Economic Analysis for Business Session V: Elasticity and its Application-1 Instructor Sandeep Basnyat [email protected]

Economic Analysis Economic Analysis for Businessfor Business

Session V: Elasticity and its Session V: Elasticity and its Application-1Application-1

InstructorInstructorSandeep BasnyatSandeep [email protected][email protected]

CHAPTER 5 ELASTICITY AND ITS APPLICATION

You design websites for local businesses. You charge $200 per website, and currently sell 12 websites per month. Your costs are rising (including the opp. cost of your time), so you’re thinking of raising the price to $250. The law of demand says that you won’t sell as many websites if you raise your price. How many fewer websites? How much will your revenue fall, or might it increase?

You design websites for local businesses. You charge $200 per website, and currently sell 12 websites per month. Your costs are rising (including the opp. cost of your time), so you’re thinking of raising the price to $250. The law of demand says that you won’t sell as many websites if you raise your price. How many fewer websites? How much will your revenue fall, or might it increase?

A scenario…A scenario…


ElasticityElasticityBasic idea: Elasticity measures how

much one variable responds to changes in another variable. ◦One type of elasticity measures how much

demand for your websites will fall if you raise your price.

Definition: Elasticity is a numerical measure of the responsiveness of Qd or Qs to one of its determinants.

Elastic and Inelastic demand and supply.


Price Elasticity of DemandPrice Elasticity of Demand

Price elasticity of demand measures how much Qd responds to a change in P.

Price elasticity of demand

=Percentage change in Qd

Percentage change in P

Loosely speaking, it measures the price-sensitivity of buyers’ demand.



Price elasticity of demand equals

P

Q

D

Q2

P2

P1

Q1

P rises by 10%

Q falls by 15%

15%

10%= 1.5




Example:



P

Q

D

Q2

P2

P1

Q1





Calculating Percentage Calculating Percentage ChangesChanges

P

Q

D

$250

8

B

$200

12

A

Demand for your websites

Standard method of computing the percentage (%) change:

end value – start value

start valuex 100%

Going from A to B, the % change in P equals

($250–$200)/$200 = 25%


Calculating Percentage Calculating Percentage ChangesChanges

P

Q

D

$250

8

B

$200

12

A


Problem:

The standard method gives different answers depending

on where you start.

From A to B, P rises 25%, Q falls 33%,elasticity = 33/25 = 1.33

From B to A, P falls 20%, Q rises 50%, elasticity = 50/20 = 2.50


Calculating Percentage Calculating Percentage ChangesChanges So, we instead use the midpoint method:

end value – start valuemidpoint

x 100%

The midpoint is the number halfway between the start & end values, also the average of those values.

It doesn’t matter which value you use as the “start” and which as the “end” – you get the same answer either way!


Calculating Percentage Calculating Percentage ChangesChangesUsing the midpoint method, the % change

in P equals

$250 – $200$225

x 100% = 22.2%

The % change in Q equals

12 – 810

x 100% = 40.0%

The price elasticity of demand equals

40/22.2 = 1.8

AA CC TT II VV E LE L EE AA RR NN II NN G G 11: : Calculate an elasticityCalculate an elasticity

Use the following information to calculate the price elasticity of demand for hotel rooms:

if P = $70, Qd = 5000

if P = $90, Qd = 3000

11

AA CC TT II VV E LE L EE AA RR NN II NN G G 11: : AnswersAnswers

Use midpoint method to calculate % change in Qd

(5000 – 3000)/4000 = 50%

% change in P

($90 – $70)/$80 = 25%

The price elasticity of demand equals

12

50%25%

= 2.0

Calculating Price Elasticity of Calculating Price Elasticity of DemandDemand

Arc Elasticity:

◦ where indicates change.Example

◦ If a 1% increase in price results in a 3% decrease in quantity demanded, the elasticity of demand is = -3%/1% = -3.

