive change) will cause quantity demanded to fall (negative change). A negative value divided by a positive value will always be negative.

Here’s an example. Suppose a 1% increase in price caused quantity demanded to decrease by 3%. Here’s the calculation.

Fig02 A Primer on Elasticity

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Later, we’ll call an elasticity whose absolute value is greater than 1.0 elastic demand.

Elasticity of Demand for Coffee

Perloff and Brander[2] estimated a demand curve for coffee:

Fig03 A Primer on Elasticity

Price (p) is in dollars per pound. Quantity demanded (sales, Q) is in million tons per year. We can draw a graph of this demand curve.[4]

Fig04 A Primer on Elasticity

The price of coffee (wholesale, raw beans) was $2.20 per pound. At this price, coffee roasting firms will buy

Fig05 A Primer on Elasticity

Suppose the price increases by $0.022. That’s a 1% price increase:

Fig06 A Primer on Elasticity

Quantity demanded will be

Fig07 A Primer on Elasticity

The change in quantity demanded is

Fig08 A Primer on Elasticity

which is

Fig09 A Primer on Elasticity

so elasticity is

Fig10 A Primer on Elasticity

As any coffee drinker will tell you, the stuff is addictive. Personally, I need two cups in the morning to start my heart. That’s part of the reason quantity demanded doesn’t change much when price changes.

At this point, I have to add a warning. The elasticity as calculated above only works for very small changes in p and Q. If you want to work with larger changes, look up arc elasticity of demand.

Tesla Model S[5]

Tesla has a monopoly on producing the Model S. They sustain their monopoly with patents, restrictions on where you can get the car serviced (Tesla dealers only), and from being the first major electric car producer in the U.S. Reputation promotes customer loyalty, a source of monopoly power.

Perloff and Brander[6] estimated a demand curve for the Model S:

Fig11 A Primer on Elasticity

Price is in thousand dollars per vehicle. Quantity demanded (sales) is in thousand cars per year. We can draw a graph of this demand curve.[7]

Fig12 A Primer on Elasticity

The price of a Model S was $80,000. At this price, Tesla customers will buy

Fig13 A Primer on Elasticity

Suppose the price increases by $800. That’s a 1% price increase:

Fig14 A Primer on Elasticity

Quantity demanded will be

Fig15 A Primer on Elasticity

The change in quantity demanded is

Fig16 A Primer on Elasticity

which is

Fig17 A Primer on Elasticity

so elasticity is

Fig18 A Primer on Elasticity

Jargon

Demand is price elastic if the absolute value of elasticity is greater than 1.0. Demand for Tesla’s Model S is price elastic. The absolute value of its elasticity is 1.6.

Demand is price inelastic if the absolute value of elasticity is between 0.0 and 1.0. Demand for coffee is price inelastic. The absolute value if its elasticity is 0.224.

Demand is unit elastic if the absolute value of elasticity is exactly 1.0. Examples are rare.

Elasticity must always be negative because demand curves always slope downward (a negative slope).

Why Elasticity is Important

Total spending on a product is price x quantity. Ignoring sales taxes, tariffs, and other taxes, the total amount buyers pay for a product is equal to total revenue for the seller(s). There’s a simple relationship between price changes, total spending, and elasticity.

  • If demand is inelastic, a small increase in price causes total spending on a product to increase.
  • If demand is elastic, a small increase in price causes total spending on a product to decrease.
  • If demand is unit elastic, a small increase in price causes total spending on a product to increase.

These rules are limited to small changes because elasticity changes along a linear demand curve (the two demand curves in this article). A large change could cross the price between elastic and inelastic demand.[9]

We changed price by 1% in both examples. There are some issues with units – coffee is priced in dollars per pound while sales are in million tons per year – but simple arithmetic fixes those. Here’s the result from the Excel workbook:

Fig19 A Primer on Elasticity

(click for larger image)

Conclusion

Next up: applying what we’ve learned here to the market for ceiling fans.

Endnotes

  1. Based on Karl Case, Ray Fair, and Sharon Oster Principles of Economics (13e), chapter 5. Pearson Higher Education Publishing, 2020.There are many other elasticities. Price elasticity of supply, income elasticity of demand, and cross-price elasticity of demand are three examples.
  2. Parts of this article are based on Jeff Perloff and Jim Brander, Managerial Economics and Strategy (3e), chapters 2 and 3. Pearson Higher Education Publishing, 2020. I did some work producing ancillary materials for this textbook.
  3. See above.
  4. Economists put price on the vertical axis, despite its role as the independent variable. We do this because price is the dependent variable for a supply curve. We arbitrarily chose the supply curve to label the axes.
  5. Perloff and Brander, chapter 10 pages 320-321.
  6. See above.
  7. Economists put price on the vertical axis, despite its role as the independent variable. We do this because price is the dependent variable for a supply curve. We arbitrarily chose the supply curve to label the axes.
  8. Based on Karl Case, Ray Fair, and Sharon Oster Principles of Economics (13e), chapter 5. Pearson Higher Education Publishing, 2020.
  9. The price that separates elastic and inelastic demand is halfway up a linear demand curve. Above that price, demand is elastic. Below that price, demand is inelastic.

 

 

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About Tony Lima

Retired after teaching economics at California State Univ., East Bay (Hayward, CA). Ph.D., economics, Stanford. Also taught MBA finance at the California University of Management and Technology. Occasionally take on a consulting project if it's interesting. Other interests include wine and technology.