In the modern age, the monopolies rarely exist. Most of the products have their competing substitutes and complementing goods. It is imperative for managers to know how price variation in substitutes and complements can play havoc with a demand for their own products. If you are unable to determine the impact of such fluctuations on the demanded quantity of your product, you would be unable to respond quickly to meet the challenge.

Support your competitive substitute producer cuts the prices, and your buyers are diverted to him. How will you respond to meet the challenge of falling demand? Similarly, when your competitor increases the prices, how will you handle the problem to meet the high demand of the consumers?

As a manager, it is your utmost goal to maximize profits for your organization, whether public or private. The cross-price elasticity of demand helps you to decide timely to maximize your profits. It is expressed with CPEoD.

Generally, the competing producers decrease their prices to allure more customers to them. You will have either of the two options to meet the challenge:

1- Decrease price of your own products

2- Introduce novelties which attract more customer

While analyzing CPEoD, you will find three kinds of products in relation to your own products:

1- Substitutes

2- Complements

3- Unrelated Products

Your competitors are offering substitutes for your products. For example, Pepsi is a competitor to Coca-Cola. Similarly, wheat and rice, butter and margarine, tea and coffee, laptops and Ipads are competitors as well as substitutes for each other.

On the increase in the price of the Pepsi, the demand for Coca-Cola increases. On the increase in the price of wheat, the demand for rice goes up. Similarly, an increase in the price of tea shall increase demand for coffee. However, technical innovations in IPad are reducing demand for laptops and computers.

In this graph, we can see that change in the price of a substitute shifts the demand curve of your product to the right. In case of substitutes, the cross price elasticity of products is always positive and expressed with CPEoD>0.

However, the decrease in the price of substitutes of the branded products may not profoundly impact the demanded quantity of the branded products. Suppose the Marlboro decreases its prices. It will affect the demand for smokers of Dunhill but not too much.

The complementaries are different products but having joint demand. For example, you use bread and butter or margarine for your breakfast. Similarly, coffee and sugar are different products, but they are demanded jointly. In case of such products, a price variation in one product shall affect quantity demanded of the other product.

For example, an increase in wheat price shall cause an increase in the price of bread and shift the consumers towards rice. This shall also affect the demand for butter and margarine as both are complements to the bread. Similarly, an increase in the price of sugar shall add up to the price of coffee and resultantly decrease the demanded quantity of coffee.

In case of complements, we must keep in mind that a closer relation of complementary products shall affect the demand of each other more than distance relation products. Furthermore, the demand curve shall shift to left. The result of the division of negative numerator (top) with positive denominator (bottom) shall always be a negative cross price elasticity of demand. It is expressed in CPEoD<0.

If you are selling Coca-Cola, an increase in the price of wheat is not going to influence demanded quantity of your product. In such a situation your product is neither substitution nor complement to the grain. It is expressed as CPEoD=0.

We can measure cross-price elasticity by dividing percent change in quantity demanded of product A by percent change in the price of the product B while assuming that all other variables remain constant.

We can calculate the cross-price elasticity of substitutes by jotting down old and new values of the demanded quantity of a product and prices of the second product as:

Q1: 40

Q2: 55

P1: 40

P2: 50

We can find percent change in Quantity of product A as under:

= Q2-Q1/Q1

= 55-40/40

= 0.375

We can find percent change in price of the product B as under:

= P2-P1/P1

= 50-40/40

= 0.25

CPEoD = 0.375/0.25= 1.50

We will get a positive value.

We can calculate CPEoD in case of complements as under by taking data from the above graphs:

Q1: 40

Q2: 20

P1: 40

P2: 50

We can find percent change in quantity of the product A as under:

= Q2-Q1/Q1

= 20-40/40

= -0.5

We can calculate percent change in price of the product B as under:

= P2-P1/P1

= 50-40/40

= 0.25

CPEoD= -0.5/0.25

= -2

The value of the cross price elasticity of demand shall always be negative in case of complements.