Q

p

p

Q

pp

QQ

p

Q

%

%

Two Ways: Arc elasticity Calculation and Point Elasticity Calculation

Important Note:

Along a D curve, P and Q move in opposite directions, which would make price elasticity negative most of the cases. (E <0)

Important Note:

Along a D curve, P and Q move in opposite directions, which would make price elasticity negative most of the cases. (E <0)

Calculating Price Elasticity of Calculating Price Elasticity of DemandDemandUse of derivative: dQ/dP : denotes rate at which

quantity changes with respect to Price:

For a linear demand equation: dQ/dP is constant.

Eg: Equation of a linear demand curve is: And, the derivative of the equation is: b.

Therefore, Where b is the

slope

◦ From the Arc elasticity concept, the elasticity of demand is:

bpaQ

p

Qb

Q

pb

Q

p

p

Q

Point Elasticity: Elasticity at a particular point (price)

p

Q

Calculating slopes of the demand and supply curves

Assume the following markets for oranges:Price (p) in $) Demand(q) Supply(q)

0.20 14 00.40 12 00.60 10 40.80 8 81.00 6 121.20 4 16

Calculate the slope of the Demand and Supply curves

Calculating slopes of the demand and supply curves

Assume the following markets for oranges:Price (p) in $) Demand(q) Supply(q)

0.20 14 00.40 12 00.60 10 40.80 8 81.00 6 121.20 4 16

Calculate the slope of the Demand and Supply curves

• To find the slope of the demand curve, pick any two points (quantity demanded) on it and their corresponding prices.

• For example, pick points 8 on quantity demanded and it’s corresponding price $0.80. So, the first coordinate is (8, 0.80).

• Similarly, pick another coordinates as (12, 0.40). • Using the slope formula, Slope of the demand curve is:

(12-8)/(0.40−0.80) = 4/- 0.40 = -10Find the slope of the supply curve !!

AnswAnswerer

Calculating Price Elasticity of Calculating Price Elasticity of DemandDemandThe estimated linear demand function

for pork is:Q = 286 -20p

◦ where Q is the quantity of pork demanded in million kg per year and p is the price of pork in $ per year.

◦ At the equilibrium point of p = $3.30 and Q = 220 Find the elasticity of demand for pork:

Calculating Price Elasticity of Calculating Price Elasticity of DemandDemandThe estimated linear demand function

for pork is:Q = 286 -20p

◦ where Q is the quantity of pork demanded in million kg per year and p is the price of pork in $ per year.

◦ At the equilibrium point of p = $3.30 and Q = 220 the elasticity of demand for pork:

3.0220

30.320

Q

pb

Numerical exampleNumerical example

Consider a competitive market for which the quantities demanded and supplied (per year) at various prices are given as follows:Price($) Demand (millions) Supply (millions)

60 22 1480 20 16100 18 18120 16 20

Calculate the price elasticity of demand when the price is $80. When the price is $100.

Solution to Numerical exampleSolution to Numerical example

.P

Q

Q

P

P

PQ

Q

E D

D

D

D

D

From the above question, with each price increase of $20, the quantity demanded decreases by 2. Therefore,

QD

P

2

20 0.1.

At P = 80, quantity demanded equals 20 and

ED 80

20

0.1 0.40.

Similarly, at P = 100, quantity demanded equals 18 and

ED 100

18

0.1 0.56.

Some more questionsSome more questionsWhat are the equilibrium price and

quantity?

Suppose the government sets a price ceiling of $80. Will there be a shortage, and, if so, how large will it be?

Some more questionsSome more questionsWhat are the equilibrium price and

quantity?Equilibrium price is $100 and the equilibrium quantity is 18 million.

Suppose the government sets a price ceiling of $80. Will there be a shortage, and, if so, how large will it be?With a price ceiling of $80, consumers would like to buy 20 million, but producers will supply only 16 million. This will result in a shortage of 4 million.

Non-linear demand function-Numerical Non-linear demand function-Numerical ExampleExampleConsider the following non-linear demand

function:Q = Pα

If the value of α = -2, is the demand Price elastic or inelastic?

