1. BUS 525: Managerial Economics
Lecture 3
Quantitative Demand Analysis

2. Overview I. The Elasticity Concept II. Demand Functions
Own Price Elasticity
Elasticity and Total Revenue
Cross-Price Elasticity
Income Elasticity
II. Demand Functions
Linear
Log-Linear
III. Regression Analysis
So far our analysis of the impact of changes in price and income on consumer behavior has been rather qualitative rather than quantitative
Business managers question-
How much do we have to cut price to achieve 3.2 percent sales growth?
If we cut our price by 6.5 percent how many more units do we sell? Do we have sufficient inventories on hand to accommodate this increase in sales? If not, do we have enough workers to increase production? How much our revenues and cash flow change as a result of the price cut?
How much will our sales change if rivals cut their price by 2 percent or a recession hits and household incomes decline by 2.5 percent?
Qx = f(Px, Py, M, H)

3. The Elasticity Concept
Elasticity is a measure of the responsiveness of a variable to a change in another variable: the percentage change in one variable that arises due to a given percentage change in another variable
How responsive is variable “G” to a change in variable “S”?
Grade and study
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.

4. The Elasticity Concept Using Calculus
An alternative way to measure the elasticity of a function G = f(S) is
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.

5. Own Price Elasticity of Demand
A measure of the responsiveness of the demand for a good to changes in the price of that good: the percentage change in the quantity demanded of the good divided by the percentage change in the price of the good
Negative according to the “law of demand.”
Two aspects of an elasticity are important: (1) whether it is positive or negative and (2) whether it is greater or less than 1, in absolute value
By the law of demand, there is an inverse relationship between price and quantity demanded: thus own price elasticity of demand is generally a negative number (except for inferior goods)
Conceptually, the quantity consumed of a good is relatively responsive to a change in price when the demand is elastic and relatively unresponsive to changes in price when demand is inelastic. i.e. price increases will reduce demand very little when demand is inelastic. However, when demand is elastic, a price increase will reduce demand considerably. Unitary elastic?
For example, if the own price elasticity of demand for a product is -2, we know that a 10 percent increase in product price leads to a 20 percent decline in the quantity demanded of the good, since -20%/10% = -2
Elastic:
Inelastic:
Unitary:

6. Perfectly Elastic & Inelastic Demand
Price
Price D D
Demand is perfectly elastic if the own price elasticity is infinite in absolute value. In this case the demand curve is horizontal. A manager who raises price even slightly will find that none of the good is purchased. Example?
Demand is perfectly inelastic if the own price elasticity is zero. In this case the demand curve is vertical. Consumer do not respond at all to changes in price. Example? Demand the same amount irrespective of the price.
Quantity
Quantity

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

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

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

10. 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

11. 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

12. 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

13. Elasticity, Total Revenue and Linear DemandP TR
100
Elastic 80 60
1200
Inelastic 40
Slope and elasticity are not the same. Slope of a linear demand curve is the same but elasticity is different at different points.
Qxd = Px, The slope of this linear demand curve is constant, -2. But elasticity increases in absolute value as Px increases. Thus, own price elasticity of demand varies along a linear demand curve 20
800 Q 10 20 30 40 50 Q 10 20 30 40 50
Elastic
Inelastic

14. 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.
Total revenue will remain unchanged

15. 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

16. Class Exercise I
Research department of an airline estimates that the own price elasticity of demand for a particular route is If the airline cuts price by 5 percent, will the ticket sales increase enough to increase overall revenues?
If so, by how much?
Research department of an airline estimates that the own price elasticity of demand for a particular route is If the airline cuts price by 5 percent, will the ticket sales increase enough to increase overall revenues?
Since the demand is elastic, the price cut results in a greater than proportional increase in sales, and thus increases the firm’s total revenues. Ticket sales will increase by 8.5 percent if prices are reduced by 5 percent.

