Demand Elasticity (2024)

The concept of elasticity is used extensively ineconomics. It is not a difficult concept to master once you understand whatelasticity tells the economist about the demand for a good. The word elasticitybasically means responsiveness or sensitivity in everyday language. In fact,when the economist wants to know how "price elastic" the demand forapples is, all he really wants to know is how the demand for apples"responds" to a change in the price of apples.

The Price Elasticity of Demand:

Concept:

The demand function can be written as Q_x^D= f (P_x). This simply means that the quantity demanded of good X (Q_x^D)will depend upon the price of good X (P_x). The price elasticity ofdemand, therefore, simply tells us just "how much" the demand for goodX depends upon the price of good X.

Algebraically:

E_D = % Q_x^D
% P_x

Where (Delta) means "change in." The larger the elasticity, the moreresponsive or sensitive the demand for good X is to a change in its price.

BUT WAIT!! Because of the law of demand, the price elasticity of demand coefficient will always be negative. When the price goes up, quantity demanded goes down and vice versa. However, it is always read as the absolute value -- as positive. Don't forget this. Always drop the negative sign when reading the elasticity coefficient.

Economists define the elasticity coefficient such that:

if E_{D >}1, then demand is elastic

if E_D = 1, then demand is unitelastic

if E_D < 1, then demand isinelastic

If demand is relatively responsive—inpercentage terms—to changes in price, it is "elastic" (E_Dis greater than one). If E_D is less than one, the amount demanded isrelatively unresponsive—in percentage terms—to changes in price. In thiscase, demand is said to be "inelastic." When E_D is equal toone at a point (or between points) demand is said to be "unitaryelastic" at that point (or between those points).

Example: Let’s answer the following question: SupposeAntonio’s raises the price of pizzas by ten percent and finds that thepurchase of pizzas by customers falls by five percent. What is the elasticity ofdemand for pizzas with respect to their price at Antonio's?

The calculation is simple: Use the second term inthe above equation and simply plug in the amounts:

E_D = % Q_x^D = -5 = -.5
% P_x 10

So what exactly does the elasticity coefficient tell us?

**This means that each one percent rise in theprice of pizzas results in a one-half of one percent decline in the consumptionof pizzas.

What About How the Demand Curve Looks?

It must be noted that economists, in addition to determining whether certain points on a demand curve are elastic, unitary elastic, or inelastic, also refer to a range of prices along an individual's curve as beingrelatively elastic, unitary elastic, or relatively inelastic -- or sometimes perfectlyinelastic or perfectly elastic. Graphs:

What we really mean to say is that the curve iselastic or inelastic over the relevant range of prices and quantities.Market demand curves are not completely inelastic (or elastic, of course) over theentire price range.

For example, when we observe consumers in acertain market, they usually only consume "so many" of some good perweek (for example) and the prices are usually within a certain range. We referto a range of prices and quantities which are relevant (the curve) aselastic or inelastic.

Influences on the Price Elasticity of Demand:

1. Time.

2. The proportion of one's budgetspent on the good.

*3. Availability and closeness ofknown substitutes.

An Important Application: Pricing Your Good

An important relationship to understand is theone between elasticity and total revenue or total receipts (where total revenueor total receipts = P X Q):

Total Revenue = Price x Quantity

Total Revenue - Total Costs = Profit

If total revenue rises when P_xfalls, the demand is elastic.

If total revenue falls when P_xrises, the demand is elastic.

If total revenue remains constant when P_xfalls, the demand is unitary elastic.

If total revenue remains constant when P_xrises, the demand is unitary elastic.

If total revenue falls when P_xfalls, the demand is inelastic.

If total revenue rises when P_xrises, the demand is inelastic.

When you think about it, all of this makes sense.If the demand for pizzas is responsive to changes in price, when the pricefalls, people will increase the number of pizza they demand. Therefore, althougheach pizza costs less, total revenue increases because people are buying so manymore pizzas. On the other hand, if the demand for pizzas is not responsive tochanges in price, a fall in the price of pizzas will also mean a fall in totalrevenue. This is because the same (or close to the same) number of pizzas aredemanded, but each one is sold for a lower price.

Note: Short-run is less than a year. Long-run is more than a year.

Source: http://www.mackinac.org/article.aspx?ID=1247

In addition to the price elasticity of demand,there are other elasticities of interest to economists. These include:

The Income Elasticity of Demand:

Concept:

E_I = % Q_x^D
% Income

(Note: The sign here will tell us something aboutwhat "kind" of good X is—normal or inferior).

Otherwise the elasticity is read the same as always - it is always positive.

Economists have estimated the following income elasticities:

The Cross Price Elasticity of Demand:

Concept:

E_xy = % Q_x^D
% P_Y

(Note: The sign here will tell us something aboutthe relationship between X and Y – substitutes or complements).

Otherwise the elasticity is read the same as always - it is always positive.

Economists have estimated the following cross-price elasticities. Note that the same cross-price elasticity does not come about with the same two goods - it depends upon how it is calculated. Does this make sense?