ECON111 Tutorial 4 Week 5

Elasticity

Rudi Kurniawan

• Price elasticity – Percentage change in quantity of a good demanded if the price is changed by 1%, cet. par.

• Income elasticity – Percentage change in quantity of a good demanded if income is changed by 1%, cet. par.

• Cross price elasticity of X and Y – Percentage change in quantity of X demanded if the price of Y is changed by 1%, cet. par.

Price elasticity

• Cet. Par. assumption should be satisfied

• We can calculate price elasticity of demand for X

• Price elasticity of demand for Y cannot be calculated, because in every case where price of Y changes, cet. Par. Doesn’t hold.

Price elasticity

0

1

1 0

0

1

1 0

0.20

0.25

0.25 0.20 0.05

210,000

200,000

200,000 210,000 10,000

P

P

P P P

Q

Q

Q Q Q

0 1 0 0

0 1 0 0

0.20 10,000

210,000 0.05

2,000

10,500

0.19

0.19

P

P Q Q P Q

Q P P Q P

Point formula, May 1 against M ay 3

Income elasticity

• Cet. Par. assumption should be satisfied, i.e. the price of X and Y must remain constant.

• We can calculate income elasticity for X: May 2 and 3

• We can calculate income elasticity for Y: May 2 and 3

Income elasticity

1 2

1 2

( )

(120 125) 5,000

(200,000 205,000) 5

0.60

I

I I QX

Q Q I

1 2

1 2

( )

(120 125) 5,000

(310,000 315,000) 5

0.40

I

I I QY

Q Q I

Note: Positive sign for income elasticity of demand if good is a normal good.

Cross price elasticity

• Cross price elasticity for X: – What is the percentage change in quantity of X if the

price of Y is changed by 1%, cet. par.

• For Y: – What is the percentage change in quantity of Y if the

price of X is changed by 1%, cet. par.

Cross price elasticity

• To calculate cross price elasticity of demand, cross price must change, cet. par. (i.e. own price and income must be constant).

• There are no suitable figures for calculating cross price elasticity of demand for good X.

• In this case, we can only calculate the cross price elasticity of demand for good Y.

Cross price elasticity

,1 ,2

,1 ,2

( )

(0.20 0.25) 5,000

(305,000 310,000) 0.05

0.07

X X YX Y X

XY Y

P P QQ P

PQ Q

Note: Positive sign indicates that X and Y are substitutes.

Question?

Question 2

a. Explain in words, the meaning of price elasticity of demand?

b. Write the point formula and the mid-point formula for calculating price elasticity of demand.

– Explain the two formulas.

– Why do we need two formulas?

Answer for a.

• The price elasticity of demand is the responsiveness of the quantity demanded to a change in price,

• measured by dividing the percentage change in the quantity demanded of a product by the percentage change in the product’s price.

Answer for b. • Point formula • Mid-point formula

1 0 1 0

0 0

1 0 1 0

0 0

0 1 0 0 1 0

1 0 0 0 1 0

0

0

%

%

100%

100%

Q

P

Q Q Q Q

Q Q

P P P P

P P

P Q Q P Q Q

P P Q Q P P

P Q

Q P

1 0

1 0 1 0

1 0

1 01 0

1 0

1 0

1 0

1 0

%

%

2 2

22

2

2

Q

P

Q Q Q

Q Q Q Q

P P P

P PP P

P P

Q

Q QP

P P Q

Q Q P

• At a point, using the POINT FORMULA

• We express the change in price as a percentage of the original price, and the change in the quantity demanded as a percentage of the original quantity demanded.

• At the mid-point, using the MID-POINT FORMULA

• We express the change in price as a percentage of the average price (the average of the original and new price), and the change in the quantity demanded as a percentage of the average quantity demanded (the average of the original and new quantity).

• Why do we need two formulas?

– The mid-point formula has the convenient property that it will give the same elasticity over a given range of the demand curve, regardless of whether the price rises or falls.

– For example see the calculation of price elasticity in Question 1.

• Using point formula

• In the case of May 1 against May 2

– price elasticity = 0.19

– (absolute value)

• What about the case of May 2 against May 1?

– Price elasticity = 0.25

– (absolute value)

• DIY

• Using mid-point formula, we will get the same results for both cases. (DIY)

• 0.22 (in absolute value)

Back to Price elasticity calculation in Question 1

c. Why isn’t elasticity just measured by the slope of the demand curve?

– The slope of a linear demand curve is constant and can be written as ΔP/ΔQ. Therefore slope and elasticity are not the same thing.

– The formula for elasticity illustrates several important points:

• The formula for elasticity illustrates several important points: – Elasticity is clearly not equal to the slope of a linear

demand curve.

– Although a linear demand curve has a constant slope, the elasticity will be different for every segment of the demand curve.

– Since relatively high values for price are associated with relatively low values of quantity demanded (and vice versa), the absolute values for elasticity will be high at high prices and relatively low at low prices.

Question 3 • The figure below shows the

demand curve for DVD rentals. a. What is the quantity

demanded

– when price equals $3?

– when price equals $5?

Answer: – When price falls by one dollar, quantity

demanded increases by 25.

– So, when the price is $3 quantity demanded equals 75.

– Then, when the price is $5 the quantity demanded equals 25.

b. Calculate the elasticity of demand when the price rises from $3 to $5 a DVD.

– Use the mid-point formula to do the calculation.

1 0

1 0

%

%

(5 3) 25 75

(25 75) 5 3

8 50

100 2

400

200

2 2

P

P PQ Q

P Q Q P

P =$3, Q= 75. P =$5, Q= 25.

c. At what price is the price elasticity of demand equal to 1?

– Use the point formula to do this calculation

Answer:

Price elasticity always equals 1 at the mid-point of a linear demand curve.

• For example:

When P = $3, Q = 75

or 1 in absolute value

0

0

3 50 1501

75 2 150

P

P Q

Q P

75

3

Mid-point of a linear demand curve 1P