17. Factors Affecting Own Price Elasticity
Available substitutes
The more substitutes available for the good, the more elastic the demand.
Broader categories of goods have more inelastic demand than more specifically defined categories.
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 comprise a small share of consumer’s budgets tend to be more inelastic than goods for which consumers spend a large portion of their incomes.
Expenditure share
House, Car, Salt

18. Some Elasticity Estimates
1-18
Some Elasticity Estimates
Table 3-2 Selected Own Price Elasticities
Market
Own Price Elasticity
Transportation
-0.6
Motor vehicles
-1.4
Motorcycles and bicycles
-2.3
Food
-0.7
Cereal
-1.5
Clothing
-0.9
Women’s clothing
-1.2
Table 3-3 Selected Short and Long-Term Own Price Elasticities
Market
Short-Term Own Price Elasticity
Long-Term Own Price Elasticity
Transportation
-0.6
-1.9
Food
-0.7
-2.3
Alcohol and tobacco
-0.3
-0.9
Recreation
-1.1
-3.5
Clothing
-2.9
Broader categories of goods have more inelastic demand than more specifically defined categories. Food is lightly inelastic, cereal is elastic, many substitutes for cereal but no substitute for food, same is true for clothing (inelastic) women’s clothing is more elastic. Transportation, motor vehicles, motorcycles and bicycles
Demand tends to be more elastic in the long run. Time allows people to seek out substitutes. Flight in 30 minutes, whatever price asked by taxi driver

19. The Arc Price Elasticity of Demand
How can the percentage changes in Q and P be calculated in order to derive the own price elasticity of demand?
Q Q
(Q1 + Q2)/ (Q1 + Q2)
EQX,PX = =
P P
(P1 + P2)/ (P1 + P2) 3 3

20. Class Exercise II Price
Consider a Demand Curve Q = 40,000, ,500P
Calculate arc elasticity of demand from the given data
Price
16,000
P2=12, B
P1=12, A Q
,750, ,000,000
10,000,000 17

21. How sensitive are consumers to a change in the avg
How sensitive are consumers to a change in the avg. price of automobiles?
We calculate the arc price elasticity of demand between A and B as:
10,000,000-8,750,000
(10,000,000+8,750,000)/2
Ep = =
12, ,500
(12, ,500)/2 4 4

22. Interpretation
Between points A and B (or between the price range from $12,000 to $12,500), a one-percent increase in the average price of cars will bring about, on average, a reduction of sales by 3.267%, ceteris paribus.
Because the price elasticity of demand is calculated between two points on a given demand curve, it is called the arc price elasticity of demand. 5 5

23. Caveat
Elasticity measure depends on the price at which it is measured.
It is not generally a constant (because the demand curve is not likely to be a straight line).

24. The Point Price Elasticity of Demand
It measures the price elasticity of demand at a given price or a particular point on the demand curve.
Q P
ep = (-----)(----)
P Q 7 7

25. Class Exercise III Other things being equal,
Qxd = -2,500Px + 1,000M PY - 1,000,000H+ 0.05AX
Other things being equal,
if P1 = $12,000, Q1 = 10,000,000.
Calculate point elasticity of demand.
What's the point elasticity of demand at
P2 = $12,500?
Calculate arc elasticity of demand.

26. Calculation of the point elasticity using the demand for automobile equation
Qxd = -2,500Px + 1,000M PY - 1,000,000H+ 0.05AX
Other things being equal,
if P1 = $12,000, Q1 = 10,000,000.
The point price elasticity is:
Q P
ep = (-----) (---)
P Q
= (-2,500)(12,000/10,000,000)
= - 3 8 8

27. Point price elasticity (cont.)
What's the point elasticity of demand at
P2 = $12,500?
At this price, Q = 8,750,000.
Hence,
Q P
ep = (-----) (---)
P Q
= (-2,500)(12,500/8,750,000) = 9 9

28. Two versions of the elasticity of demand – Point vs. Arc
Price
16,000
ep=
Ep=
12,500
ep= -3.0
12,000 Q
8,750,000
10,000,000

29. From Concept to Applications
We began with a definition of the elasticity of demand based on,
%in Qxd
EQx, Px =
%  in Px
If we know the price elasticity of demand (Ep), the formula will let us answer a number of "what if" questions. 10 10

30. Examples
(1) How great a price reduction is necessary to increase sales by 10%?
(2) What will be the impact on sales of a 5% price increase?
(3) Given marginal cost and price elasticity information, what is the profit-maximizing price? 11 11

31. Class Exercise IV Supposing that the elasticity of
demand for diesel is -0.5, how much
prices must go up to reduce gasoline
use by 1%?

