Econ 2113: Principles of Microeconomics Spring 2009 ECU

Chapter 4 Elasticity

Elasticity  

So far, we have studied how S and D shifts affect P* and Q* We know that a supply increase will cause Q to increase and P to decrease.   But how much do P and Q change?  

 

The magnitude of the change in Q in response to a change in P depends on   shape

of, location on the demand curve   responsiveness of quantity demanded to a change in price

Demand Slope: Problems  

We would like to have a measure of the sensitivity of the quantity demanded to its price that does not depend on the units of measurement

 

Proposed concept: Elasticity of demand

 

Elasticity is unit-less

Elasticity  

Elasticity: a measure of responsiveness

 

We will introduce: Price elasticity of demand   Income elasticity of demand   Cross-price elasticity of demand   Price elasticity of supply  

Price Elasticity of Demand  

Elasticity is a units-free measure of the responsiveness of quantity demanded to a change in price.

 

Definition: percentage change in quantity demanded that results from a one percent change in its price

Price elasticity of demand ε = (Percentage change in quantity demanded) ÷ (Percentage change in price) Examples: * Price goes up 1%, quantity demanded goes down 3%. What’s the elasticity? * Elasticity is 4. Price goes up 1%. How much does quantity demanded change?

Price elasticity of demand Note: price elasticity is often expressed as a positive number, for convenience  

 

We know that P and Q always move in opposite directions so price elasticity of demand will always negative. We are interested in the magnitude of changes, so we use absolute value

ε > 1 ⇒ elastic ε < 1 ⇒ inelastic ε = 1 ⇒ unit elastic

Two special cases P

P ε = infinity ε=0 D D Perfectly elastic demand Q

Perfectly inelastic demand

Q

Alternative mathematical expressions for price elasticity of demand  

ε = %ΔQ /%ΔP = (ΔQ/Q) / (ΔP/P)   now

 

ε = (ΔQ/Q)×(P/ΔP )=(ΔQ/ΔP) × (P/Q) =   to

 

just rearrange...

get…

ε = (P / Q) × (1 / slope)   “point-slope

method”

Graphical interpretation of elasticity    

D: Flatter curve ⇒ more elastic D': Steeper curve ⇒ more inelastic (less elastic) P A

P

D D' Q

Q

Elasticity: Example  

You operate your own business selling college t-shirts. The demand schedule for your t-shirts is P = 25 – Q/2 (inverse demand curve)

 

What is the price elasticity of demand when P=10? If P = 10 10 = 25 - Q/2 Q = 30 1/Slope = -2 (for any price and quantity, since demand is linear) EQ,P = -2 (10/30) = -2/3

 

Notice that elasticity is measured at a point. In general, a given demand function will have a different elasticity at each point, except for some special cases

Factors Affecting Elasticity  

Availability of substitutes   The more substitutes there are available for the good, the more elastic the demand   Example: Apples vs. insulin

 

Time   Demand tends to be more inelastic in the short term than in the long term   Time allows consumers to find substitutes   Example: We expect the demand for gasoline to be more elastic over the next 20 years than in the next month. Why???

 

Expenditure Share   Goods that comprise a small share of consumer’s budgets tend to have a more inelastic demand than goods for which consumers spend a large portion of their incomes   Example: Salt vs. housing

Statistical Estimates of Price Elasticities in the US Good or service

Price elasticity

Green peas

2.80

Restaurant meals

1.63

Automobiles

1.35

Electricity

1.20

Beer

1.19

Movies

0.87

Air travel (foreign)

0.77

Shoes

0.70

Coffee

0.25

Theater, opera

0.18

Elasticity and Linear Demand  

Price elasticity changes along a straight-line demand curve P Po

ε>1 ε=1

Po/2

ε 0, then X and Y are substitutes. Why? If EQX,PY < 0, then X and Y are complements. Why?

Income Elasticity Measures the percent of change in the quantity demanded of good X for a 1% increase in income

If EQX,M > 0, then X is a normal good. If EQX,M < 0, then X is a inferior good.

Uses of Elasticities        

Pricing Impact of changes in competitors’ prices Impact of economic booms and recessions And lots more!

Example 1:Pricing and Cash Flows

According to an FTC report, AT&T’s own price elasticity of demand for long distance services is -8.64   AT&T needs to boost revenues in order to meet it’s marketing goals   To accomplish this goal, should AT&T raise or lower it’s price?  

Quantifying the Change in Quantity

 

If AT&T lowered price by 3 percent, what would happen to the volume of long distance telephone calls routed through AT&T?

Answer •  Calls would increase by 25.92 percent!

Example 2: Impact of a change in a competitor’s price

 

According to an FTC Report, AT&T’s cross price elasticity of demand for long distance services (with respect to other carriers prices) is +9.06

 

If competitors reduced their prices by 4 percent, what would happen to the demand for AT&T long distance services?

Answer •  AT&T’s demand would fall by 36.24 percent!

Price elasticity of supply   εS

 

= (% change in Qs)/(% change in P)

Just like price elasticity of demand, but computed with the supply curve

  εS

= (P/Q)(1/slope)

Extreme Cases P

P

S

S

Q

Q

Determinants of the elasticity of supply

1. 

Ability to produce with substitute inputs: the greater the ability to produce with substitute inputs, the higher is the elasticity of supply.

2. 

Time: the greater is the time horizon, the higher is the elasticity of supply.

Elasticity & Volatility of Q and P  

 

When supply and demand are relatively inelastic, prices tend to be volatile, but the quantity bought and sold in the market is relatively stable. Example: California energy market. P

S

D

Q

Elasticity & Volatility  

When supply and demand are relatively elastic, the quantity bought and sold in the market is relatively volatile, but prices tend to be stable. P S

D Q