Cross-Price Elasticity of Demand

A Primer on the Cross-Price Elasticity of Demand

Woman selects yogurt from grocery store
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Cross-Price Elasticity of Demand (sometimes called simply "Cross Elasticity of Demand) is an expression of the degree to which the demand for one product -- let's call this Product A -- changes when the price of Product B changes. Stated in the abstract, this might seem a little difficult to grasp, but an example or two makes the concept clear -- it's not difficult. 

Examples of Cross-Price Elasticity of Demand

Assume for a moment you've been lucky enough to get in on the ground floor of the Greek Yogurt craze. Your Greek yogurt product B, is immensely popular, allowing you to increase the single cup price from around $0.90 a cup to $1.50 a cup. Now, in fact, you may continue to do well, but at least some persons will revert back to the good old non-Greek yogurt (Product A) at the $.090/cup price. By changing the price of Product B you've increased the demand for Product A, even though they're not highly similar products. In fact, they can be quite similar or quite different -- the essential point is that there will often be some correlation, strong, weak or even negative between the demand for one product when the price of another one changes. At other times, there may be no correlation.

Substitute Goods

The aspirin example shows what happens to the demand for good B when the price of good A increases. Manufacturer A's price has increased, demand for its aspirin product (for which there are many substitute goods) decreases.

Since aspirin is so widely available, there probably won't be a great increase in each of these many other brands; however, in instances where there are only a few substitutes, or perhaps only one, the demand increase may be marked.

Gasoline vs. electric automobiles is an interesting instance of this. In practice, there really are only a few automobile alternatives: gasoline automobiles, diesel, and electrics. Gasoline and diesel prices, as you'll remember, have been extremely volatile since the late 1980s. As U.S. gasoline prices reached $5/gallon in some West Coast cities, the demand for electric cars increased. However, since 2014 gasoline prices have fallen. With that, demand for electrics fell with them, putting automobile manufacturers in a peculiar bind. They needed to sell electrics to keep their fleet mileage averages down, but consumers began buying gasoline trucks and larger gasoline autos again. This forced manufacturers --Fiat/Dodge is a case in point -- to lower the price of electrics below their actual production cost in order to keep selling gasoline-powered trucks and muscle cars without triggering a federal government penalty. 

Complimentary Goods

A local Seattle band has a breakthrough hit -- millions and millions of streams, many, many downloads and a hundred thousand albums sold, all in a few weeks. The band begins touring and in response to demand, ticket prices begin climbing. But now something interesting happens: as the ticket prices increase, the audience becomes smaller -- no problem so far because what's happening essentially is that the band is playing smaller venues but at greatly increased ticket prices -- still a win. But then, the band's management sees a problem. As the audience grows smaller, so do the sales of all those high mark-up collectibles -- band T-shirts, coffee mugs, photo albums and so on: the "merch."

Our Seattle band has more than doubled the ticket price at $60.00 and is still selling about half as many tickets at each venue. So far so good: 500 tickets times $60.00 is more money than 1,000 tickets times $25.00. However, the band had enjoyed robust merch sales averaging $35 a head. Now the equation looks a little different: 500 tix x $(60.00 + $35.00) is less than 1,000 tix x ($25.00+35). The drop in ticket sales at a higher price created a proportionate drop in merch sales. The two products are complementary. As the price increases for band tickets, the demand for band merch drops. 

The Formula

You can calculate the Cross Price Elasticity of Demand (CPoD) as follows:

CPEoD = (% Change in Quantity Demand for Good A) ÷ (% Change in Price for Good A)