Transcript Session6-ElasticityandItsApplication-1
Economic Analysis for Business
Session V: Elasticity and its Application-1
Instructor
Sandeep Basnyat 9841892281 [email protected]
A scenario…
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? CHAPTER 5 ELASTICITY AND ITS APPLICATION
Elasticity
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 Q
d
or Q
s
to one of its determinants. Elastic and Inelastic demand and supply.
CHAPTER 5 ELASTICITY AND ITS APPLICATION
Price Elasticity of Demand
Price elasticity of demand = Percentage change in
Q d
Percentage change in
P
Price elasticity of demand
much Q
d
measures how responds to a change in P.
Loosely speaking, it measures the price sensitivity of buyers’ demand. CHAPTER 5 ELASTICITY AND ITS APPLICATION
Price Elasticity of Demand
Price elasticity of demand = Example: Price elasticity of demand equals 15% 10% = 1.5
Percentage change in
Q d
Percentage change in
P P P
rises by 10%
P
2
P
1
CHAPTER 5 ELASTICITY AND ITS APPLICATION
Q
falls by 15%
Q
2
Q
1
D Q
Price Elasticity of Demand
Price elasticity of demand = Percentage change in
Q d
Percentage change in
P P P
2
P
1
D Q Q
2
Q
1
CHAPTER 5 ELASTICITY AND ITS APPLICATION
$250 $200
P
Calculating Percentage Changes
Demand for your websites B Standard method of computing the percentage (%) change: end value – start value start value x 100% A
D Q
Going from A to B, the % change in
P
equals ($250 –$200)/$200 = 25% 8 12 CHAPTER 5 ELASTICITY AND ITS APPLICATION
$250 $200
P
Calculating Percentage Changes
Demand for your websites
Problem :
The standard method gives different answers depending on where you start. B A From A to B,
P
rises 25%,
Q
falls 33%, elasticity = 33/25 = 1.33
D Q
From B to A,
P
falls 20%,
Q
rises 50%, elasticity = 50/20 = 2.50 8 12 CHAPTER 5 ELASTICITY AND ITS APPLICATION
Calculating Percentage Changes
So, we instead use the
midpoint method
: end value – start value x 100% midpoint 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!
CHAPTER 5 ELASTICITY AND ITS APPLICATION
Calculating Percentage Changes
Using the midpoint method, the % change in P equals $250 – $200 $225 x 100% = 22.2% The % change in
Q
equals 12 – 8 10 x 100% = 40.0% The price elasticity of demand equals 40/22.2 = 1.8
CHAPTER 5 ELASTICITY AND ITS APPLICATION
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, Q
d
= 5000 if P = $90, Q
d
= 3000 11
A C T I V E L E A R N I N G 1 : Answers Use midpoint method to calculate % change in Q
d
(5000 – 3000)/4000 = 50% % change in P ($90 – $70)/$80 = 25% The price elasticity of demand equals 50% 25% = 2.0
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Calculating Price Elasticity of Demand
Two Ways:
Arc elasticity Calculation and Point Elasticity Calculation e Arc Elasticity: % % D D
Q p
D
Q
D
p Q p
D D
Q p p Q
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) ◦ 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.
Calculating Price Elasticity of Demand
Point Elasticity: Elasticity at a particular point (price)
Use of derivative: d Q/ d P : denotes rate at which quantity changes with respect to Price: D
Q
D
p
For a linear demand equation: dQ/dP is constant.
Eg: Equation of a linear demand curve is:
Q
a
And, the derivative of the equation is: b. Therefore,
bp b
D
Q
D
p
Where b is the slope ◦ From the Arc elasticity concept, the elasticity of demand is: e D
Q
D
p p Q
b p Q
Calculating slopes of the demand and supply curves
Assume the following markets for oranges:
Price (p) in $)
0.20
0.40
0.60
Demand(q)
14 12 10
Supply(q)
0 0 4 0.80
1.00
8 6 8 12 1.20
4 16
Calculate the slope of the Demand and Supply curves
Calculating slopes of the demand and supply curves
Answer Assume the following markets for oranges:
Price (p) in $)
0.20
0.40
0.60
Demand(q)
14 12 10
Supply(q)
0 0 4 0.80
1.00
8 6 8 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 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 = -10 Find the slope of the supply curve !!
Calculating Price Elasticity of Demand
The estimated linear demand function for pork is:
Q
= 286 -20
p
◦ ◦ 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 the elasticity of demand for pork:
Q
= 220 Find
Calculating Price Elasticity of Demand
The estimated linear demand function for pork is:
Q
= 286 -20
p
◦ ◦ 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
elasticity of demand for pork: = $3.30 and
Q
= 220 the e
b p Q
20 3 .
30 220 0 .
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Numerical example
Consider a competitive market for which the quantities demanded and supplied (per year) at various prices are given as follows: Price($) Demand (millions) Supply (millions) 60 22 14 80 100 20 18 16 18 120 16 20 Calculate the price elasticity of demand when the price is $80. When the price is $100.
Solution to Numerical example D
Q D E D
Q D
D
P
P Q D
D
Q D
D
P
.
P
From the above question, with each price increase of $20, the quantity demanded decreases by 2. Therefore, D
Q D
D
P
2 20 0.1.
At P = 80, quantity demanded equals 20 and
E D
80 20 0.1
0.40.
Similarly, at P = 100, quantity demanded equals 18 and
E D
100 18 0.1
0.56.
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?
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.
Non-linear demand function-Numerical Example Consider the following non-linear demand function: Q = P α If the value of α = -2, is the demand Price elastic or inelastic?
