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Elasticity Of Demand And Cross Price Elasticity

1. Elasticity of demand

The extent to which the demand for a service or good responds to a decrease or an increase in its price is known as Elasticity of Demand. (Moffat 2010)

2. Cross-price elasticity (include substitutes and complements)

A proportionate change in the demand for one item in response to a variation in the price of another good is referred to as cross-price elasticity. (Moffat 2010)

The cross-price elasticity is 'positive' where the two items are mutual substitutes, and any rise in the price of one (such as in the case of butter) will result in a rise in the demand for the substitute (such as margarine). In the case of complementary items, it is 'negative' as any increase in the price of one (such as in the case of cars), will result in a decrease in the demand for the substitute (such as tires).

Income elasticity (include normal and inferior goods)

The Income Elasticity of Demand is the rate at which the quantity that is demanded responds to a variation (increase or decrease) in the income of the consumer. (Moffat 2010)

Goods, whose demand increases, at each price level, with the rise in the consumer’s income, are said to be normal goods. They have a positive income elasticity of demand. A distinction is made between normal necessities and normal luxuries (both these categories of normal goods have a positive coefficient of income elasticity).

The elasticity of demand for income is between 0 and +1 for normal goods. Demand increases as the consumer’s income increases, but less than proportionately. Often this is because there is a limited requirement to consume additional quantities of necessary goods as the consumer’s real living standards increase. Typical examples of this would be the demand for newspaper, toothpaste and fresh vegetables. Demand is not very sensitive to changes in consumer’s income and the total market demand is more or less stable.

Normal luxury goods, on the other hand, have an income elasticity of demand > +1. The rate of increase in demand is more than the proportionate increase in consumer’s income. Luxuries are items we can do without during periods when income levels are below average and in times of falling consumer confidence. When incomes are display a strong rising tendency and consumers have the confidence that this tendency will continue the demand for luxury goods will keep on increasing. Conversely, in a recession or economic slowdown, spending on these items will be reduced first as consumers restrict their spending and start rebuilding their savings.

Certain luxury goods are said to be ‘positional goods’. These are products which give the consumer satisfaction and they also have a utility, not merely from consuming the good or service itself, but also from being seen by others to be a consumer.

Demand for inferior goods falls as income rises as they have a negative income elasticity of demand. In a recession, demand for inferior goods might actually rise (which is dependent on the extent of any change in income and the absolute co-efficient of income elasticity of demand). For instance, if the income elasticity of demand for cigarettes is -0.4, then a 6% drop in the average real incomes of consumers might result in a 2.4% drop in the total demand for cigarettes (all other things remaining unchanged).

B.  Explain the elasticity coefficients for each of the three terms defined in part A.

1. Elasticity of Demand coefficient

As elasticity measures responsiveness, it has to be in numbers or elasticity coefficients. ‘Responsiveness’ implies that there is a reaction as a result of some change (or stimulus). A certain change (stimulus) has caused consumers to react by changing their behavior. The coefficient of elasticity is a measure of the extent to which consumers react. (Businessdictionary.com 2010)

The coefficient of price elasticity of demand measures the extent to which people respond in their purchasing decisions to changes in price. The coefficient of price elasticity of demand is calculated as:

e = (percentage change in quantity demanded) / (percentage change in price of the item).

(i.e. elasticity is the percentage variation in quantity divided by the percentage variation in price.)

If the price rises by 10% and the consumers respond by reducing their purchases by 20% the coefficient works out to -2. It has a negative value because a rise in price (a positive number) results in a decrease in buying (a negative number). Generally, many economists disregard the negative sign, as due to the law of demand.

An elasticity coefficient of 2 is indicative of high degree of responsiveness to a change in price. Conversely, if a 10% change in price results in a 5% change in sales demand, the elasticity coefficient will work out to be 1/2. In this case demand is said to be inelastic. It is inelastic whenever the elasticity coefficient is less than one. If the coefficient is greater than one, economists refer to the demand as ( Amosweb 2010)

As the price of good Y rises, the demand for good X falls. Two goods complement each other and show a negative cross elasticity of demand.

As the price of good Y rises, the demand for good X rises. Two goods are substitutes and have a positive cross elasticity of demand

Two goods that are independent have a zero cross elasticity of demand: as the price of good Y rises, the demand for good X remains unchanged and constant

Figure 1 -A

Figure 1-B

Figure 1-C

(En.wikipedia.org 2007)

2. Cross-price elasticity coefficient

e = (percentage change in quantity demanded of good X) / (percentage change in price of the good Y).

Where the two goods are substitutes the cross elasticity of demand will be greater than zero (0) or positive, so that if the price of one goes up the demand of the other will also increase. For example, if there is a rise in the price of carbonated soft drinks, the demand for non-carbonated soft drinks will rise. If the products are perfect substitutes, the cross elasticity of demand is equal to positive infinity. (Ingrimayne 2010)

In case the two goods are independent, the cross elasticity of demand is zero: when the price of one good varies, there will be no change in the demand for the other product.Products with relatively few good substitutes have a smaller coefficient of elasticity of demand than products having many substitutes. Generally, more broadly defined goods have a smaller elasticity coefficient than narrowly defined products. The price elasticity of demand for meat will be lower than the elasticity of pork, and the price elasticity for soft drinks will be less elastic than the elasticity for colas, which will be less elastic than the price elasticity for Pepsi.

