1. Quantitative Demand Analysis Elasticity and its Applications
Managerial Economics
Lecture 3:
Quantitative Demand Analysis
Elasticity and its Applications

2. Overview The Elasticity Concept Demand Functions Regression Analysis
Own Price Elasticity
Elasticity and Total Revenue
Cross-Price Elasticity
Income Elasticity
Demand Functions
Linear
Log-Linear
Regression Analysis

3. Elasticity Concept

4. Elasticity Concept Quantitative Questions
Our previous two lectures addressed qualitative method of tackling managerial issues. This lecture will look at ‘detailed’ quantitative answers to questions like:
How much do we have to cut our price to achieve 3.2 percent sales growth?
If we cut prices by 6.5 percent, how many more units will we sell?
How much will our sales change if rivals cut their prices by 2 percent or a recession hits and household incomes decline by 2.5 percent?
Economics is about decisions and choices. However, decisions and choices are made because of scarcity. There are three MBA streams: MBA (regular), MBA (Sandwich) and MBA (distance). My question is why did you decide to enroll on an MBA distance programme.

5. Elasticity Concept
Scenario
Suppose some variable, such as the price of a product, reduced by 10 percent. What would happen to the quantity demanded of the good?
Based on our previous lecture and the law of demand, a fall in price will lead to a rise in quantity demanded.
However, it will be useful for a manager to know the magnitude of the rise in quantity demanded, whether it will be 5% 10% or any amount rise.
We primarily use the concept of elasticity to establish such a magnitude.
Economics is about decisions and choices. However, decisions and choices are made because of scarcity. There are three MBA streams: MBA (regular), MBA (Sandwich) and MBA (distance). My question is why did you decide to enroll on an MBA distance programme.

6. The Elasticity Concept
How responsive is variable “G” to a change in variable “S”
For instance: the elasticity of your grade with respect to studying is the percentage change in your grade that will result from a given percentage change in the time you spend studying. In other words.
If EG,S > 0, then S and G are directly related.
If EG,S < 0, then S and G are inversely related.
If EG,S = 0, then S and G are unrelated.

7. The Elasticity Concept
The Elasticity Concept Using Calculus
An alternative way to measure the elasticity of a function G = f(S) is
BEAR IN MIND: If the absolute value of the elasticity is greater than 1, the numerator is larger than the denominator in the elasticity formula, and we know that a small percentage change in S will lead to a relatively large percentage change in G and the reverse is true.

8. The Elasticity Concept
The Elasticity Concept Using Calculus
NOTE: Two aspects of an elasticity are important: (1) its sign and (2) whether it is greater or less than 1 in absolute value.

9. Types of Elasticity

10. Types of Elasticity of Demand
There are three main types of elasticity:
Point/Own Price Elasticity of Demand
Cross-Elasticity of Demand
Income Elasticity of demand
Economics is about decisions and choices. However, decisions and choices are made because of scarcity. There are three MBA streams: MBA (regular), MBA (Sandwich) and MBA (distance). My question is why did you decide to enroll on an MBA distance programme.

11. Point/Own Price Elasticity of Demand

12. Point/Own Price Elasticity of Demand
Businesses cannot directly control demand.
They can seek to influence demand by utilizing a variety of strategies and tactics but ultimately the consumer decides whether to buy a product or not.
One important way in which consumer behavior can be influenced is through a firm changing the price of its good.
Thus, an understanding of the price elasticity of demand is important in anticipating the likely effects of changes in price on demand.
Price elasticity of demand measures how much the quantity demanded responds to change in price.
This means that an elasticity of 0.7 means that a 1 percent change in price leads to 0.7 percent change in quantity demanded.
Economics is about decisions and choices. However, decisions and choices are made because of scarcity. There are three MBA streams: MBA (regular), MBA (Sandwich) and MBA (distance). My question is why did you decide to enroll on an MBA distance programme.

13. Point/Own Price Elasticity of Demand
Computing the Price Elasticity of Demand
The price elasticity of demand is computed as the percentage change in the quantity demanded divided by the percentage change in the price. That is,
It can also be expressed as
It is always Negative because of the ‘law of demand’.
Economics is about decisions and choices. However, decisions and choices are made because of scarcity. There are three MBA streams: MBA (regular), MBA (Sandwich) and MBA (distance). My question is why did you decide to enroll on an MBA distance programme.
Elastic:
Inelastic:
Unitary:

14. Demand Curves according to their Elasticity
Fairly elastic demand
Demand is described as fairly elastic when a small percentage change in price leads to larger percentage in quantity demanded. P E P1 B Po D Q1 Q0
Qty
In the figure, price increases from Po to P1 (a relatively small margin) and quantity demanded decreases from Qo to Q1 (a bigger margin). Here the absolute value of the elasticity is greater than 1. An example of such a good is a good that has close substitutes. For instance, Milo, Ideal Milk, Uncle Sam, Geisha Mackerel and so on.