Non-linear demand function-Numerical Example Consider the following non-linear demand function: Q = P α If the value of α = -2, is the demand Price elastic or inelastic?
Solution:
Differentiating Q = = P α dQ/dP = α P α -1 Therefore, E = α P α -1 (P /Q) = (α P α -1+1 ) / Q = (α P α ) / Q Since, Q = P α
E = α
If, α = -2, E = -2. So, the demand is Price Elastic.
What determines the Elasticity of Demand? EXAMPLE 1: Wai Wai vs. Yogurt or curd The prices of both of these goods rise by 20%. For which good does
Q
d
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.
CHAPTER 5 ELASTICITY AND ITS APPLICATION
EXAMPLE 2: “Blue Jeans” vs. “Clothing” The prices of both goods rise by 20%. For which good does
Q
d
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.
CHAPTER 5 ELASTICITY AND ITS APPLICATION
EXAMPLE 3: Insulin vs. Caribbean Cruises The prices of both of these goods rise by 20%. For which good does
Q
d
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.
CHAPTER 5 ELASTICITY AND ITS APPLICATION
EXAMPLE 4: Gasoline in the Short Run vs. Gasoline in the Long Run The price of gasoline rises 20%. Does Q
d
in the short run or the long run? Why?
drop more ◦ 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.
CHAPTER 5 ELASTICITY AND ITS APPLICATION
The Determinants of Price Elasticity: A 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. CHAPTER 5 ELASTICITY AND ITS APPLICATION
The Variety of Demand Curves
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. CHAPTER 5 ELASTICITY AND ITS APPLICATION
“Perfectly inelastic demand” (one extreme case) Price elasticity = of demand % change in
Q
% change in
P
0% = 10% = 0
P D
curve: vertical Consumers’ price sensitivity: 0
P
1
P
2
D
Elasticity: 0
P
falls by 10%
Q
1
Q
changes by 0%
Q
CHAPTER 5 ELASTICITY AND ITS APPLICATION
“Inelastic demand” Price elasticity = of demand % change in
Q
% change in
P
< 10% = 10% < 1
D
curve: relatively steep Consumers’ price sensitivity: relatively low Elasticity: < 1
P P
1
P
2
P
falls by 10% CHAPTER 5 ELASTICITY AND ITS APPLICATION
D Q
1
Q
2
Q
rises less than 10%
Q
“Unit elastic demand” Price elasticity = of demand % change in
Q
% change in
P
= 10% 10%
D
curve: intermediate slope Consumers’ price sensitivity: intermediate Elasticity: 1
P
falls by 10%
P
1
P
2
P
= 1
D Q
1
Q Q
2
Q
rises by 10% CHAPTER 5 ELASTICITY AND ITS APPLICATION
“Elastic demand” Price elasticity = of demand % change in
Q
% change in
P
= > 10% 10%
P D
curve: relatively flat Consumers’ price sensitivity: relatively high
P
1
P
2
Elasticity: > 1 > 1
D P
falls by 10% CHAPTER 5 ELASTICITY AND ITS APPLICATION
Q
1
Q
2
Q
rises more than 10%
Q
“Perfectly elastic demand” (the other extreme) Price elasticity = of demand % change in
Q
% change in
P
= any % 0% = infinity
D
curve: horizontal Consumers’ price sensitivity: extreme Elasticity: infinity
P
2
=
P
1
P
changes by 0%
P D
CHAPTER 5 ELASTICITY AND ITS APPLICATION
Q
1
Q
2
Q
changes by any %
Q
Elasticity of a Linear Demand Curve
$30
P
20 10 $0 0
E
= 200% = 5.0
40%
E
= 67% 67% = 1.0
E
= 40% 200% = 0.2
Q
20 40 60 The slope of a linear demand curve is constant, but its elasticity is not. CHAPTER 5 ELASTICITY AND ITS APPLICATION
Price Elasticity and Total Revenue
Continuing 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. CHAPTER 5 ELASTICITY AND ITS APPLICATION
Price Elasticity and Total Revenue
Price elasticity of demand = Percentage change in
Q
Percentage change in
P
Revenue =
P
x
Q
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. CHAPTER 5 ELASTICITY AND ITS APPLICATION
Price Elasticity and Total Revenue
Elastic demand (elasticity = 1.8) If
P
= $200,
Q
= 12 and revenue = $2400. $250
P
your websites lost to higher
P
revenue due to lower
Q
$200 If
P
= $250,
Q
= 8 and revenue = $2000.
D Q
When
D
is elastic, a price increase causes revenue to fall. CHAPTER 5 ELASTICITY AND ITS APPLICATION 8 12
Price Elasticity and Total Revenue
Price elasticity of demand = Percentage change in
Q
Percentage change in
P
If demand is inelastic, then price elast. of demand < 1 Revenue =
P
% change in Q < % change in P x
Q
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. CHAPTER 5 ELASTICITY AND ITS APPLICATION
Price Elasticity and Total Revenue
Now, demand is inelastic: elasticity = 0.82
If
P
= $200,
Q
= 12 and revenue = $2400. $250
P
your websites to higher
P
lost revenue due to lower
Q
$200 If
P
= $250,
Q
= 10 and revenue = $2500.
D
When
D
is inelastic, a price increase causes revenue to rise. CHAPTER 5 ELASTICITY AND ITS APPLICATION 10 12
Q
A C T I V E L E A R N I N G 2 : Elasticity and expenditure/revenue
A.
B.
Pharmacies raise the price of insulin by 10%. Does total expenditure on insulin rise or fall? 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
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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