Cross Elasticity of Demand: Proportionate change in demand with change in price

Cross Elasticity of Demand

Some goods are related to each other. So a fall in the price of a commodity causes change in the demand for other commodity. As for example, demand for tea is related to the price of substitute, coffee. When the price of coffee increases, the demand for tea increases. Hence, cross elasticity of demand means the responsiveness of quantity demanded of a commodity to the change in price of other commodity. The cross elasticity of demand is defined as the percentage in the quantity demand of good x resulting from a 2 percent change in the price of good y.

According to C. E. Ferguson, “Cross elasticity is the proportionate change in the quantity demanded of good x divided by the proportionate change in the price of y.”

The formula to calculate cross elasticity is,

Cross Elasticity = ^{Proportionate change in quantity demanded of x}/_{Proportionate change in price of y}

Symbolically, Ec = ^Δqx/_Δpy x ^Py/_Qx

The concept of cross elasticity can be illustrated by the help of a numerical example. Suppose that x and y are two substitute goods. Suppose when the initial price of y is $4.50, the initial quantity of x is 60kg. Now when the price of y increases to $5, the quantity demanded of x increases to 70kg. The cross elasticity is calculated as,

Ec = ^Δqx/_Δpy x ^Py/_Qx 
= 10/5.0 x 4.5/60 = 3/2 = 1.5

1.5 coefficient shows that the cross elasticity is positive.

Types of Cross Elasticity

The goods may be either substitutes or complements. So the cross elasticity is of two types as follows:

1. Positive Cross Elasticity (Ec > 1)

When two goods are substitutes of each other, the cross elasticity is positive. As for example, tea and coffee. The increase in price of one commodity leads to an increase in quantity demanded of other commodity. Because, people substitute one commodity for other.

Positive Cross Elasticity

In the figure, demand curve DD shows positive cross elasticity. Because, with the increase in price X from OP to OP1, demand for Y has increased from OM to OM1.

2. Negative Cross Elasticity (Ec < 0)

When two goods are complements, cross elasticity is negative. As for example, shoe and shoelaces. The increase in price of one commodity causes fall in the quantity demanded of other commodity.

Negative Cross Elasticity

In the figure, demand curve DD shows negative cross elasticity. Because due to the increase in price of X from OP to OP1, demand for Y has declined from OM to OM1.

When the goods are not related to each other, the cross elasticity is zero. As for example, book and coat. The change in price of one does not affect the demand for other. Hence, the demand curve will be a vertical straight line. But this is not counted as cross elasticity.

---

You may also like to read:

• Meaning of Elasticity of Demand

• Uses of Price Elasticity of Demand in Managerial Decision Making

• Factors Determining Elasticity of Demand

• Meaning of Income Elasticity of Demand

• Theory of Consumer's Behavior

• Measurement of Price Elasticity: Total Outlay Method

---

Various uses of income and cross elasticity of demand in business decision-making

The use of income elasticity of demand for a firm’s is to determine the growth opportunities of the firm, useful in targeting marketing efforts, success at different stages of business cycles. Following are the theoretical and practical importance:

1. Estimate the effects of changes in economic activity

During the periods of expansion, incomes are rising and firms selling luxury items that the demand for their products will increase at a faster rate than the rate of income growth.

During a recession, demand may decrease rapidly. Knowledge of income elasticity can be useful in targeting marketing efforts. If per capita or household income is found to be an important determinant of the demand for a particular product, this can affect the location and nature of sales outlets. It can also have an impact on advertising and other promotional activities.

2. Uses in capitalist economics

The concept of income elasticity of demand takes an important place among the analytical tools applied for business research. This concept is of income sensitivity of consumption expenditure. Income sensitivity has a co-efficient which measures the percentage increase in rupee expenditure associated with one percent change in disposable income in the same period. The income sensitivity estimates are of great use in business forecasting.

3. Planned developing economies

In the developing countries like Nepal, as levels of living rise, demand for some commodities is expected to go up much faster than the demand for others. In the earlier stages, income elasticity of demand for food tends to be high. As income rises, there is a shortage of food, which not satisfied, leads to inflation. If the planners know income elasticity of demand for goods and services of general use, steps can be taken to balance demand and supply by using appropriate method.

4. Marketing activity and making market strategy

The concept of income elasticity of demand has important role in marketing activities of the firm. People demand goods and services on the basis of their income level. The level of income of the people affects the location and nature of sales. The high-income elasticity of demand indicates the significant promotional efforts in the business.

It is also useful in making marketing strategy. The business firm should concentrate its marketing efforts in media that reaches to the high-income group of the people.

Importance of Cross Elasticity of Demand

The concept of cross-elasticity is useful for the following main purposes:

1. Useful in inter-commodity relations: It is important for the firm to be awared of how the demand for its products likely to respond to changes in the prices of other goods; this information is necessary for formulating the firm’s own pricing policy and for analyzing the risk associated with various products. This is particularly important for the firms with extensive product lines, where significant substitution or complementary interrelationships exists between the various products. The concept of cross elasticity of demand is very useful in handling the inter-commodity relations.
2. Classification of markets and market structure: The classification of markets of commodities and services is mainly based on the concept of cross elasticity of demand of one seller in relation to the other. It is used in industrial organization to measure the interrelationships among industries. The cross price elasticity between the firm’s product and products in related industries is large and positive, the firm, even though it may be a monopolist in a narrow sense, will not be able to raise its prices without losing sales to other firms in related industries.
3. Importance for anti-monopoly legislation: The concept of cross elasticity of demand has been of practical use in sponsoring anti-monopoly legislation. When a particular seller tries to estimate or buy up substitutes of his own product through unfair means, there is a case of monopoly practice against him. But, it is only of drawing a clear-cut line between fair competition and monopoly, however, it is basic concept of doing so.

  SOME RELATED LINKS:   

• Cross Elasticity of Demand: Proportionate change in demand with change in price

• Uses of Price Elasticity of Demand in Managerial Decision-making

• Elasticity of Demand: Types of Price Elasticity of Demand

• Income Elasticity of Demand: Proportionate change in quantity demanded per change in income

• Measurement of Price Elasticity: Total Outlay Method