15. Demand Curves according to their Elasticity
Fairly Inelastic demand
Demand is described as fairly inelastic when a large percentage change in price leads to a small percentage in quantity demanded. P E P1 Po B D Q1 Q0
Qty
In the figure, price increases from Po to P1 (a relatively large margin) and quantity demanded decreases from Qo to Q1 (a smaller margin). Here the absolute value of the elasticity is less than 1 but greater than zero. An example of such a good is a good that has no close substitutes. For instance, Petrol, Diesel, Alcohol and so on.

16. Demand Curves according to their Elasticity
Unitary elastic demand
With unitary elastic demand, quantity demanded changes by exactly the same percentage change in price. The demand curve is rectangular hyperbola. P P1 Po Q1 Qo
Qty
In the figure, price increases from Po to P1 (a relatively small or large margin) and quantity demanded decreases from Qo to Q1 (a same margin). Here the absolute value of the elasticity is equal to 1.

17. Demand Curves according to their Elasticity
Perfectly Elastic & Inelastic Demand
Price
Price D D
Quantity
Quantity
When demand is perfectly elastic, a manager who raises price even slightly will find that none of the good is purchased.
when demand is perfectly inelastic, consumers do not respond at all to changes in price.

18. Demand Curves according to their Elasticity
Problem:
Suppose that the own price elasticity of demand for a product is -2. If the price of this product fell by 5%, by what percentage would the quantity demanded for a product change?
The demand equation for a product is Qd = P. Calculate the own-price elasticity of demand if P= 2. Interpret the result.
Economics is about decisions and choices. However, decisions and choices are made because of scarcity. There are three MBA streams: MBA (regular), MBA (Sandwich) and MBA (distance). My question is why did you decide to enroll on an MBA distance programme.

19. Price Elasticity of Demand: the Midpoint/Arc Formula

20. Price Elasticity of Demand: the Midpoint/Arc Formula
Economics is about decisions and choices. However, decisions and choices are made because of scarcity. There are three MBA streams: MBA (regular), MBA (Sandwich) and MBA (distance). My question is why did you decide to enroll on an MBA distance programme.

21. Price Elasticity of Demand: the Midpoint/Arc Formula
Problem
Suppose that the price and quantity demanded for a good are GHC 5.00 and 20 units respectively. Suppose further that the price of the product increases to GHC20.00 and the quantity demanded falls to 5 units. Calculate the price elasticity of demand.
At a price of GHC25.00, the quantity demanded of good X is 500 units. Suppose that the price elasticity of demand is if the price of the good increases to GHC26.00, what will be the new quantity demanded of this good?
Economics is about decisions and choices. However, decisions and choices are made because of scarcity. There are three MBA streams: MBA (regular), MBA (Sandwich) and MBA (distance). My question is why did you decide to enroll on an MBA distance programme.

22. Factors Influencing Price Elasticity

23. Factors that Influence Price Elasticity of Demand
Availability of close substitutes
The more substitutes available to a good, the more elastic the demand and vise versa. For instance, ideal milk, pork, Toyota cars, Geisha mackerel
Time
Demand tends to be more inelastic in the short term than in the long term.
Time allows consumers to seek out available substitutes.
Expenditure Share
Goods that attract a small share of consumer’s budgets tend to be more inelastic than goods for which consumers spend a large portion of their incomes. For example, spending on salt, pepper, matches (inelastic) and Cars (elastic).

24. Factors that Influence Price Elasticity of Demand
Number of uses of the Good
The greater the number of possible uses of a product, the greater the elasticity of demand.
This is because a price reduction in price will lead to a greater proportionate change in quantity demanded for the various uses.
For instance, palm oil, which can be used for soap making, margarine, cooking and so on will tend to have higher elasticity than butter.
Number of New Buyers
Goods that a person normally requires only one at a time (for instance, television), it is new buyers instead of additional demand by existing users that has a major effect on the market demand curve.
Thus when the prices of such goods fall within the reach of numerous lower income groups, demand will increase, and demand will tend to be elastic.

25. Factors that Influence Price Elasticity of Demand
Addictiveness of a product
When a product is addictive, its elasticity is inelastic
Necessities verses Luxury
Necessities tend to have relatively inelastic demands
For instance if the price of gas and electricity rose together, people will not demand grammatically less of them.
They might try and be more energy efficient and reduce their demand a little.
Luxuries such as pizza are highly elastic in nature in that, when their prices rise the quantities demanded fall substantially.

