Unit 1: Law of Demand and Elasticity of Demand - 3 Chapter Notes | Business Economics for CA Foundation PDF Download

Cross - Price Elasticity of Demand

Price of Related Goods and Demand

The demand for a specific commodity can fluctuate due to changes in the prices of related goods, which may include either complementary or substitute goods. This relationship is examined under the concept of 'Cross Demand'. Cross demand pertains to the quantities of a commodity or service purchased in relation to price changes of other interrelated commodities, while assuming other factors remain constant. It can be defined as the quantities of a commodity that consumers acquire over a specific time frame at varying prices of a 'related article', assuming other factors remain unchanged. The assumption of 'other things remaining the same' implies that the consumer's income and the price of the commodity in question will stay constant.

(a) Substitute Products and Demand
In the case of substitute goods, the cross-demand curve has a positive slope, indicating that the demand for a commodity increases when the price of a substitute commodity rises. In the illustrative figure, the quantity demanded of tea is plotted on the X-axis, while the Y-axis represents the price of coffee, a substitute for tea. When the price of coffee goes up, the demand for coffee decreases due to the law of demand, prompting consumers to opt for tea instead. The price of tea is considered constant. Thus, an increase in the price of one commodity leads to a rise in demand for its substitute commodity. 

(b) Complementary Goods 
In the case of complementary goods, as illustrated in figure 11 below, a change in the price of one good will inversely affect the demand for the other related commodity. For example, an increase in demand for solar panels will also boost the demand for batteries. This relationship holds true for other complementary goods like bread and butter, cars and petrol, or electricity and electrical devices. When the demand for solar panels decreases due to a rise in their prices, the demand for batteries will also decline, not because the price of batteries has increased, but due to the higher price of solar panels. Therefore, we observe an inverse relationship between the price of one commodity and the demand for its complementary good (assuming all other factors remain constant). 

The cross-price elasticity of demand between two goods assesses how a change in the price of one good influences the quantity demanded of another good. This concept examines the impact of price changes within a market on demand patterns. A shift in the demand for one good in reaction to a price change of another good is indicative of the cross elasticity of demand for the first good relative to the second. It is calculated as the percentage change in the quantity demanded of one good divided by the percentage change in the price of the other good. 

Symbolically, (mathematically)

Where

E_c stands for cross elasticity.

q_x stands for original quantity demanded of X.

∆q_x stands for change in quantity demanded of X

py stands for the original price of good Y.

∆p_y stands for a small change in the price of Y. 

In the case of the cross-price elasticity of demand, the sign (plus or minus) is very important: it tells us whether the two goods are complements or substitutes. 

When two goods X and Y are substitutes, the cross-price elasticity of demand is positive: a rise in the price of Y increases the demand for X and causes a rightward shift of the demand curve. When the cross-price elasticity of demand is positive, its size is a measure of how closely substitutable the two goods are. Greater the cross elasticity, the closer is the substitute. Higher the value of cross elasticity, greater will be the substitutability. 

• If two goods are perfect substitutes for each other, the cross elasticity between them is infinite. 
• If two goods are close substitutes, the cross-price elasticity will be positive and large. 
• If two goods are not close substitutes, the cross-price elasticity will be positive and small.
• If two goods are totally unrelated, the cross-price elasticity between them is zero. 

When two goods are complements (like tea and sugar), the cross elasticity between them is negative, meaning that an increase in the price of one leads to a decrease in the quantity demanded of the other, resulting in a leftward shift of the demand curve. The magnitude of the cross-price elasticity of demand indicates the strength of their complementarity: a value slightly below zero suggests weak complements, while a highly negative value indicates strong complements.

However, classifying goods solely based on these definitions may not always be accurate. Goods with positive cross elasticity are labeled substitutes, but those with negative cross elasticity are not always complementary. This is because negative cross elasticity can also occur when the income effect from the price change is particularly strong.

The concept of cross elasticity of demand is valuable for managers making pricing decisions regarding products with substitutes and complements. If the cross elasticity in response to price changes of substitutes exceeds one, the firm risks losing customers by raising prices and may benefit from lowering them. Understanding cross elasticity enables firms to develop strategies to mitigate the impacts of price fluctuations in substitutes and complements.

