CROSS ELASTICITY OF DEMAND

It is the degree of responsiveness of demand for one commodity as a result of a change in the price of another.
It is the measure of effect of a change in demand for one commodity as a result of a change in price of another, especially when the two commodities are in competitive demand; i.e. they are substitute. It is the extent to which demand for meat changes when the price of a substitute, like fish, increases or decreases.

Substitute goods have positive cross elasticity; it is because price and demand move in same direction. Secondly, close substitute goods, e.g. meat and fish, have high cross elasticity; and substitute goods which are not close, e.g. yam and garri, have a low cross elasticity.
Price and demand for complementary goods move in the opposite direction, and they have negative cross elasticity. Secondly, close complementary goods, e.g. tea and sugar, have high cross elasticity. And complementary goods, e.g. tea and egg, paper and ruler, etc, that are not close complement tend to have low cross elasticity.
If 10% change in price of B causes 20% change in quantity demanded of A, the cross elasticity will be positive if the two commodities are substitute: beef and fish; and it is negative if they are complementary: Car and petrol.

Measuring cross elasticity (Ec)

We measure cross elasticity of demand through the use of the following formula. Cross elasticity is abbreviated as ‘Ec’.

Example

Consequent upon (due to) a rise in price of fish (F) from N200 to N250 per kilo, the quantity demanded of beef (B) rises from five kilos to seven kilos per week. Calculate the cross elasticity of demand.

Let us also adopt tabular approach (means of a table) in finding a solution to the above question. It is given below.

The cross elasticity for Beef and Fish is elastic because the elasticity, which is 1.6, is greater than 1.

Factors influencing elasticity of demand

The following are some of the factors that make demand to be either elastic or inelastic.

Close substitute: The demand for a product is very elastic if there is a very close substitute within the same price range. For instance, a slight increase in price of butter or beef induces consumers to switch to (buy) the substitutes: margarine, pork or fish and less of butter and beef. The products without close substitutes’ tend to have inelastic demand. Even though their prices have doubled or quadrupled, consumers tend to buy virtually (almost) the same quantity because there are no alternative items; e.g. salt, pepper, water, etc.
Level of income: The higher the level of a person’s income, the more inelastic his demands become. For instance, the demand of a millionaire for all goods are inelastic as he purchases almost the same quantity of the goods irrespective of increase in prices. But for a poor man, any increase in price compels him to buy a substitute or even an inferior good whose price remains constant. Thus the demand of a poor man for goods tends to be elastic.
Habit: Once a habit is formed, it takes some time before it can be changed. The demand for cigarette, drink, etc, tend to be inelastic because smokers or drunkard acquire them even though their prices have quadrupled (increased).
Cheap products: Many goods whose prices are relatively low usually hare inelastic demand. It is because the proportion of one’s income spent on them is very small. Even though their prices have increased tenfold, consumers buy virtually (almost) the same quantity. Good examples are salt, matches, pencil, needle, etc. Thus they have perfectly inelastic demand; the quantity demanded almost remains the same wherever the price.
Unavoidable commodity – goods of necessity: Certain goods are quite indispensable in life. Except they are acquired nothing can be properly or meaningfully done. The most important example is food to all living organisms. Others include water, firewood, drugs, and services of doctors, transporters, and other basic necessities of life: clothes and houses. Even though their prices have gone up hundred fold, some people may even sell some of their property to acquire them. Thus their demand is perfectly inelastic.
Luxury: Luxurious goods are items of comfort. They include expensive cars, clothes (lace), chairs, gold, etc. They can be avoided, especially by low income earners. Thus an increase in their prices leads to more than proportionate change in the quantity demanded (cause a fall in their demand). Their demand is therefore elastic.
Time Factor: In the short run demand tends to be inelastic. It is because it may not be possible to find good substitutes (other similar goods) within the same price range. Secondly, it may not be very easy to change one’s habit. While in the long run (after a long period like a year or two) it is possible to find close substitutes and change one’s habit. Thus demand becomes elastic.
Proportion of total income spent on a commodity: Goods on which people spend a very small part of their income e.g. salt, pepper, matches etc tend to have inelastic demand. While goods on which consumers spend a large part of their income have elastic demand.

Summary

A product with close substitutes has elastic demand e.g. fish. While those without close substitutes have inelastic demand e.g. salt.
A person with high income has inelastic demand for goods and services e.g. millionaires, While a poor man has elastic demand, e.g. beggars, low income earners.
People with strong habit of consumption of goods have inelastic demand, e.g. drunkard, smoker, etc.
All cheap products have inelastic demand e.g. salt, matches.
All goods of necessity (unavoidable items) have inelastic demand e.g. food.
Luxurious goods have elastic demand e.g. luxurious cars.
In the short-run, demand for goods tends to be inelastic; but it is elastic in the long run.
Goods that take a small part of one’s income have inelastic demand, and vice versa.

Certain groups of products like foodstuffs, beverages (tea), furniture, clothes, detergents (soap), etc ., have inelastic demand. But their individual brand, like fish, beef, chicken and shrimps regarding food, tend to have elastic demand because of closeness of Substitutes.

Importance of Elasticity of Demand

Increase in revenue: It helps the producers or sellers to increase their revenue in a bid to raise the prices of their commodities. This will depend on whether their goods are inelastic or elastic.
Determination of maximum output: It also helps the producers to determine the maximum output to produce in order to ensure higher turnover and profit.
Determination of cross elasticity: It helps the producer to determine which goods to produce more when goods of the same substitutes exist.
Imposition of taxes by government: Elasticity of demand helps the government in determining the imposition of taxes on goods and services.

Elasticity of demand and producers’ revenue

How price elasticity affects producers’ revenue is discussed under three types of price elasticity: elastic, inelastic and unitary.

1) Elastic demand

If demand is elastic, a decrease in price makes total revenue to be greater than previous total revenue. Rectangle OPIEIQI of figure 13 is greater than rectangle OPEQ. While a rise in price makes total revenue to be smaller than previous total revenue; rectangle OPEQ is smaller than rectangle OPIEIQI. Thus a producer of a product with elastic demand will reduce its price if he wishes to increase total revenue.

2) Inelastic demand

If demand is inelastic, a fall in price makes total revenue to be smaller then the pervious total revenue. Rectangle OPIEIQ1 of figure 14 is smaller than rectangle OPEQ. And restoring the price to OP, or increase in price makes total income of the producer to be greater than the previous total income. For instance, rectangle OPEQ is greater than rectangle OPIEIQ1. Thus a producer of a product with inelastic demand have to increase price if he wishes to increase total revenue.

3) Unit elastic

The total revenue of a producer (seller) remains constant after either increase or decrease in price if elasticity of demand is unitary. This is illustrated in figure 15. The percentage (10%) decrease or increase in price leads to 10% increase or decrease in demand. Thus total revenue is always constant. Rectangle OPEQ equals rectangle OPIEIQ1 in figure 15.

Summary

If price elasticity of demand is inelastic, an increase in price raise the total revenue of the seller; while decrease in price reduces the total revenue. However, if price elasticity of demand is elastic, an increase in price reduces his total revenue; while a decrease in price raises his total revenue. But in unit elasticity either increase or decrease in price doesn’t affect the total revenue; total revenue remains the same.