32. The price increase needed to reduce diesel consumption by 1%
Supposing that the elasticity of demand for diesel is -0.5, how much prices must go up to reduce gasoline use by 1%?
- 0.01
= ,
%Pd
%Pd = (-0.01/-0.5) = or 2% 12

33. Marginal Revenue and the Own Price Elasticity Of Demand
Demand and marginal revenue
For a linear demand curve marginal revenue curve lies exactly halfway between the demand curve and the vertical axis
Marginal revenue is less than the price of each unit sold
When demand is elastic (-∞<E<-1), marginal revenue is positive
When demand is unitary elastic (E=-1), marginal revenue is zero
When demand is inelastic (-1<E<0), marginal revenue is negative
Unitary P Q TR MR 5 1 - 4 2 8 3
Elastic
Unitary
Inelastic MR
MR = P[(1+E)/E]
When -∞<E<1, demand is elastic, MR is positive, When E=-1, demand is unitary elastic, MR is zero. Finally when -1<E<0, demand is inelastic, MR is negative
TR = P x Q
dTR/dQ = P. dQ/dQ + Q. dP/ dQ
= P {1+(Q/P.dP/dQ)}
= P (1+1/Ep)
= P [(Ep +1)/ Ep]

34. Cross Price Elasticity of Demand
A measure of the responsiveness of the demand for a good to changes in the price of a related good: the percentage change in the quantity demanded of the good divided by the percentage change in the price of a related good
Clothing and food have a cross price elasticity of This means that if the price of food increases by 10 percent, the demand for clothing will decrease by 1.8 percent: food and clothing are complements
Transportation and recreation: -0.05
Food and recreation: 0.15, substitutes
If the price of recreation increases by 15 percent, demand for food to increase by 2.25 percent
If EQX,PY > 0, then X and Y are substitutes.
If EQX,PY < 0, then X and Y are complements.

35. Income Elasticity If EQX,M > 0, then X is a normal good.
A measure of the responsiveness of the demand for a good to changes in consumer income: the percentage change in the quantity demanded divided by the percentage change in income
If EQX,M > 0, then X is a normal good.
Income elasticity of Transportation: 1.80
Income elasticity is positive : Normal good; Greater than 1, elastic, expenditure on transportation grow more rapidly than income
Income elasticity of Food : 0.8
Income elasticity is positive : Normal good; Less than 1, elastic, expenditure on food grow less rapidly than income. When income declines, expenditure on food decreases less rapidly than income
Income elasticity of Radish : -1.94: Change in income : 10%
Income elasticity is negative : Inferior good; More than 1, elastic, expenditure on Radish will decreases by 1.94 percent for every 1 percent rise in consumer income. Orders will decrease during boom and increase during recession. Expect to sell Radish by 19.4 percent, if consumer income is expected to rise by 10 percent
If EQX,M < 0, then X is a inferior good.

36. Some Elasticity Estimates
1-36
Table 3-4 Selected Cross-Price Elasticities
Cross-Price Elasticity
Transportation and recreation
-0.05
Food and recreation
-0.15
Clothing and food
-0.18
Table 3-5 Selected Income Elasticities
Income Elasticity
Transportation
1.80
Food
0.80
Ground beef, nonfed
-1.94
Table 3-6 Selected Long-Term Advertising Elasticities
Advertising Elasticity
Clothing
0.04
Recreation
0.25

37. Other Elasticities Advertising elasticity
A measure of the responsiveness of the demand for a good to changes in advertising expenditure: the percentage change in the quantity demanded divided by the percentage change in advertising expenditure
Advertising elasticity of clothing: 0.04
Advertising elasticity is positive but clothing is not very advertising elastic
Advertising must increase by hefty 60 percent to
increase the demand for recreation by 15 percent

38. Class Exercise V Advertising elasticity of recreation : 0.25
How much should advertising increase to increase the demand for recreation by 15%?
Advertising elasticity of recreation : 0.25
How much should advertising increase to increase the demand for recreation by 15%?
Advertising elasticity of recreation : 0.25
How much should advertising increase to increase the demand for recreation by 15%?
Advertising elasticity of recreation : 0.25
How much should advertising increase to increase the demand for recreation by 15%?
Advertising must increase by hefty 60 percent to
increase the demand for recreation by 15 percent

39. Uses of Elasticities Pricing. Managing cash flows.
Impact of changes in competitors’ prices.
Impact of economic booms and recessions.
Impact of advertising campaigns.
And lots more!

40. Example 1: Pricing and Cash Flows
According to a BTRC Report by Zahid Hussain, BTCL’s own price elasticity of demand for long distance services is
BTCL needs to boost revenues in order to meet it’s marketing goals.
To accomplish this goal, should BTCL raise or lower it’s price?

