Elasticity Reading: 2.4-2.5, 4.3 Supply-Demand model can predict the direction of changes in P & Q. It can also predict the degree of change in P & Q

Elasticity

• Reading: 2.4-2.5, 4.3

• Supply-Demand model can predict the direction of changes in P & Q.

• It can also predict the degree of change in P & Q.

• Income up → P up. Will P goes up only slightly or greatly? This depends on the slope of S and D curves.

What would be the price and quantity response if income increases?

Quantity Quantity

Price

S

D S

D

Q0

P0 P0

Q0

Case 1 Case 2

Elasticity• Slope (∆P/∆Q) can help indicate the response of Q to P

(∆Qd/∆P, ∆Qs/∆P; ∆ means change in …). • But slope is not a good measurement. Its value is differ

ent if measurement units of P or Q are different. • P up: US$1→US$2. Q down: 200→100.

∆Q/∆P = -100/1 = -100.• P now quoted in HK$: P up: HK$7.8→HK$15.6. ∆Q/∆

P = -100/7.8 = -12.82.

Elasticity: Demand

• A better measurement of responsiveness shouldn’t be affected by measurement unit → elasticity

• Own-price demand elasticity:

PP

QQ

Ed

dd

/

/

pricein change %

demandedquantity in change %

Elasticity: Demand

• E.g. price of pork up from $10 to $11 → quantity demanded down from 1 million pounds to 950,000 pounds.

• P up by 10%, Qd down by 5%

• Ed = -5%/10% = -0.5

• Ed < 0 because D curve is downward-sloping.

Elasticity: Demand

• There is a calculation problem, however.• P up from $10 to $11 → up 10%• P down from $11 to $10 → down 9%• Q down from 1 million to 950,000 → down 5%• Q up from 950,000 million to 1 million → up

5.3%• Ed is different even for the same degree of

movement. Direction of movement matters.

Elasticity: Demand• Explore methods to get rid of this direction-

dependence problem.

• For calculating elasticity for two points, we can take an average of Q or P after and before change.

Q

PP

QE DP Δ

Δ

Elasticity: Demand

D

Quantity (100K)

Price($ per unit)

11

9.5

10

10

• Two points of P: $10, $11 → average P = $10.5• ∆P/P = 1/10.5 = 9.5%

• Two points of Q: 1 million, 950,000 → average = 975000• ∆Q/Q = 50000/975000 = 5%

• Ed = - 5%/9.5% = -0.53

Elasticity: Demand

• Elasticity calculated for two points by this method: arc elasticity of demand.

• Its value won’t be different due to the direction of movement: from A to B, or from B to A.

• This invariance property can also be achieved by shortening the distance between two points.

Elasticity: Demand

• The shorter the distance between point A and B, the elasticities calculated from either direction is closer to each other.

• When point A and B converges to one point, the elasticity is completely “invariant” with direction of movement.

• This is point elasticity.

Elasticity: Demand

• To measure point elasticity, we have to know the slope of the demand curve.

• Ed• Slope of a D curve = ∆P/∆Qd • Point Ed = (P/Q) (slope of D curve)• E.g. Qd = 8 – 2P, ∆Qd/∆P = -2.

Point Ed at (P = 1, Qd = 6): Ed = (1/6)(-2) = -1/3

Point Ed at (P = 2, Qd = 4): Ed = (2/4)(-2) = -1

P QdQd PQd P Q P

Point Elasticity• Measuring point Ed is much easier for linear

demand function because the slope is constant.

• But even for non-linear demand function, it can be measured. Again, use Ed = (P/Q) (slope of D curve).

Point Elasticity

D

Price($ per unit)

11

9.5

• Ed = ∆Qd/Qd ∆P/P = (P/Q)(∆Qd/∆P)• Slope = ∆P/∆Qd = -1 at

A• Ed = (11/9.5)/(-1) = -1.16

at point AA

Q

Elasticity: Demand

• Arc elasticity is probably more intuitive. But economists more often use point elasticity.

• Point elasticity measures the quantity response to a very small change in price.

Elasticity: Demand

• Patterns in elasticities:

- Elastic: % change in Qd > % change in P

(|Ed| > 1)

- Inelastic: % change in Qd < % change in P (|Ed| < 1)

- |.| means absolute value.

- Along a demand curve, point Ed is different at different points.

Elasticity: Demand

Q

Price

4

8

2

4

Ep = -1

Ep = 0

EP = -

Elastic

Inelastic

Demand Curve

Q = 8 – 2P

Application: Elasticity, Consumption Expenditure, Sales Revenue

• To stimulate sales, price must be lower.

• To increases sale volume, sales revenue may not be higher.

• Px increases with x at first and then decreases.

• If % P reduction < % quantity reduction, Px increases.

X1 2 3 4 5 6 70

1

2

3

Price of x

4

5

6

7

Demand)

|Ed| > 1

|Ed| < 1

|Ed| =1

Total expenditure

Elasticity: Demand

• Special types of D curve:

- Horizontal D curve: ∆Qd/∆P = ∞ (∆P/∆Qd = 0). Perfectly elastic at all point.