26. Price Elasticity and Total Revenue

27. Price elasticity and Total Revenue
Suppose a firm sells ideal milk at Ȼ3.00 and it is able to sell 100 tins, what will be its total revenue?
Do you know why?
What will happen to total revenue if price reduces to Ȼ2.50 and sales increase to 150 tins?
What did you get?
What will happen to total revenue if price increases to Ȼ4.00 and sales fall to 50 tins?

28. Price elasticity and Total Revenue
What do these scenarios inform you?
It means the extent to which quantity demanded changes as a result of price changes (elasticity of demand) influence revenue.

29. Own-Price Elasticity and Total Revenue
Increase (a decrease) in price leads to a decrease (an increase) in total revenue.
Inelastic
Increase (a decrease) in price leads to an increase (a decrease) in total revenue.
Unitary
Total revenue is maximized at the point where demand is unitary elastic.

30. The Relationship between Price Changes and Changes in Total Revenue
/Ep/
Absolute terms ΔP ΔQ
ΔTR
˃ 1 - +
˂ 1 _

31. Elasticity, Total Revenue and Linear DemandP TR
100 10 20 30 40 50 Q Q

32. Elasticity, Total Revenue and Linear DemandP TR
100 80
800 Q 10 20 30 40 50 Q 10 20 30 40 50

33. Elasticity, Total Revenue and Linear DemandP TR
100 80 60
1200
800 Q 10 20 30 40 50 Q 10 20 30 40 50

34. Elasticity, Total Revenue and Linear DemandP TR
100 80 60
1200 40
800 Q 10 20 30 40 50 Q 10 20 30 40 50

35. Elasticity, Total Revenue and Linear DemandP TR
100 80 60
1200 40 20
800 Q 10 20 30 40 50 Q 10 20 30 40 50

36. Elasticity, Total Revenue and Linear DemandP TR
100
Elastic 80 60
1200 40 20
800 Q 10 20 30 40 50 Q 10 20 30 40 50
Elastic

37. Elasticity, Total Revenue and Linear DemandP TR
100
Elastic 80 60
1200
Inelastic 40 20
800 Q 10 20 30 40 50 Q 10 20 30 40 50
Elastic
Inelastic

38. Elasticity, Total Revenue and Linear DemandP TR
100
Unit elastic
Elastic
Unit elastic 80 60
1200
Inelastic 40 20
800 Q 10 20 30 40 50 Q 10 20 30 40 50
Elastic
Inelastic

39. Demand, Marginal Revenue (MR) and Elasticity
When
MR > 0, demand is elastic;
MR = 0, demand is unit elastic;
MR < 0, demand is inelastic. P
100
Elastic
Unit elastic 80 60
Inelastic 40 20 Q 10 20 40 50 MR

40. Cross-Price Elasticity of Demand

41. Cross-Price Elasticity of Demand
It reveals the responsiveness of the demand for a good to changes in the price of a related good. This elasticity helps managers ascertain how much its demand will rise or fall due to a change in the price of another firm’s product.
If EQX,PY > 0, then X and Y are substitutes.
If EQX,PY < 0, then X and Y are complements.

42. Cross-Price Elasticity of Demand
Scenario:
Cross-price elasticities play an important role in the pricing decisions of firms that sell multiple products. Indeed, many drinking bars offer lime for under Ȼ1.00 because their managers realize that Herb Afrik and lime are complements: When consumers buy Herb Afrik, lime typically accompanies the purchase. Thus, by lowering the price of Herb Afrik, a drinking bar affects its revenues from both Herb Afrik sales and lime sales. The precise impact on these revenues depends on the own price and cross-price elasticities of demand.

43. Predicting Revenue Changes from Two Products
Suppose that a firm sells two related goods. If the price of X (Herb Afrik) changes, then total revenue will change by:

44. Cross-Price Elasticity of Demand
Example:
Suppose a drinking bar earns Ȼ4,000 per week in revenues from Herb Afrik sales ( product X) and Ȼ2,000 per week from lime sales (product Y). Thus, Rx = Ȼ4,000 and Ry = Ȼ2,000. If the own price elasticity of demand for Herb Afrik is -1.5 and the cross-price elasticity of demand between lime and Herb Afrik is -4.0, what would happen to the firm’s total revenues if it reduced the price of Herb Afrik by 1 percent?

