A measure of the responsiveness of the quantity demanded of a good to a change in its price. A measure of the responsiveness of the quantity demanded of a good to a change in its price.

The price elasticity of demand measures the sensitivity of the quantity demanded to changes in the price. Demand is inelastic if it does not respond much to price changes, and elastic if demand changes a lot when the price changes.

• Necessities tend to have inelastic demand.

• Luxuries tend to have elastic demand.

• Demand is elastic when there are close substitutes.

• Elasticity is greater when the market is defined more narrowly: food vs. ice cream. • Elasticity is greater in the long run, as people are freer to adjust their behavior.

Price elasticity of demand =

Percentage change in quantity demanded/Percentage change in price

• We use this formula instead of the slope, because the slope is sensitive to the units of measurement of price and quantity. • Mankiw adopts the convention of reporting the absolute value of the price elasticity. • Elasticity depends on where we are on the demand curve. For a straight line demand curve, elasticity is highest when the price is high (and quantity is low).• For the elasticity between two points, the formula can depend on whether we move from point A to point B, or point B to point A.

A: Price = $4, Quantity = 120

B: Price = $6, Quantity = 80

A to B: Elasticity = (40/2)(4/120) = 2/3

B to A: Elasticity = (40/2)(6/80) = 1.5

Alternative Ways of Measuring Elasticity:

Two alternative elasticity measures avoid or minimize these shortcomings of the basic elasticity formula: point-price elasticity and arc elasticity.

Point-price elasticity:

One way to avoid the accuracy problem described above is to minimize the difference between the starting and ending prices and quantities. This is the approach taken in the definition of point-price elasticity, which uses differential calculus to calculate the elasticity for an infinitesimal change in price and quantity at any given point on the demand curve:

In other words, it is equal to the absolute value of the first derivative of quantity with respect to price (dQd/dP) multiplied by the point's price (P) divided by its quantity (Qd).

Consider the market for sales of ice cream cones at a state fair. The table below gives the market quantity demand, given that all sellers at the fair charge the same price.

Price of Ice Cream($)| Quantity Demanded

(millions)|

0.50| 16|

1.00| 13|

1.50| 10|

2.00| 7|

2.50| 4|

3.00| 1|

We can calculate the market price elasticity of demand using the information contained in the table. For example, suppose you decide to calculate the price elasticity of demand at $2.00 by examining a price decrease from $2.00 to $1.50 per cone. In this case, the demand for ice cream would increase from 7 million cones to 10 million cones. You can use these figures to calculate the price elasticity of demand as follows:

This implies the following:

The price elasticity of demand for ice cream cones at a price of $2.00, according to the demand schedule provided, is –1.72.

Arc elasticity (Mid-point elasticity):

A second solution to the asymmetry problem of having a PED dependent on which of the two given points on a demand curve is chosen as the "original" point and which as the "new" one is to compute the percentage change in P and Q relative to the average of the two prices and the average of the two quantities, rather than just the change relative to one point or the other. Loosely speaking, this gives an "average" elasticity for the section of the actual demand curve—i.e., the arc of the curve—between the two points. As a result, this measure is known as the arc elasticity, in this case with respect to the price of the good. The arc elasticity is defined mathematically as:

This method for computing the price...