- Vertical D curve: ∆Qd/∆P = 0 (∆P/∆Qd = ∞). Perfectly inelastic at all point.

Perfectly elastic demand

DP*

Quantity

Price

EP = at every point

Perfectly inelastic demand

Quantity

Price

Q*

D

EP = 0 at every point

Elasticity: Demand

• Some elasticity results:

- Soft drink: elastic

- Toilet papers: elastic

- Toothpaste: inelastic

- Tissue: inelastic

Elasticity: Demand

• Income elasticity of demand:

I

Q

Q

I

II

QQ

E

d

d

dd

I

/

/

incomein change %

demandedquantity in change %

Elasticity: Demand

• EI > 0, normal good• EI < 0, inferior good (nothing to do with

inferior quality)• EI > 1, superior good. Income share of

superior good increases with income. • Some facts associated with EI:- Necessities usually have EI between 0 and 1.- Luxury goods usually have high EI.

Elasticity: Demand

• Cross-price elasticity of demand: it measures how the price of a good affects the quantity demanded of another good.

Y

X

X

Y

YY

XX

XY

P

Q

Q

P

PP

QQ

E

/

/

Y good of pricein change %

X good of demandedquantity in change %

Elasticity: Demand

• EXY > 0. X and Y are substitutes. E.g. coffee and tea. P of coffee up, D for tea goes up → Qd of tea up.

• EXY < 0. X and Y are complements. E.g. coffee and coffee mate. P of coffee up, D for coffee mate down → Qd of coffee mate down.

Elasticity: Supply

• Own-price elasticity of supply:

P

Q

Q

P

PP

QQ

E

s

s

Ss

s

/

/

pricein change %

suppliedquantity in change %

Elasticity: Supply

• For an upward-sloping S curve, Es > 0.

• For a horizontal S curve, Es = 0.

• Since S curve may be down-sloping (not often happens), Es < 0 is possible.

• Elastic supply: |Es| > 1

• Elastic supply: |Es| < 1

Elasticity: Long run vs Short run

• P up. Q will change. But when will we measure the change in Qs, or Qd?

• Time is important because it takes time for consumers to change their consumption habit, and for firms to change their production capacity.


• Long run: enough time is allowed for consumers or producers to fully adjust to the P change.

• Short run: time is not enough for this complete adjustment.


• It is widely believed that D is more elastic in LR than in SR.

• Reason: (1) When P up, it takes time to change consumption habit. (2) It takes time to search substitutes for a good.

• This phenomenon is called “second law of demand”. But this “law” is not widely recognized to be “law”.


DSR

DLR

Quantity of Gasoline

Price•People cannot easily adjust consumption in short run.•In the long run, people tend to drive smaller and more fuel efficient cars.


• Counterexample: (Steven Cheung) P up for cross-harbour tunnel, Qd drops in SR, recovers in LR.

• Reason: Substitutes for the tunnel (other tunnels) are well known, need no time to search. In contrast, consumers find out substitutes for the tunnel are not so useful as initially imagined. Revert to tunnel finally.


• Counterexample: (Pindyck & Rubinfeld) Durable goods are more elastic in SR than in LR.

• Reason: Consumers hold a much larger stock of old durables than newly produced durables per year. Replacing old durables takes time. E.g. P for cars up, delay replacing old cars, Qd for new cars drop sharply. Old cars gradually wear out and must be replaced. Qd picks up again.


DSR

DLR

•Initially, people may put off immediate car purchase•In long run, older cars must be replaced.

Quantity of Cars

Price


• For the same reason, income elasticity is also smaller in SR but higher in LR. Changing habit and searching substitutes takes time.

• Again, for durables, EI more inelastic in LR. Income down, Qd for new cars down sharply. Old cars gradually wear out. Qd picks up again.


• Elasticity for petrol (in US):

Years after the price change

(oil shock 1974):

1 2 3 5 10 20

Ed -0.11 -0.22 -0.32 -0.49 -0.82 -1.17

EI 0.07 0.13 0.20 0.32 0.54 0.78


• Elasticity for cars (in US):

Years after the price change

(1980s-1990s):

1 2 3 5 10 20

Ed -1.20 -0.93 -0.75 -0.55 -0.42 -0.40

EI 3.00 2.33 1.88 1.38 1.02 1.00


• Durables: D is more elastic in SR. The business is more pro-cyclical than non-durables. Indicators of economic fluctuation. E.g. sales of new houses frequently cited as signs of economic recovery.


• Normally, supply is also more elastic in LR than in SR.

• In SR, there are fixed factors or production capacity constraint. Even P up, Qs can’t expand beyond capacity. Can only pay workers to work overtime. In LR, Qs can expand more.

• This is the so-called Le Châtelier principle.

Documents

Elasticity Reading: 2.4-2.5, 4.3 Supply-Demand model can predict the direction of changes in P & Q. It can also predict the degree of change in P & Q