Econ 201 Lecture 8 Price Elasticity of Demand A measure of the responsiveness of quantity demanded to changes in price. Highly responsive = "elastic" Highly unresponsive = "inelastic" Price elasticity of demand = The percentage change in the quantity demanded that results from a one percent change in price. Example 8.1. If a 1 percent rise in the price of shelter caused a 2 percent reduction in the quantity of shelter demanded, the price elasticity of demand for shelter would be -2. The price elasticity of demand will always be negative (or zero) because price changes always move in the opposite direction from changes in quantity demanded. For convenience, we usually drop the negative sign and speak of price elasticities in absolute value terms. The demand for a good is said to be elastic with respect to price if its price elasticity is more than 1. The demand for a good is inelastic with respect to price if its price elasticity is less than 1. Demand is unit elastic with respect to price if its price elasticity is equal to 1.

Inelastic Elastic

Unit elastic

0 1 2 3 A more general formula for price elasticity: Let P = the current price of a good; Q = the quantity demanded at that price; ΔP = a small change in the current price and ΔQ = the resulting change in the quantity demanded Elasticity = percentage change in quantity / percentage change in price = (ΔQ/Q)/(ΔP/P) A Geometric Interpretation of Price Elasticity

Q

P

D

Q

P

P - ΔP

Q + ΔQ

ΔP

ΔQ

Elasticity = (ΔQ/Q)/(ΔP/P)

= (ΔQ/ΔP) (P/Q) ΔP/ΔQ = the slope of the demand curve, so ΔQ/ΔP = 1/slope. Elasticity = (P/Q)(1/slope) Example 8.2. Find the price elasticity of demand at point A on the demand curve below:

2 Price

Quantity

1086

42

0 1 2 3 4 5

D

A

slope = 10/5 = 2, so 1/slope = 1/2 P/Q at point A = 4/3 So elasticity = P/Q • 1/slope = 2/3 In the diagram below, the absolute value of the price elasticity of demand at point D is equal to

a. 3. b. 2 c. 0.5 d. 0.25 e. 1/3.

P

Q

100

75

50

25

20010050 150

A

B

C

D

E

Elasticity = (P/Q)(1/slope) = (25/150)(200/100) = 1/3 For straight-line demand curves:

Price

Quantity D

A

Slope is the same at every point, so 1/slope is also the same at every point. The ratio P/Q declines as we move downward along the demand curve. So elasticity, which equals (P/Q)(1/slope), declines as we move downward along a straight-line demand curve. Two polar cases:

3

P

Q

P

Q

Perfectly elasticdemand (elasticity = )

D

Perfectly inelasticdemand (elasticity = 0)

D

The Unit-Free Property of Elasticity Q. Why measure price-responsiveness with elasticity, which is relatively complex, rather than with the slope, which is relatively simple? A. Because elasticity is unit-free, whereas slope is not. P ($/gallon)

Q

C34

50 gallons/day

slope=0.02

elasticity=3

P ($/ounce)

Q

C0.02343750.03125

50 gallons/day

slope=0.00015625elasticity=3

Some Representative Elasticity Estimates Good or Service Price Elasticity __________________________________________ green peas 2.8 electricity 1.2 beer 1.2 movies 0.9 air travel (foreign) 0.8 shoes 0.7 theater, opera 0.2 __________________________________________ Elasticity and Total Expenditure "Will more be spent on the product if we sell more units at a lower price or fewer units at a higher price?" Example 8.3. Suppose you are the administrator in charge of setting tolls for the Golden Gate Bridge. At the current toll of $1/trip, 100,000 trips per hour are taken across the bridge. If the price elasticity of demand for trips is 2.0, what will happen to the number of trips taken per hour if you raise the toll by 10 percent?

A 10 percent increase in price will produce a 20 percent reduction in quantity. Thus the number of trips will fall to 80,000/hr. Total expenditure at the higher toll will be (80,000 trips/hr)($1.10/trip) = $88,000/hr. Note that this is smaller than the total expenditure of $100,000/hr that occurred under the $1 toll. Example 8.4. Now suppose that the price elasticity had been not 2.0 but 0.5. How would the number of trips and total expenditure then be affected by a 10 percent increase in the toll?

