1. Economic Analysis for Business Session V: Elasticity and its Application-1
Instructor Sandeep Basnyat

2. 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…
We will follow this scenario throughout the first section of this chapter (the section on price elasticity of demand) to illustrate and motivate several important concepts, such as the impact of price changes on sales and revenue.
CHAPTER 5 ELASTICITY AND ITS APPLICATION

3. 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 Qd or Qs to one of its determinants.
Elastic and Inelastic demand and supply.
Here, Qd and Qs are short for quantity demanded and quantity supplied, as in the PowerPoint for Chapter 4.
CHAPTER 5 ELASTICITY AND ITS APPLICATION

4. Price Elasticity of Demand
Price elasticity of demand =
Percentage change in Qd
Percentage change in P
Price elasticity of demand measures how much Qd responds to a change in P.
Loosely speaking, it measures the price-sensitivity of buyers’ demand.
CHAPTER 5 ELASTICITY AND ITS APPLICATION

5. Price Elasticity of Demand
Price elasticity of demand =
Percentage change in Qd
Percentage change in P P Q
Example: D
P rises by 10%
Price elasticity of demand equals P2 Q2 P1 Q1
15%
10%
= 1.5
Q falls by 15%
CHAPTER 5 ELASTICITY AND ITS APPLICATION

6. Price Elasticity of Demand
Price elasticity of demand =
Percentage change in Qd
Percentage change in P P Q D P2 Q2 P1 Q1
It might be worth explaining to your students that “P and Q move in opposite directions” means that the percentage change in Q and the percentage change in P will have opposite signs, thus implying a negative price elasticity.
To be consistent with the text, the last statement in the green box says that we will report all price elasticities as positive numbers. It might be slightly more accurate to say that we will report all elasticities as non-negative numbers: we want to allow for the (admittedly rare) case of zero elasticity.
CHAPTER 5 ELASTICITY AND ITS APPLICATION

7. Calculating Percentage Changes
Standard method of computing the percentage (%) change:
Demand for your websites
end value – start value
start value
x 100% P Q
$250 8 B D
Going from A to B, the % change in P equals
$200 12 A
($250–$200)/$200 = 25%
CHAPTER 5 ELASTICITY AND ITS APPLICATION

8. Calculating Percentage Changes
Problem:
The standard method gives different answers depending on where you start.
Demand for your websites P Q
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
$250 8 B D
$200 12 A
CHAPTER 5 ELASTICITY AND ITS APPLICATION

9. Calculating Percentage Changes
So, we instead use the midpoint method:
end value – start value
midpoint
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!
CHAPTER 5 ELASTICITY AND ITS APPLICATION

10. 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%
These calculations are based on the example shown a few slides back: points A and B on the website demand curve.
The price elasticity of demand equals
40/22.2 = 1.8
CHAPTER 5 ELASTICITY AND ITS APPLICATION

11. 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 11

12. 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
50%
25%
= 2.0 12

13. 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 <0)
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.

14. 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:

15. Calculating slopes of the demand and supply curves
Assume the following markets for oranges:
Price (p) in $) Demand(q) Supply(q)
Calculate the slope of the Demand and Supply curves

16. Calculating slopes of the demand and supply curves
Assume the following markets for oranges:
Price (p) in $) Demand(q) Supply(q)
Calculate the slope of the Demand and Supply curves
Answer
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/ = -10
Find the slope of the supply curve !!

17. Calculating Price Elasticity of Demand
The estimated linear demand function for pork is:
Q = 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 Q = 220 Find the elasticity of demand for pork:

18. Calculating Price Elasticity of Demand
The estimated linear demand function for pork is:
Q = 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 Q = 220 the elasticity of demand for pork:

19. 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)  
Calculate the price elasticity of demand when the price is $80. When the price is $100.

20. 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

21. 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?

22. 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.

23. Non-linear demand function-Numerical Example
Consider the following non-linear demand function:
Q = Pα
If the value of α = -2, is the demand Price elastic or inelastic?

24. Non-linear demand function-Numerical Example
Consider 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 = α
If, α = -2, E = -2. So, the demand is Price Elastic.