45. Income Elasticity of Demand

46. Income Elasticity of Demand
It is a measure of the responsiveness of consumer demand to changes in income.
If EQX,M > 0, then X is a normal good.
If EQX,M < 0, then X is an inferior good.

47. Income Elasticity of Demand
Problem
Your firm’s research department has estimated the income elasticity of demand for electric heater to be You have just read in the papers that due to an upturn in the economy, consumer incomes are expected to rise by 10 percent over the next three years. As a manager of an electrical shop, how will this forecast affect your purchases of electric heater?

48. Income Elasticity of Demand
Solution
Since electric heater has an income elasticity of and consumer income is expected to rise by 10 percent, you can expect to sell 19.4 percent less electric heater over the next three years. Therefore, you should decrease your purchases of electric heater by 19.4 percent, unless something else changes.

49. Linear Demand Function and Elasticities

50. Linear Demand Function and Elasticities
General Linear Demand Function and Elasticities:
Own Price
Elasticity
Cross Price
Elasticity
Income
Elasticity

51. Linear Demand Function and Elasticities
Problem:
The daily demand for ODIKE Ventures shoes is estimated to be
Where Ax represents the amount of advertising spent on shoes (X), Px is the price of good X, Py is the price of good Y, and M is average income. Suppose good X sells at Ȼ25 a pair, good Y sells at Ȼ35, the company utilizes 50 units of advertising, and average consumer income is Ȼ20,000. Calculate and interpret the own price, cross-price, and income elasticities of demand.

52. Uses of Elasticities Pricing Managing cash flows
Impact of changes in competitors’ prices
Wage negotiations by Trade Unions
Impact of advertising campaigns.

53. Example 1: Pricing and Cash Flows
According to an IEA Report by Mrs. Mensah, Vodafone’s own price elasticity of demand for long distance services is
Vodafone needs to boost revenues in order to meet it’s marketing goals.
To accomplish this goal, should Vodafone raise or lower it’s price?

54. Answer: Lower price!
Since demand for Vodafone services is elastic, a reduction in price will increase quantity demanded by a greater percentage than the price decline, resulting in more revenues for Vodafone.

55. Example 2: Quantifying the Change
If Vodafone lowered price by 3 percent, what would happen to the volume of long distance telephone calls routed through Vodafone?

56. Answer: Calls Increase!
Calls would increase by percent!

57. Example 3: Impact of a Change in a Competitor’s Price
According to an IEA Report by Mrs. Mensah, Vodafone’s cross price elasticity of demand for long distance services is 9.06.
If competitors (MTN, Airtel, Glo and so on) reduced their prices by 4 percent, what would happen to the demand for Vodafone’s services?

58. Answer: Vodafone’s Demand Falls!
Vodafone’s demand would fall by percent!

59. How does elasticity influence wage negotiation and advertising?
When the demand for a good or service produced by labor has inelastic demand, unions could negotiate for high wages.

60. How does elasticity influence wage negotiation and advertising?
When the demand for a good or service produced by labor has inelastic demand, unions could negotiate for high wages.
Firms will try to make their products more inelastic using advertisements for instance, so that they are ensured a decent quantity demanded regardless of their set price. For instance, Alomo bitters

61. Interpreting Demand Functions
Mathematical representations of demand curves.
Example:
Law of demand holds (coefficient of PX is negative).
X and Y are substitutes (coefficient of PY is positive).
X is an inferior good (coefficient of M is negative).

62. Example of Linear Demand
Qd = P.
Own-Price Elasticity: (-2)P/Q.
If P=1, Q=8 (since = 8).
Own price elasticity at P=1, Q=8:
(-2)(1)/8=

63. Regression Analysis One use is for estimating demand functions.
Important terminology and concepts:
Least Squares Regression model: Y = a + bX + e.
Least Squares Regression line:
Confidence Intervals.
t-statistic.
R-square or Coefficient of Determination.
F-statistic.

64. An Example
Use a spreadsheet to estimate the following log-linear demand function.

65. Summary Output

66. Interpreting the Regression Output
The estimated log-linear demand function is:
ln(Qx) = ln(Px)
Own price elasticity: (inelastic)
How good is our estimate?
t-statistics of 5.29 and indicate that the estimated coefficients are statistically different from zero.
R-square of 0.17 indicates the ln(PX) variable explains only 17 percent of the variation in ln(Qx).
F-statistic significant at the 1 percent level.

67. Conclusion
Elasticities are tools you can use to quantify the impact of changes in prices, income, and advertising on sales and revenues.
Given market or survey data, regression analysis can be used to estimate:
Demand functions
Elasticities
A host of other things, including cost functions
Managers can quantify the impact of changes in prices, income, advertising, etc.