Cross- price elasticity of demand 

Illustration 7: A shopkeeper sells only two brands of note books Imperial and Royal. It is observed that when the price of Imperial rises by 10% the demand for Royal increases by 15%.What is the cross price elasticity for Royal against the price of Imperial?
Sol:


The two brands of note book Imperial and Royal are substitutes with significant substitutability

Illustration 8:  The cross price elasticity between two goods X and Y is known to be - 0.8. If the price of good Y rises by 20%, how will the demand for X change?
Sol: Inserting the values in the formula:
-0.8 = X/ 20%
% change in quantity demanded of X = 20% x - 0.8 = - 16%
Since cross elasticity is negative, X and Y are complementary goods

Illustration 9: The price of 1kg of tea is ₹ 30. At this price 5kg of tea is demanded. If the price of coffee rises from ₹ 25 to ₹ 35 per kg, the quantity demanded of tea rises from 5kg to 8kg. Find out the cross price elasticity of tea.
Sol:


The elasticity of demand of tea is +1.5 showing that the demand of tea is highly elastic with respect to coffee. The positive sign shows that tea and coffee are substitute goods. 

Illustration 10: The price of 1 kg of sugar is ₹ 50. At this price 10 kg is demanded. If the price of tea falls from 30 to ₹ 25 per kg, the consumption of sugar rises from 10 kg to 12 kg. Find out the cross price elasticity and comment on its value.
Sol:


Since the elasticity is -1.2, we can say that sugar and tea are complementary in nature. 

Advertisement Elasticity

Advertisement elasticity of sales, or promotional elasticity of demand, refers to how demand for a product responds to variations in a company's advertising expenditure. It quantifies the percentage change in demand resulting from a one percent alteration in advertising spending. This metric evaluates the effectiveness of an advertising campaign in generating new sales. Generally, advertising elasticity of demand is positive; a higher advertising elasticity value indicates a stronger responsiveness of demand to changes in advertising efforts.

Advertisement elasticity varies between zero and infinity. It is measured by using the formula;

Where ∆ Qd denotes increase in demand

∆ A denotes additional expenditure on advertisement

Qd denotes initial demand

A denotes initial expenditure on advertisement

As far as a business firm is concerned, the measure of advertisement elasticity is useful in understanding the effectiveness of advertising and in determining the optimum level of advertisement expenditure.

Summary

Key factors influencing demand include:

• Price of the commodity
• Price of related goods
• Consumer income
• Tastes and preferences of consumers
• Future price expectations
• Population size
• Population composition
• National income level and distribution
• Consumer credit availability and interest rates

The law of demand states that consumers will buy more at lower prices and less at higher prices, assuming other factors remain constant.

• A demand schedule is a table showing various prices and the corresponding quantities demanded. There are two types of demand schedules: individual demand schedule and market demand schedule.
• According to Marshall, the downward slope of the demand curve is due to the law of diminishing marginal utility, while Hicks and Allen attribute it to income and substitution effects.
• Typically, the demand curve slopes downward; however, it can slope upward in certain cases such as with conspicuous goods, Giffen goods, conspicuous necessities, future price expectations, demand for necessaries, and speculative goods.
• A decrease in quantity demanded due to a price increase is termed contraction of demand, while an increase in quantity demanded due to a price decrease is termed extension of demand.
• The demand curve shifts right with increases in income (unless the good is inferior), increases in the price of substitutes, decreases in the price of complements, population growth, or favorable changes in consumer tastes. Conversely, the demand curve shifts left with opposite changes.

Elasticity of demand measures the sensitivity of demand to changes in its determinants, classified mainly into four types:

• Price elasticity of demand
• Income elasticity of demand
• Advertisement elasticity
• Cross elasticity of demand

Price elasticity of demand measures the percentage change in quantity demanded resulting from a percentage change in the commodity's price. Given the downward slope of the demand curve, price elasticity is typically negative, although we focus on the absolute value instead.

• Point elasticity assesses elasticity at a specific point on the demand curve, while arc elasticity is used for larger price changes between two points on the curve.
• Income elasticity of demand measures the percentage change in quantity demanded due to a percentage change in consumer income. Goods are classified as luxuries, normal, or inferior based on spending responsiveness to income changes.
• Cross elasticity of demand reflects the percentage change in quantity demanded of good X due to a percentage change in the price of related good Y, with positive values indicating substitutes and negative values indicating complements.
• Advertisement elasticity measures demand responsiveness to changes in advertising expenditure.
• Demand forecasting is the practice of predicting future demand for a product or service based on past behaviors and current trends.

Common techniques for demand forecasting include:

• Surveys of buyer intentions
• Collective opinion method
• Expert opinion method
• Barometric method
• Statistical methods (e.g., trend projection, graphical methods, least squares, regression analysis)
• Market studies (e.g., controlled experiments, laboratory experiments)