25. What determines the Elasticity of Demand. EXAMPLE 1: Wai Wai vs
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 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.
Suggestion: For each of these examples, display the slide title (which lists the two goods) and the first two lines of text (which ask which good experiences the biggest drop in demand in response to a 20% price increase). Give your students a quiet minute to formulate their answers. Then, ask for volunteers.
CHAPTER 5 ELASTICITY AND ITS APPLICATION

26. EXAMPLE 2: “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.
You might need to clarify the nature of this thought experiment.
Here, we look at two alternate scenarios. In the first, the price of blue jeans (and no other clothing) rises by 20%, and we observe the percentage decrease in quantity of blue jeans demanded.
In the second scenario, the price of all clothing rises by 20%, and we observe the percentage decrease in demand for all clothing.
CHAPTER 5 ELASTICITY AND ITS APPLICATION

27. EXAMPLE 3: Insulin 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.
CHAPTER 5 ELASTICITY AND ITS APPLICATION

28. EXAMPLE 4: Gasoline in the Short Run vs. Gasoline in the 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.
CHAPTER 5 ELASTICITY AND ITS APPLICATION

29. 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.
This slide is a convenience for your students, and replicates a similar table from the text.
If you’re pressed for time, it is probably safe to omit this slide from your presentation.
CHAPTER 5 ELASTICITY AND ITS APPLICATION

30. 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

31. “Perfectly inelastic demand” (one extreme case)
Price elasticity of demand =
% change in Q
% change in P 0%
= 0
10%
D curve: P Q D
vertical Q1 P1
Consumers’ price sensitivity: P2
If Q doesn’t change, then the percentage change in Q equals zero, and thus elasticity equals zero.
It is hard to think of a good for which the price elasticity of demand is literally zero. Take insulin, for example. A sufficiently large price increase would probably reduce demand for insulin a little, particularly among people with very low incomes and no health insurance.
However, if elasticity is very close to zero, then the demand curve is almost vertical. In such cases, the convenience of modeling demand as perfectly inelastic probably outweighs the cost of being slightly inaccurate.
P falls by 10%
Elasticity:
Q changes by 0%
CHAPTER 5 ELASTICITY AND ITS APPLICATION

32. Price elasticity of demand
“Inelastic demand”
Price elasticity of demand =
% change in Q
% change in P
< 10%
< 1
10% D
D curve: P Q
relatively steep Q1 P1
Consumers’ price sensitivity: P2 Q2
relatively low
An example: student demand for textbooks that their professors have required for their courses.
Here, it’s a little more clear that elasticity would be small, but not zero. At a high enough price, some students will not buy their books, but instead will share with a friend, or try to find them in the library, or just take copious notes in class.
Another example: gasoline in the short run.
P falls by 10%
Elasticity:
< 1
Q rises less than 10%
CHAPTER 5 ELASTICITY AND ITS APPLICATION

33. Price elasticity of demand
“Unit elastic demand”
Price elasticity of demand =
% change in Q
% change in P
10%
= 1
10% D
D curve: P Q
intermediate slope Q1 P1
Consumers’ price sensitivity: P2 Q2
intermediate
This is the intermediate case: the demand curve is neither relatively steep nor relatively flat. Buyers are neither relatively price-sensitive nor relatively insensitive to price.
This is also the case where price changes have no effect on revenue.
P falls by 10%
Elasticity: 1
Q rises by 10%
CHAPTER 5 ELASTICITY AND ITS APPLICATION

34. Price elasticity of demand
“Elastic demand”
Price elasticity of demand =
% change in Q
% change in P
> 10%
> 1
10% D
D curve: P Q
relatively flat Q1 P1
Consumers’ price sensitivity: P2 Q2
relatively high
A good example here would be Rice Krispies, or nearly anything with readily available substitutes.
An elastic demand curve is flatter than a unit elastic demand curve (which itself is flatter than an inelastic demand curve).
P falls by 10%
Elasticity:
> 1
Q rises more than 10%
CHAPTER 5 ELASTICITY AND ITS APPLICATION

35. “Perfectly elastic demand” (the other extreme)
Price elasticity of demand =
% change in Q
% change in P
any %
= infinity 0%
D curve: P Q
horizontal
P2 = P1 D
Consumers’ price sensitivity: Q1 Q2
extreme
“Extreme price sensitivity” means the tiniest price increase causes demand to fall to zero.
“Q changes by any %” – when the D curve is horizontal, the quantity is indeterminant. Consumers might demand Q1 units one month, Q2 units another month, and some other quantity later. Q can change by any amount, but P always “changes by 0%” (i.e. doesn’t change).
If perfectly inelastic is one extreme, this (perfectly elastic) is the other.
Here’s a good real-world example of a perfectly elastic demand curve, which foreshadows an upcoming chapter on firms in competitive markets. Suppose you run a small family farm in Iowa. Your main crop is wheat. The demand curve in this market is downward-sloping, and the market demand and supply curves determine the price of wheat. Suppose that price is $5/bushel.
Now consider the demand curve facing you, the individual wheat farmer. If you charge a price of $5, you can sell as much or as little as you want. If you charge a price even just a little higher than $5, demand for YOUR wheat will fall to zero: Buyers would not be willing to pay you more than $5 when they could get the same wheat elsewhere for $5. Similarly, if you drop your price below $5, then demand for YOUR wheat will become enormous (not literally infinite, but “almost infinite”): if other wheat farmers are charging $5 and you charge less, then EVERY buyer will want to buy wheat from you.
Why is the demand curve facing an individual producer perfectly elastic? Recall that elasticity is greater when lots of close substitutes are available. In this case, you are selling a product that has many perfect substitutes: the wheat sold by every other farmer is a perfect substitute for the wheat you sell.
P changes by 0%
Elasticity:
infinity
Q changes by any %
CHAPTER 5 ELASTICITY AND ITS APPLICATION