Non-linear demand function-Numerical Non-linear demand function-Numerical ExampleExampleConsider the following non-linear demand

function:Q = Pα

If the value of α = -2, is the demand Price elastic or inelastic?

Solution:

Differentiating Q = = Pα

dQ/dP = α Pα-1

Therefore, E = α Pα-1 (P /Q) = (α Pα-1+1) / Q = (α Pα) / Q

Since, Q = Pα

E = αIf, α = -2, E = -2. So, the demand is Price Elastic.


What determines the Elasticity of Demand? What determines the Elasticity of Demand? EXAMPLE 1:EXAMPLE 1:

Wai Wai vs. Yogurt or curdWai Wai vs. Yogurt or curd The prices of both of these goods rise by 20%.

For which good does Qd drop the most? Why?

◦Wai Wai has lots of close substitutes (e.g., Rum Pum, Mayoz etc.), so buyers can easily switch if the price rises.

◦Yogurt has no close substitutes, so consumers would probably not buy much less if its price rises.

Lesson: Price elasticity is higher when close substitutes are available.


EXAMPLE 2:EXAMPLE 2:

“Blue Jeans” vs. “Clothing”“Blue Jeans” vs. “Clothing” The prices of both goods rise by 20%.

For which good does Qd drop the most? Why?

◦For a narrowly defined good such as blue jeans, there are many substitutes (khakis, shorts, Speedos, or even cotton pant).

◦There are fewer substitutes available for broadly defined goods. (Can you think of a substitute for clothing, other than living in a nudist colony?)

Lesson: Price elasticity is higher for narrowly defined goods than broadly defined ones.



Insulin vs. Caribbean CruisesInsulin vs. Caribbean Cruises

The prices of both of these goods rise by 20%. For which good does Qd drop the most? Why?

◦To millions of diabetics, insulin is a necessity. A rise in its price would cause little or no decrease in demand.

◦A cruise is a luxury. If the price rises, some people will forego it.

Lesson: Price elasticity is higher for luxuries than for necessities.



Gasoline in the Short Run vs. Gasoline in Gasoline in the Short Run vs. Gasoline in the Long Runthe Long Run

The price of gasoline rises 20%. Does Qd drop more in the short run or the long run? Why?

◦There’s not much people can do in the short run, other than ride the bus or carpool.

◦In the long run, people can buy smaller cars or live closer to where they work.

Lesson: Price elasticity is higher in the long run than the short run.


The Determinants of Price Elasticity: The Determinants of Price Elasticity: A SummaryA Summary

The price elasticity of demand depends on: the extent to which close substitutes are

available

whether the good is a necessity or a luxury

how broadly or narrowly the good is defined

the time horizon: elasticity is higher in the long run than the short run.

The price elasticity of demand depends on: the extent to which close substitutes are

available

whether the good is a necessity or a luxury

how broadly or narrowly the good is defined

the time horizon: elasticity is higher in the long run than the short run.


The Variety of Demand The Variety of Demand CurvesCurvesEconomists classify demand curves

according to their elasticity.

The price elasticity of demand is closely related to the slope of the demand curve.

Rule of thumb: The flatter the curve, the bigger the elasticity. The steeper the curve, the smaller the elasticity.

The next 5 slides present the different classifications, from least to most elastic.


Q1

P1

D

““Perfectly inelastic demand” Perfectly inelastic demand” (one extreme (one extreme case)case)

P

Q

P2

P falls by 10%

Q changes by 0%

0%

10%= 0

Price elasticity

of demand

=% change in Q

% change in P=

Consumers’ price sensitivity:

D curve:

Elasticity:

vertical

0

0


D

““Inelastic demand”Inelastic demand”

P

QQ1

P1

Q2

P2

Q rises less than 10%

< 10%

10%< 1

Price elasticity

of demand

=% change in Q

% change in P=

P falls by 10%


D curve:

