Economic Analysis for Business Session V: Elasticity and its Application-1

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Economic Analysis for BusinessSession V
Elasticity and its Application-1
InstructorSandeep Basnyat 9841892281 Sandeep_basn
yat_at_yahoo.com
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A scenario
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• 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 youre thinking of raising the
  price to 250.
• The law of demand says that you wont sell as
  many websites if you raise your price. How many
  fewer websites? How much will your revenue fall,
  or might it increase?

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Elasticity
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• Basic 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.

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

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

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Price Elasticity of Demand
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Example
P rises by 10

• Price elasticity of demand equals

Q falls by 15
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Price Elasticity of Demand
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Calculating Percentage Changes
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Standard method of computing the percentage ()
change
Demand for your websites
Going from A to B, the change in P equals
(250200)/200 25
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Calculating Percentage Changes
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Problem The standard method gives different
answers depending on where you start.
Demand for your websites
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

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Calculating Percentage Changes
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• So, we instead use the midpoint method

• The midpoint is the number halfway between the
  start end values, also the average of those
  values.
• It doesnt matter which value you use as the
  start and which as the end you get the same
  answer either way!

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Calculating Percentage Changes
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• Using the midpoint method, the change in P
  equals

• The change in Q equals

• The price elasticity of demand equals

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A C T I V E L E A R N I N G 1 Calculate 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

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A C T I V E L E A R N I N G 1 Answers

• 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

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Calculating Price Elasticity of Demand
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 lt0)

• Arc Elasticity
• where D indicates change.
• Example
• If a 1 increase in price results in a 3
  decrease in quantity demanded, the elasticity of
  demand is e -3/1 -3.

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Calculating Price Elasticity of Demand
Point Elasticity Elasticity at a particular
point (price)

• Use 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

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Calculating slopes of the demand and supply curves
Assume the following markets for oranges
Price (p) in ) Demand(q) Supply(q) 0.20 14
0 0.40 12 0 0.60 10 4 0.80 8
8 1.00 6 12 1.20 4 16 Calculate
the slope of the Demand and Supply curves
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Calculating slopes of the demand and supply curves
Assume the following markets for oranges
Price (p) in ) Demand(q) Supply(q) 0.20 14
0 0.40 12 0 0.60 10 4 0.80 8
8 1.00 6 12 1.20 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 its 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 -10
• Find the slope of the supply curve !!

Answer
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Calculating Price Elasticity of Demand

• The 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

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Calculating Price Elasticity of Demand

• The 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

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Numerical 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 14
• 80 20 16
• 100 18 18
• 120 16 20 
• Calculate the price elasticity of demand when the
  price is 80. When the price is 100.

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Solution to Numerical example
From the above question, with each price increase
of 20, the quantity demanded decreases by 2.
Therefore,
At P 80, quantity demanded equals 20 and
Similarly, at P 100, quantity demanded equals
18 and
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Some more questions

• What 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?

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Some more questions

• What 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.

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Non-linear demand function-Numerical Example

• Consider the following non-linear demand
  function
• Q Pa
• If the value of a -2, is the demand Price
  elastic or inelastic?

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Non-linear demand function-Numerical Example

• Consider the following non-linear demand
  function
• Q Pa
• If the value of a -2, is the demand Price
  elastic or inelastic?
• Solution
• Differentiating Q Pa
• dQ/dP a Pa-1
• Therefore, E a Pa-1 (P /Q) (a Pa-11) / Q
  (a Pa) / Q
• Since, Q Pa
• E a
• If, a -2, E -2. So, the demand is Price
  Elastic.

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What determines the Elasticity of Demand? EXAMPLE
1Wai Wai vs. Yogurt or curd
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• 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.

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EXAMPLE 2Blue Jeans vs. Clothing
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• 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.

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EXAMPLE 3Insulin vs. Caribbean Cruises
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• 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.

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EXAMPLE 4Gasoline in the Short Run vs. Gasoline
in the Long Run
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• The price of gasoline rises 20. Does Qd drop
  more in the short run or the long run? Why?
• Theres 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.

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The Determinants of Price Elasticity A Summary
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• 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.

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The Variety of Demand Curves
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• Economists 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.

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Perfectly inelastic demand (one extreme case)
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0
0
10
D curve
vertical
Consumers price sensitivity
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P falls by 10
Elasticity
0
Q changes by 0
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Inelastic demand
0
lt 10
lt 1
10
D curve
relatively steep
Consumers price sensitivity
relatively low
P falls by 10
Elasticity
lt 1
Q rises less than 10
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Unit elastic demand
0
10
1
10
D curve
intermediate slope
Consumers price sensitivity
intermediate
P falls by 10
Elasticity
1
Q rises by 10
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Elastic demand
0
gt 10
gt 1
10
D curve
relatively flat
Consumers price sensitivity
relatively high
P falls by 10
Elasticity
gt 1
Q rises more than 10
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Perfectly elastic demand (the other extreme)
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any
infinity
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D curve
horizontal
P1
P2
Consumers price sensitivity
extreme
P changes by 0
Elasticity
infinity
Q changes by any
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Elasticity of a Linear Demand Curve
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• The slope of a linear demand curve is constant,
  but its elasticity is not.

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Price Elasticity and Total Revenue
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• Continuing our scenario, if you raise your
  pricefrom 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.

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Price Elasticity and Total Revenue
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Revenue P x Q

• If demand is elastic, then
• price elast. of demand gt 1
• change in Q gt change in P
• The fall in revenue from lower Q is greater than
  the increase in revenue from higher P, so
  revenue falls.

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Price Elasticity and Total Revenue
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• Elastic demand(elasticity 1.8)

increased revenue due to higher P
Demand for your websites
lost revenue due to lower Q
When D is elastic, a price increase causes
revenue to fall.
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Price Elasticity and Total Revenue
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Revenue P x Q

• If demand is inelastic, then
• price elast. of demand lt 1
• change in Q lt 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.

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Price Elasticity and Total Revenue
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• Now, demand is inelastic elasticity 0.82

increased revenue due to higher P
Demand for your websites
lost revenue due to lower Q
When D is inelastic, a price increase causes
revenue to rise.
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A C T I V E L E A R N I N G 2 Elasticity
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?

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A C T I V E L E A R N I N G 2 Answers

• 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.

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A C T I V E L E A R N I N G 2 Answers

• 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.

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Thank you