36. Elasticity of a Linear Demand CurveP Q
$30 20 10 $0 40 60
The slope of a linear demand curve is constant, but its elasticity is not.
200%
40%
= 5.0
E =
67%
= 1.0
E =
40%
200%
= 0.2
E =
The material on this slide is not used anywhere else in the textbook. Therefore, if you are pressed for time and looking for things to cut, you might consider cutting this slide. (Note that this is my personal recommendation and is not necessarily the official position of Greg Mankiw or Thomson/South-Western.)
Due to space limitations, this slide uses “E” as an abbreviation for elasticity, or more specifically, the price elasticity of demand, and the slide omits the analysis of revenue along the demand curve.
Calculations of percentage changes use the midpoint method. (This is why the increase from Q=0 to Q=20 is 200% rather than infinity.)
As you move down a linear demand curve, the slope (the ratio of the absolute change in P to that in Q) remains constant:
From the point (0, $30) to the point (20, $20), the “rise” equals -$10, the “run” equals +20, so the slope equals -1/2 or -0.5.
From the point (40, $10) to the point (60, $0), the “rise” again equals -$10, the “run” equals +20, and the slope again equals -0.5.
However, the percentage changes in these variables do not remain constant, as shown by the different colored elasticity calculations that appear on the slide.
The lesson here is that elasticity falls as you move downward & rightward along a linear demand curve.
CHAPTER 5 ELASTICITY AND ITS APPLICATION

37. 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.
We return to our scenario. It’s not hard for students to imagine being in this position – running their own business and trying to decide whether to raise the price.
To most of your students, it should be clear that making the best possible decision would require information about the likely effects of the price increase on revenue. That is why elasticity is so helpful, as we will now see….
CHAPTER 5 ELASTICITY AND ITS APPLICATION

38. 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

39. Price Elasticity and Total Revenue
Elastic demand (elasticity = 1.8)
increased revenue due to higher P
Demand for your websites P Q
lost revenue due to lower Q
$200 12
If P = $200, Q = 12 and revenue = $2400. D
$250 8
If P = $250, Q = 8 and revenue = $2000.
In the “Normal” view (edit mode), the labels over the graph look cluttered, like they’re on top of each other. This is not a mistake – in “Slide Show” mode (presentation mode), they will be fine – try it!
Point out to students that the area (outlined in blue) representing lost revenue due to lower Q is larger than the area (outlined in yellow) representing increased revenue due to higher P. Hence, the net effect is a fall in revenue.
When D is elastic, a price increase causes revenue to fall.
CHAPTER 5 ELASTICITY AND ITS APPLICATION

40. Price Elasticity and Total Revenue
Price elasticity of demand =
Percentage change in Q
Percentage change in P
Revenue = P x Q
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.
CHAPTER 5 ELASTICITY AND ITS APPLICATION

41. Price Elasticity and Total Revenue
Now, demand is inelastic: elasticity = 0.82
increased revenue due to higher P
Demand for your websites P Q
lost revenue due to lower Q
$200 12
If P = $200, Q = 12 and revenue = $2400. D
$250 10
If P = $250, Q = 10 and revenue = $2500.
Again, the slide appears cluttered in “Normal” view (edit mode), but everything is fine when displayed in “Slide Show” mode (presentation mode).
Point out to students that the area representing lost revenue due to lower Q is smaller than the area representing increased revenue due to higher P. Hence, the net effect is an increase in revenue.
The knife-edge case, not shown here but worth mentioning in class, is unit-elastic demand. In that case, an increase in price leaves revenue unchanged: the increase in revenue from higher P exactly offsets the lost revenue due to lower Q.
When D is inelastic, a price increase causes revenue to rise.
CHAPTER 5 ELASTICITY AND ITS APPLICATION

42. 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?
These problems, perhaps similar to those you might ask on an exam, are complex in that they test several skills at once: Students must determine whether demand for each good is elastic or inelastic, and they must determine the impact of a price change on revenue/expenditure.
So far, we’ve been talking about how elasticity determines the effects of an increase in P on revenue. Part (b) asks your students to determine the effects of a decrease in P. 42

43. 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. 43

44. 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.
The first part of the explanation discusses the opposing effects on revenue; its purpose is to clarify the effects of a price decrease on revenue, as we have previously only discussed the effects of a price increase. 44

45. Thank you