This time the number of trips will fall by 5 percent to 95,000/hr, which means that total expenditure will rise to (95,000 trips/hr)($1.10/trip) = $104,500/hr. If your goal as an administrator is to increase the total revenue collected from the bridge toll, you will need to know something about the price elasticity of demand for trips before deciding whether to raise the toll or to lower it.

4 A price reduction will increase total revenue if and only if the price elasticity of demand is greater than 1. An increase in price will increase total revenue if and only if the price elasticity of demand is less than 1.

M

P

Q

Elasticity > 1: A price reduction increasestotal expenditure; a price increase reduces it.

Elasticity < 1: A price reduction reducestotal expenditure; a price increase increases it.

Elasticity = 1: Total expenditure isat a maximum.

If demand is... A price increase will... A price reduction will...

elastic

inelastic

reduce totalexpenditure

increase totalexpenditure

increase totalexpenditure

reduce totalexpenditure

P Q PQx = P Q PQx =

P PQx =QP Q PQx =(ε > 1)

(ε < 1)

Example 8.5: What happens to total expenditure on shelter when the price is reduced from $12/sq yd to $10/sq yd?

0

161412108642

Price ($/sq yd)

(sq yds/wk) 4 6 8 10 122

Reduction in expenditure from sale at a lower price

Increase in expenditure from additional sales

F

E

G

14 16Quantity

When price goes down, total expenditure will rise [fall] if the gain from sale of additional units is larger [smaller] than the loss from the sale of existing units at the lower price.

5

A director of a big bus company said, "For each 1 percent fare hike, we lose 0.2 percent of our riders." We can conclude that: a. a fare increase will increase total revenue. b. demand for bus service will go up as fares increase. c. demand is price elastic. d. a 10 percent fare hike will produce a 20 percent reduction in riders. e. the price elasticity is -5.

We are told that when ΔP/P = 1%, ΔQ/Q = 0.2%. Elasticity = (ΔQ/Q)/( ΔP/P) = 0.2. (inelastic) So answer a is correct. Determinants of Price Elasticity of Demand •Substitution Possibilities Vaccine against rabies: no good substitutes; highly inelastic Salt: no good substitutes, highly inelastic. Morton's salt: perfect substitutes, highly elastic. Morton's salt at Wegman's: still more elastic •Budget Share. Items that occupy a large share of a consumer's budget tend to have higher price elasticity of demand. Example: price elasticity of demand for cigarettes higher for teenagers than for adults. •Time. Because substitution takes time, demand is more elastic in the long run than in the short run. THE PRICE ELASTICITY OF SUPPLY The percentage change in quantity supplied that occurs in response to a one percent change in price. price elasticity of supply = (ΔQ/Q)/(ΔP/P) = (P/Q)x(ΔQ/ΔP). Since (ΔQ/ΔP) is the reciprocal of the slope of the supply curve, we have Elasticity of supply = (P/Q)x(1/slope), which is the same as the equation for price elasticity of demand. Price and quantity are always positive, as is the slope of the typical supply curve, which implies that price elasticity of supply will be a positive number at every point. Example 8.6. Find the price elasticity of supply at point A on the supply curve shown:

3

2

100 150 Quantity

PriceS

ΔP

ΔQ

A

B

The slope of this supply curve is 1/50, so the reciprocal of this slope is 50. Using the formula, this means that the price elasticity of supply at A is (2/100)x(50) = 1. The corresponding expression at B, (3/150)x(50), yields exactly the same

6 value. Indeed, because the ratio P/Q is the same at every point along the supply curve shown, price elasticity of supply will be exactly one at every point along this curve. The special property that explains why price elasticity equals one at every point along the supply curve in Example 6.6 is the fact that the supply curve was a straight line through the origin.

For movements along any such line, both price and quantity always change in exactly the same proportion. Elasticity is not constant, however, along straight-line supply curves like the one below, which does not pass through the origin. Although the slope of this supply curve is equal to 1/100 at every point, the ratio P/Q declines as we move to the right along the curve. Elasticity at A is equal to (2/100)x(100) = 2, and declines to (3/200)x(100) = 3/2 at B.

3

2

100 200 Quantity

PriceS

ΔP

ΔQ

A

B

1

Determinants of Supply Elasticity

Flexibility of inputs. Mobility of inputs. Ability to produce substitute inputs Time