Economics

EC202 Principles of Microeconomics Elasticity page 1

Elasticity Elasticity is a tool that is used to describe the relationship between two variables. It is defined as the percentage change in a dependent variable “caused” by a percentage change in an independent variable.

variable tindependen an in %

variable dependent a in % Elasticity

�

� �

While elasticity can be calculated and used for any two related variables there are four basic coefficients of elasticity used in principles of economics

�� “Own” price elasticity of demand This is a measure of the percentage change in the quantity demanded “caused” by a percentage change in price. Because the demand function is an inverse relationship between price and quantity the coefficient of price elasticity will always be negative:

priceinchange DemandedQuantityinchange

demandofelasticityice %

% Pr �

�� Income elasticity. It is used to describe how a change in buyers’ income shifts the demand function for a good

Incomeinchange Demandinchange

ElasticityIncome % %

�

�� Cross elasticity is a measure of the responsiveness of buyers of a good to changes in the prices of related goods.

Ygoodofpricetheinchange Xgoodfordemandtheinchange

elasticityCross %

% �

�� Elasticity of Supply is a measure of the responsiveness of sellers to changes in the price of a good.

priceinchange pliedQuantityinchange

plyofElasticity %

sup% sup �

“Own” price elasticity of demand The price elasticity of demand can be calculated at a specific price and quantity. This is called the point price elasticity and is different at every price. To calculate point price elasticity use the formula

1

1 Q P

P Q

orEelasticitypricePo PP � �

� �� �int

functiondemandtheofslopetheis P Q

�

�

P1 is the original price

Q1 is the original quantity

The average price elasticity can be calculated between two price-quantity combinations. The average or “Arc” elasticity is calculated by the formula

21

21 QQ PP

P Q

EP �

� �

�

� �

functiondemandtheofslopetheis P Q

�

�

P1 is the original price, P2 is the new price

Q1 is the original quantity, Q2 is the new quantity

EC202 Principles of Microeconomics Elasticity page 2

1 2 3 4 5 6 7 8 9 11 13 15 17 19 21 23

19

1 2 3 4 5 6 7 8 9

10 11 12 13 14 15 16 17 18

(P )

P ri

c e

Xebecs (QX)

Demand Q = 24 – 1.5P P = 16 - .667Q

-7

-1

-.455

-2.02

-.68

Unitary Elasticity is at the midpoint. Top of demand function is “elastic,” bottom is “inelastic.”

Questions and Exercises Given the demand function Q = 24 – 1.5P

1. Construct the demand function on the graph. 2. Calculate the point price elasticity at a price of $14

3. Calculate the point price elasticity at a price of $8 4. Calculate the point price elasticity at a price of $5 5. Calculate the arc elasticity between $8 and $14 6. Calculate the arc elasticity between $5 and $8 7. Calculate the arc elasticity between $5 and

$14

EP = (�Q/�P)*(P/Q) = (-1.5)*(14/3 )= (-1.5)*(4.667) = -7.001

EP = (�Q/�P)*(P/Q) = (-1.5)*(8/12 )= (-1.5)*(.667) = -1

EP = (�Q/�P)*(P/Q) = (-1.5)*(5/16.5 )= (-1.5)*(.303) = -.455

EP = (�Q/�P)*(�P/�Q) = (-1.5)*(22/15 )= (-1.5)*(1.467) = -2.2

EP = (�Q/�P)*( �P/�Q) = (-1.5)*(13/28.5 )= (-1.5)*(.456) = -.684

EP = (�Q/�P)*( �P/�Q) = -1.462

EC202 Principles of Microeconomics Elasticity page 3

An application of price elasticity of demand. If the quantity demanded for milk were 100 units and the price elasticity of demand for milk was -.6 If the price of milk increased by 8%, how much would the quantity demanded change? Note, this does not imply equilibrium

% %

. % %

8 6

�

� ��

�

� �

Q P Q

EP so solving for %�Q, %.%).%)(( 8468 ����� Q

An 8% increase in price will reduce the quantity demanded by 4.8% Calculate the values for the values for the demand function in Table 1. Table 1

Demand Function QX = 120 - 5PX

Price (PX)

Quan (QX) TR EP AR MR

$25.00 $24.00 0.0 $0.00 #DIV/0! #DIV/0! $23.00 5.0 $115.00 -23 $23 $23 $22.00 10.0 $220.00 -11 $22 $21 $21.00 15.0 $315.00 -7 $21 $19 $20.00 20.0 $400.00 -5 $20 $17 $19.00 25.0 $475.00 -3.8 $19 $15 $18.00 30.0 $540.00 -3 $18 $13 $17.00 35.0 $595.00 -2.429 $17 $11 $16.00 40.0 $640.00 -2 $16 $9 $15.00 45.0 $675.00 -1.667 $15 $7 $14.00 50.0 $700.00 -1.4 $14 $5 $13.00 55.0 $715.00 -1.182 $13 $3 $12.00 60.0 $720.00 -1 $12 $1 $11.00 65.0 $715.00 -0.846 $11 -$1 $10.00 70.0 $700.00 -0.714 $10 -$3 $9.00 75.0 $675.00 -0.6 $9 -$5 $8.00 80.0 $640.00 -0.5 $8 -$7 $7.00 85.0 $595.00 -0.412 $7 -$9 $6.00 90.0 $540.00 -0.333 $6 -$11 $5.00 95.0 $475.00 -0.263 $5 -$13 $4.00 100.0 $400.00 -0.2 $4 -$15 $3.00 105.0 $315.00 -0.143 $3 -$17 $2.00 110.0 $220.00 -0.091 $2 -$19 $1.00 115.0 $115.00 -0.043 $1 -$21 $0.00 120.0 $0.00 0 $0 -$23