Understanding Cross Price Elasticity of Demand: Definition, Formula, and More

What Is Cross Price Elasticity of Demand? 

The Cross Price Elasticity of Demand (sometimes referred to as cross elasticity) is an economic concept that quantifies the responsiveness in the quantity demanded of one product when the price for another one changes.  

Key Takeaway	Details
Definition of Cross Price Elasticity of Demand	Measures the responsiveness in the quantity demanded of one product when the price of another changes.
Cross Price Elasticity Formula	Cross Price Elasticity = (% Change in Quantity Demanded of Product A) / (% Change in Price of Product B).
Complementary Products	Typically consumed together, showing negative cross elasticity (e.g., hamburger patties and buns).
Substitute Products	Competitive products, exhibiting positive cross elasticity (e.g., Coca-Cola and Pepsi).
Unrelated Products	Show near-zero cross elasticity as they do not affect each other's quantity demanded (e.g., dog food and technology products).
Implications of Positive Cross Elasticity	Indicates a relationship between substitute goods, where a price decrease in one leads to a decrease in quantity demanded for the other.
Implications of Negative Cross Elasticity	Indicates a relationship between complementary goods, where a price decrease in one leads to an increase in quantity demanded for the other.
Difference between Own-Price and Cross Price Elasticity of Demand	Cross elasticity focuses on interdependent changes between two products, unlike own-price elasticity, which is product-specific.

What Is the Formula for Cross Price Elasticity of Demand? 

The cross price elasticity formula is as follows: 

Cross Price Elasticity of Demand = (% Change in Quantity Demanded of Product A) / (% Change in Price of Product B) 

To determine the % Change in Quantity Demanded, take (new product quantity – previous product quantity) / (previous product quantity)

To determine the % Change in Price, take (new product price – previous product price) / (previous product price) 

Example of Calculating Cross Elasticity Using the Formula

Product X’s quantity of demand increases from 10,000 units to 11,000 units in response to an increase in Product B’s price from $100 to $120.  What is the Cross Price Elasticity of Demand? 

% Change in Quantity Demanded for Product A:

(11,000 – 10,000)/(10,000) = 10%

% Change in Price of Product B:

($120 - $100)/($100) = 20% 

Cross Price Elasticity of Demand =

10%/20% = 0.5 

Complementary Products (Goods) 

Complementary Products or Goods are typically consumed together.  An example is hamburger patties and hamburger buns.  The Cross Price Elasticity of Demand for complementary goods is expected to be negative. 

Example: 

The change in quantity demanded for hamburger buns is expected to increase due to a decrease in the price of hamburger patties.  From the Cross Price Elasticity of Demand formula above, we expect a positive number in the numerator and a negative number in the denominator. 

Substitute Products (Goods) 

Substitute Products or Goods are seen as competitive with one another.  An example is Coca-Cola and Pepsi, which are somewhat interchangeable based on the similar consumer need they serve.  The Cross Price Elasticity of Demand for substitute goods is expected to be positive. 

Example: 

The change in quantity demanded for Pepsi is expected to decrease due to a decrease in the price of Coca-Cola.  From the Cross Price Elasticity of Demand formula above, we expect a negative number in the numerator and a negative number in the denominator leading to a positive cross elasticity. 

Unrelated Product (Goods) 

Many products or goods are essentially unrelated.  An example is dog food and technology products. Quantity demanded of a technology product such as an HDTV for home use should not be affected by changes in the price of dog food.  The Cross Price Elasticity of Demand for these two goods should be near zero. 

What Do Negative and Positive Cross Elasticity Mean? 

What Does a Positive Cross Elasticity of Demand Indicate? 

As described above, a positive cross-elasticity is associated with substitute goods.  It indicates that if the second good lowers its price, quantity demanded for the first good will decrease.  An example is Coca-Cola and Pepsi.  If the price of Coca-Cola goes down, the quantity demanded for Pepsi will also go down.  If the price of Coca-Cola goes up, the quantity demanded for Pepsi will also go up. 

What Does a Negative Cross Elasticity of Demand Indicate? 