3. Income elasticity of demand coefficient

Income elasticity of demand can be calculated to determine the sensitivity of demand for a good to a change in income. Higher income elasticity is indicative of a more sensitive demand for a good to changes in income. High income elasticity indicates that when the income of a consumer rises, he will buy larger quantities of that item. Low price elasticity indicates just the converse, that a change in the income of a consumer has an insignificant effect on demand.

There are rules of thumb economists have devised to determine if a product is classified as luxury item, normal good or an inferior good by looking at the coefficient of income elasticity of demand:

It is a Luxury good if IEoD > 1, and it is Income Elastic

It is a Normal good if IEoD is < 1 and IEOD > 0, and is Income Inelastic

It is an Inferior Good if IEoD < 0, and Negative Income Inelastic

C.  Contrast the terms defined in part A.

1.  Explain the significance of differences among the three terms you contrasted in part C.

Elasticity of Demand

The significance of elasticity is fundamental in appreciating the response of the supply and demand mechanism in a market.

In economics the Markup rule is used to explain a firm’s pricing decisions. The price a firm will charge is equal to a markup over the firm's marginal cost, equal to one over one minus the inverse of the price elasticity of demand.

Therefore, as defined − P'(P / Q) = inverse of price elasticity of demand = − 1 / ε. Hence, P(1 − 1 / ε) = MC

or, let η be the inverse of the price elasticity of demand

Since for a price setting firm, η > 0 this means that a firm with clout in the market will charge a price above marginal cost. On the other hand, a competitive firm by definition faces a perfectly elastic demand, hence it believes η = 0 which means that it sets price equal to marginal cost.

The rule also deduces that, a monopolistic firm will never choose to be located at a point on the inelastic portion of its demand curve. Also, for equilibrium in a monopoly or an oligopoly market, the price elasticity of demand must be greater than one (1 / η < 1). (Mas-Collel).

2. Cross-price elasticity of demand

This calculates the extent of responsiveness of demand, for good A, as a result of a change in the price of good B. In contrast, the price elasticity of demand for A measures the responsiveness of demand for good A as a result of a change in its price (i.e. price of A). In cross-price elasticity the main concern is with the effect of changes in relative prices within a market on the demand patterns.

Whereas, in the price elasticity of demand we measure the responsiveness of the demand due to changes in its price, in cross-price elasticity we measure the responsiveness of demand due to changes in the prices of other goods. The other goods, in this instance may be substitutes or complementary goods.

3. Income elasticity of demand

In contrast with the aforementioned two instances, here we attempt to measure the responsiveness of demand relative to changes in the consumer income levels. There is an attempt to determine the coefficient of income elasticity of demand; i.e. how would the demand of good A respond to a change in the income level of the consumer.

Substitutes: For example, data on price indices for new cars and second hand cars is depicted in the chart below (Figure 2). Since the price of new cars in relation to consumers’ incomes has fallen, this should increase the demand for new cars and (ceteris paribus) result in a fall in the demand for second hand cars. We observe that there is a very distinct fall in the prices of second hand cars.

Figure 2

Complementary goods: Goods that have complementary demand, such as demand for DVD players and DVD videos; as the price of DVD players’ falls more DVD players are bought, leading to an expansion in market demand for DVD videos. The cross price elasticity of demand for two complements is negative

The stronger the relationship between two goods, the higher is the co-efficient of cross-price elasticity of demand. For example, when there are two close substitutes, the cross-price elasticity will be strongly positive. Similarly, when there is a strong complementary relationship between two products, the cross-price elasticity will be highly negative. Products that are unrelated have a zero cross elasticity.

D.  Explain whether demand would tend to be more or less elastic for each of the following three determinants of elasticity demand:

1.  Availability of substitutes

Elasticity of demand: If substitutes are available an increase in the price of the good would make the consumers substitute the product for another similar one. Demand would therefore be elastic, (Figure 1-B).

Cross-price elasticity of demand: In case the two goods are substitutes the cross elasticity of demand will be greater than zero (0) or positive, and if the price of one goes up the demand of the other will rise, with cross elasticity being positive. If they are perfect substitutes, the cross elasticity of demand is equal to positive infinity.

Income elasticity of demand: Most of the effect on demand due to a change in price will be as a result of changes in the relative prices of substitute goods and services. What to some people is a necessity might be a luxury to others. For a large number of products, the final income elasticity of demand might be close to zero, i.e. there is a very weak correlation between changes in income and spending decisions. In this case the “real income effect” arising from a fall in prices is likely to be relatively small.

2.  Share of consumer income devoted to a good

Elasticity of demand: When the proportion of the consumer's income expressed in percentage terms against the product's price is high, the elasticity is also high as consumers will give more consideration to its price when making a purchasing decision.

