Elasticity

The elasticity coefficient, ε a simple measure of the responsiveness of sales, Δq, to price changes, Δp, at a given initial price, p, and an initial level of sales, q.

It is akin to a sensitivity index but it also measures the link between total revenue from sales (TR) and the price. Note the following, TR = p.q: a change in TR, DTR, can be represented by the following:

When a product reaches the plateau of its product life cycle there are usually many substitutes in the product’s market. Consequently the product is classified, as having an elastic demand and if price continues to fall on the elastic demand then the TR will increase.

How does one interpret an ε coefficient of (say) 1.32 for apples? First of all we ask: what is the providence of the estimate: this is a US estimate provided by empirical studies in the 1980s. Second we ask: how reliable is the estimate: elasticity coefficients are decanal values, that is, the value is representative for a ten-year period. Finally, we ask: is the coefficient for a single good or a group. In other words, the demand elasticity for fruit (including apples) may be inelastic, with a coefficient less than 1. A price elasticity of ε= 1.32 for apples implies that if the price of apples were to fall by 10% the demand for apples would have increased by 13.2%.

Notice that the Δq = 13.2% responds more than proportionately than the Δp = 10% and hence the ratio Δq/Δp > 1, and for a given p/q ratio, when Δq/Δp > 1 the elasticity coefficient > 1. However with an inelastic demand, Δ < 1, if price continues to fall the TR would decrease. The converse also holds, given rise to what we label the TR Test:

Elastic ε> 1 Price Decreases - TR increases Price Increases - TR decreases Elastic ε<1 Price Decreases - TR decreases Price Increases - TR increases

However an elastic value can also represents the presence of a monopolist in the market place. This phenomenon arises because a traditional monopolist chooses the higher monopoly price, which is located in the elastic segment of its demand. For a linear demand of slope = Δq/Δp = 1 the value of the ε coefficient depends on the p/q ratio and at a higher price p > q hence the ε> 1.

This has become known as the ‘cellophane fallacy’ in modern antitrust, when judges in a celebrated case against DuPont in the 1950s mistakenly believed that an ε> 1 indicated that a product like cellophane had indeed many substitutes in the market thus diluting any monopoly power accruing to DuPont. Equally, an inelastic demand can arise when the product is heavily advertised or endorsed in the market, given rise to a branding effect whereby as the price increase, demand increase accordingly. The increase in price can sustain an increase in TR. This was one of the key points addressed by the late Galbraith in his The Affluent Society as to whether or not consumers end up eventually paying for the advertising expenditures of the firms. At the end of the day the demand elasticity is about the link between TR and price movements.

Illustration

In the case where price is located in the upper left hand of the demand line, we observe a high price but also an elastic segment of the demand line. Although an elastic demand may signal the presence of substitute products in the market, as note here in the illustration, a monopolist charging at the higher end of the demand line, will also exhibit an elastic coefficient. Referred to as the ‘cellophane fallacy’ it emerged during a 1950s antitrust case against DuPont whereby the judge allegedly misinterpreted an elastic coefficient as indicative of substitutes products. In retrospect it confirmed the putative dominant position that DuPont held in the market for cling-film wrapping market.

Illustration of Perfect Elasticity and Inelasticity

Why is the red demand line horizontal?

It arises because price is constant at (say) £3 and in such circumstances AR =  p = MR as illustrated by a perfectly elastic demand. The following table illustrates the congruence of the AR and the MR lines. The market structure that is represented is often referred to as PERFECT COMPETITION. In this market, no one individual firm can influence price, the price is determined by the market and is thus exogenous to the firm. This contrasts with a MONOPOLY market structure wherein the firm can influence price, and in that market the AR > MR, price is not constant, and the AR = p demand line is as illustrated in the section on PRICE AND DEMAND, with a negative slope.

Perfect Competition: AR = Price = MR
Demand is Perfectly Elastic

Price is fixed, mamagement cannot change price. TR = 6, with quantity = 2. Management want to increase TR. Focus on quantity.

Stage 1:
Price = AR = 3
Quantity = 3
TR = 9
MR = 3 (Increased from 6 to 9)

Stage 2:
Price = AR = 3
Quantity = 4
TR = 12
MR = 3 (Increased from 9 to 12)

Illustration of Perfect Elasticity and Inelasticity

Why is the red demand line vertical?

In this case the demand is perfectly inelastic and the consumer is prepared to pay any price for the good. It could represent the demand for consumers who just have to make that purchase today at any price: for once-off concert tickets, an author signed book, the latest iPOD or video game or mobile phone. It can also represent addictive demand as in the demand for drugs like heroin or cocaine where the price is ultimately determined by supply and demand but the addict just has to purchase the drug today. Once the demand line is vertical, the point of intersection of the quantity axis represents a fixed supply of the product. At the 2006 Word Cup final in Berlin there was a fixed number of tickets because of the capacity of the stadium. The price you pay for a ticket or the price you pay for a highly inelastic good depends on your ability to pay.

Key Points

To translate the elasticity formula into an illustration

To distinguish elastic and inelastic demand lines.