As described above, a negative cross-elasticity is associated with complementary goods.  It indicates that if the second good lowers its price, quantity demanded for the first good will increase.  An example is hamburger buns and hamburger patties.  If the price of hamburger patties goes down, the quantity demanded for hamburger buns will go up.  If the price of hamburger patties goes up, the quantity demanded for hamburger buns will go down. 

Why Consider Cross Price Elasticity of Demand 

Firms consider the Cross Elasticity of Demand to develop effective pricing strategies. Products with no substitutes can command higher prices because there is no Cross Price Elasticity of Demand to worry about. However, for products with close substitutes, the firm needs to pay close attention to how those substitute products are changing their prices. 

Additionally, complementary goods can be priced strategically in light of the Cross Price Elasticity of Demand. For example, hot dogs may be sold at a loss recognizing that the quantity demanded for complementary goods, such as hot dog buns and condiments, should increase. 

What Is the Difference Between Cross Elasticity of Demand and Price Elasticity of Demand (Own-Price Elasticity)? 

Cross elasticity speaks to the proportional changes in quantity demanded between two goods as their prices change. Price Elasticity of Demand (own-price elasticity) considers the change in quantity demanded of a single product due to changes in its own price. 

How to Estimate Cross Elasticity of Demand 

Most firms cannot get enough detailed and uncontaminated market data about competitors’ prices and quantity demanded to estimate Cross Elasticity of Demand with accuracy.  Even though the firm may be able to control their price changes, promotions, and advertising efforts, they cannot control the special promotions, out-of-stock conditions, or changes to advertising that their competitors may offer.  This makes it challenging for the typical firm to estimate Cross Elasticity of Demand from market observations (and econometric modeling) with a high degree of accuracy. 

Market research survey experiments, especially conjoint analysis (CBC) provide a time-proven approach to estimating both Own-Price Elasticity and Cross Price Elasticity among products. 

Using Conjoint Analysis (CBC) to Estimate Cross Price Elasticity of Demand 

With conjoint analysis, market research survey participants are shown different product profiles offered at different prices and asked which product they would choose in each scenario (choice task).  Across choice tasks, the product prices (and potentially other product features) are experimentally changed and the changes in respondent choices are noted.  An example CBC question is shown below: 

Using a statistical model, such as (individual-level) logistic regression via HB-MNL estimation, the researcher estimates the preference for brands, product features, and importantly the price sensitivity of each product in the conjoint experiment.  Using that model with its utility coefficients, the researcher creates a what-if market simulator. 

Sawtooth Software’s conjoint analysis tools make developing the conjoint experiment, fielding the survey, and analyzing the data very straightforward and efficient.  The what-if market simulator is an automatic functionality within Sawtooth Software’s tools.   

With the conjoint market simulator, the choice likelihood (proportional to quantity demanded) for each brand (good) in the marketplace is predicted based on the prices the researcher specifies in the market simulator.  Thus, the own-price elasticity for the firm’s product can be estimated by changing its price and holding prices of competing products (goods) constant.  The Cross Price Elasticity of Demand may also be estimated by changing the price of competing products in the simulation scenario and holding the firm’s price constant. 

Example Conjoint Market Simulations to Estimate Cross Elasticity 

Twelve products (A-L) are placed in a CBC conjoint analysis market simulator.  The firm’s product (A) captures 10% share of preference when prices are at status quo.  The researcher raises a key competitor’s price (Product L) from $100 to $110 (a 10% increase).  Re-running the market simulation, the share of preference for product A increases to 11%. 

The Cross Price Elasticity of Demand for Product L price changes on Product A quantity demanded is:  +10%/+10%, or 1.0.  These two brands would be seen as somewhat substitutable. 

How Can I Try Sawtooth Software’s Conjoint Analysis Tools? 

A free trial version of the Discover survey platform is available at discover.sawtoothsoftware.com.  If you are new to Discover, first create a new account.  The Discover platform lets you write standard survey questions as well as create CBC (Choice-Based Conjoint) experiments for estimating Cross Price Elasticity of Demand.