Elasticity:

relatively steep

relatively low

< 1


D

““Unit elastic demand”Unit elastic demand”

P

QQ1

P1

Q2

P2

Q rises by 10%

10%

10%= 1

Price elasticity

of demand

=% change in Q

% change in P=

P falls by 10%


Elasticity:

intermediate

1

D curve:intermediate slope


D

““Elastic demand”Elastic demand”

P

QQ1

P1

Q2

P2

Q rises more than 10%

> 10%

10%> 1

Price elasticity

of demand

=% change in Q

% change in P=

P falls by 10%


D curve:

Elasticity:

relatively flat

relatively high

> 1


D

““Perfectly elastic demand”Perfectly elastic demand” (the other (the other extreme)extreme)

P

Q

P1

Q1

P changes by 0%

Q changes by any %

any %

0%= infinity

Q2

P2 =Consumers’ price sensitivity:

D curve:

Elasticity:infinity

horizontal

extreme

Price elasticity

of demand

=% change in Q

% change in P=


Elasticity of a Linear Demand Elasticity of a Linear Demand CurveCurve

The slope

of a linear demand curve is constant, but its elasticity is not.

P

Q

$30

20

10

$00 20 40 60

200%40%

= 5.0E =

67%67%

= 1.0E =

40%200%

= 0.2E =


Price Elasticity and Total Price Elasticity and Total RevenueRevenueContinuing our scenario, if you raise your price

from $200 to $250, would your revenue rise or fall?

Revenue = P x Q A price increase has two effects on revenue:

◦Higher P means more revenue on each unit you sell.

◦But you sell fewer units (lower Q), due to Law of Demand.

Which of these two effects is bigger? It depends on the price elasticity of demand.


Price Elasticity and Total Price Elasticity and Total RevenueRevenue

If demand is elastic, then price elast. of demand > 1 % change in Q > % change in P

The fall in revenue from lower Q is greater than the increase in revenue from higher P, so revenue falls.

Revenue = P x Q


=Percentage change in Q




Elastic demand(elasticity = 1.8) P

Q

D$200

12

If P = $200, Q = 12 and revenue = $2400.

When D is elastic, a price increase causes revenue to fall.

$250

8

If P = $250, Q = 8 and revenue = $2000.

lost revenue due to lower Q

increased revenue due to higher P




If demand is inelastic, then price elast. of demand < 1 % change in Q < % change in P

The fall in revenue from lower Q is smaller than the increase in revenue from higher P, so revenue rises.

In our example, suppose that Q only falls to 10 (instead of 8) when you raise your price to $250.

Revenue = P x Q


=Percentage change in Q




Now, demand is inelastic: elasticity = 0.82

P

Q

D

$200

12

If P = $200, Q = 12 and revenue = $2400. $250

10

If P = $250, Q = 10 and revenue = $2500.When D is inelastic, a price increase causes revenue to rise.

lost revenue due to lower Q

increased revenue due to higher P


AA CC TT II VV E LE L EE AA RR NN II NN G G 22: : Elasticity and expenditure/revenueElasticity and expenditure/revenue

A. Pharmacies raise the price of insulin by 10%. Does total expenditure on insulin rise or fall?

B. As a result of a fare war, the price of a luxury cruise falls 20%. Does luxury cruise companies’ total revenue rise or fall?

42


43

A. Pharmacies raise the price of insulin by 10%. Does total expenditure on insulin rise or fall? Expenditure = P x Q Since demand is inelastic, Q will fall less than 10%, so expenditure rises.


44

B. As a result of a fare war, the price of a luxury cruise falls 20%. Does luxury cruise companies’ total revenue rise or fall? Revenue = P x Q

The fall in P reduces revenue, but Q increases, which increases revenue. Which effect is bigger?

Since demand is elastic, Q will increase more than 20%, so revenue rises.

Thank youThank you

Documents

Economic Analysis for Business Session V: Elasticity and its Application-1 Instructor Sandeep Basnyat [email protected]