Cross-price elasticity of demand: As above the greater is the percentage of the consumer’s income compared to the cost of the good, the greater will be the elasticity as a change in the price will make the consumer shift to substitutes.

Income elasticity of demand: The extent to which demand, for a good, changes due to a change in income depends upon whether the good is a necessity or a luxury. The demand for necessities will rise with rising income, but at a slower rate. This is because consumers, instead of buying more of only the necessity, will use their increased income to purchase more luxury goods. During a period of rising income, demand for luxury products tends to increase at a higher rate than the demand for necessities.

Therefore, for luxury goods income elasticity of demand is greater than 1; for a normal good the income elasticity is between 0 and 1; and for inferior goods it is less than 0 (zero).

Consumer’s time horizon

Elasticity of demand: In the case of a majority of goods the longer a price variation remains the same, the greater the elasticity, as more consumers will have the time to search for substitutes. As fuel prices rise suddenly, consumers may top-up their fuel tanks in the short run. However, when prices continue to remain high over a longer period, say several years, more people will curtail their demand by changing to carpooling or public transportation, purchasing vehicles with greater fuel economy. This is not the case for goods known as consumer durables, such as the cars. Eventually, however, it may be that consumers replace their present cars with more economical ones, so the demand is expected to become less elastic.

Time plays an important role in determining both consumer and producer-responsiveness for many items. The longer people have to make adjustments, the more adjustments they will make.

Cross-price elasticity of demand: As in the aforementioned paragraph, there will be a case of demand being elastic in the longer term.

Income elasticity of demand: Demand for luxury items the elasticity is greater than 1, for a normal good it is again between 0 and 1, and for inferior goods it will be less than 0 (zero).

F. Differentiate between perfectly inelastic demand and perfectly elastic demand.

1.  Illustrate the difference between the terms in part F with specific descriptions or graphs.

Perfectly inelastic demand

Figure -3 (Wapedia 2010)

This is where the demand is not affected by a change in the price of the product. The product does not have any substitutes and irrespective of the price consumers keep purchasing the same quantity. As shown in figure 3 above the elasticity coefficient is 0 (zero).

Perfectly elastic demand

Figure -4 (Wapedia 2010)

When demand is perfectly elastic the quantity demanded will remain constant at the equilibrium price and an increase in price will make the consumers stop buying the item. The coefficient of elasticity is infinity.

G.  Explain the relationship between elasticity of demand and total revenue for the following ranges along the demand curve, using the attached “Graphs for Elasticity of Demand, Total Revenue.” Include the impacts to quantity demanded and total revenue when there is a price decrease, ceteris paribus.

1.  Elastic range

2.  Inelastic range

3.  Unit-elastic range

Elasticity of demand can be used as an effective tool in gauging the effect of a change in the product’s price over the quantity demanded and produced by a firm. A firm contemplating a price change must determine the effect of the change in price on total revenue. Any change in price will tend to have two effects:

Price effect: an increase in unit price will result in an increase in revenue, whereas a decrease in price will result in a decrease in revenue.

Quantity effect: an increase in unit price will lead to lesser number of units that are sold, whereas a decrease in the unit price will result in more units sold.

Due of the inverse relationship between quantity demanded and price (i.e., the law of demand), the two factors affect total revenue in opposing directions. However, in ascertaining whether to decrease or increase prices, a firm will need to assess the net effect. Elasticity is the tool used for this purpose: The proportional variation in total revenue is equal to the proportional variation in the quantity demanded plus the proportional change in price. (One proportional variation will be positive, and the other will be negative.)

The relationship between elasticity of demand and total revenue can be ascertained for any item:

If the price elasticity of demand is perfectly inelastic (Ed = 0), any variations in the price will not affect the quantity demanded for the item; increasing the price will cause total revenue to rise.

If the price elasticity of demand is relatively inelastic (Ed < 1), the proportional change in quantity that is demanded is lesser than the proportional variation in price. Hence, when the price is increased, the total revenue increases, and vice versa.

If the price elasticity of demand for an item is unit (or unitary) elastic (Ed = 1), the proportional variation in quantity is equal to the proportional variation in its price, therefore, a variation in price will not affect total revenue.

If the price elasticity of demand is relatively elastic (Ed > 1), the proportional change in the quantity demanded is higher than the proportional variation in its price. Hence, when the price is increased, the total revenue drops, and vice versa.

If the price elasticity of demand for an item is perfectly elastic (Ed = infinity), any increase in the price, albeit very slight, will cause demand for the item to fall to zero. Hence, when the price is increased, the total revenue drops to zero.

As shown in Figures 5 & 6 maximum total revenue is achieved at the combination of quantity demanded and price where there is unitary elasticity of demand.

Figure 5 & 6 (Wapedia 2010)

A firm aiming to maximize profit chooses the quantity to sell which equates its marginal revenue (the change in revenue from one extra unit sold) to its marginal cost (the change in total cost due to one extra unit produced). This results in the markup rule, which states that the firm's ability to price its goods over cost depends on the extent of its market power. Market power depends on the price elasticity of demand faced by the firm. (Wapedia 2010)

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