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

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

43. Answer
Calls would increase by percent!

44. Example 3: Impact of a change in a competitor’s price
According to an BTRC Report by Zahid Hussain, BTCL’s cross price elasticity of demand for long distance services is 9.06.
If competitors reduced their prices by 4 percent, what would happen to the demand for BTCL’s services?

45. Answer
BTCL’s demand would fall by percent!

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

47. Linear Demand Functions
General Linear Demand Function:
We know the use of elasticity to make managerial decisions
How to calculate elasticities from demand functions?
Start with linear demand functions
The elasticity of demand with respect to a given variable is simply the coefficient of the variable multiplied by the ratio of the variable (own price, income etc.) to the quantity demanded.
Own price elasticity is not the slope of the demand curve. When Px =0, In other words for prices near zero, demand is inelastic. On the other hand, when prices rise, Qx decreases and the absolute value of the elasticity increases
Own Price
Elasticity
Cross Price
Elasticity
Income
Elasticity

48. Class Exercise 6 Given the demand curve, Qxd = 100- 3Px+4Py-.01M+2Ax
If Px=25, Py= 35, M= 20,000, Ax =50
Calculate (a) own price, (b) cross price, and © income elasticity of demand

49. Example of Linear Demand
Qxd = Px+4Py-.01M+2Ax.
Own-Price Elasticity: (-3)Px/Qx.
If Px=25, Py= 35, M= 20,000, Ax =50
Q=65 [since 100 – 3(25) +4(35) -.01(20,000)+2(50)] = 65
Own price elasticity of demand at Px=25, Q=65:
=(-3)(25)/65=
Cross price elasticity of demand at Py=35, Q65
=(4)(35)/65= 2.15
Income elasticity of demand at M=20,000
=(-0.1)(20,000)/65= -3.08

50. Elasticities for Nonlinear Demand Functions
Qxd = c PxβxPy βyMβMHβH
General Log-Linear Demand Function:
When the demand is log linear, the elasticity with respect to a given variable is simply the coefficient of the corresponding logarithm

51. Example of Log-Linear Demand
ln(Qd) = ln(P).
Own Price Elasticity: -2.
Demand for raincoats
ln Qxd = ln Px + 3 ln R -2 ln Ay, R = Rainfall, Ay = Level of advertising
E Qx,R = βR = 3
10 percent increase in rainfall will increase demand for raincoats by 30%

52. Graphical Representation of Linear and Log-Linear DemandQ P D D Q
Linear
Log Linear

53. Regression Analysis One use is for estimating demand functions.
Important terminology and concepts:
Least Squares Regression: Y = a + bX + e.
Confidence Intervals.
t-statistic.
R-square or Coefficient of Determination.
F-statistic.
Least square line for the equation:
Y= a+bx+c is given by Y = a^ +b^x
The parameter estimate a^ or b^ represents the values of a and b that result in the smallest sum of square errors. Y A D B C X

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

55. Summary Output

56. 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 .17 indicates we explained only 17 percent of the variation in ln(Qx).
F-statistic significant at the 1 percent level.

57. 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.

58. Lessons:
(1) The first lessons in business: Never lower your price in the inelastic range of the demand curve. Such a price decrease would reduce total revenue and might at the same time increase average production cost.
(2) When the demand is inelastic, raise the price to increase revenue and, possibly, profit.
(3) When demand is elastic, price increases should be avoided. 18 19

59. Lessons (Cont.)
But should we always cut price when the demand is elastic?
Even over the range where demand is elastic, a firm will not necessarily find it profitable to cut prices; the profitability of such an action depends on whether the marginal revenues generated by the price reduction exceed the marginal cost of the added production. 20

60. Another Example: Optimal Pricing
Step 1 – Using the relationship between MR and Ep
Given, TR = PQ,
TR  (PQ)
MR = =
Q  Q
Q P
= P(-----) + Q (-----)
Q Q
Q P
= P ( ) = P ( )
P Q ep 16

61. Optimal Pricing (Cont.)
Optimal Price is when MC = MR
i.e., MC = P (1 + 1/ep) MC
P =
(1 + 1/ep)
That is, the profit-maximizing price is determined by MC and ep 16 17

62. Predicting Revenue Changes from Two Products
Suppose that a firm sells to related goods. If the price of X changes, then total revenue will change by:
R = Rx + Ry
Rx = $4,000; Ry=$2,000
Own price elasticity of burger sales
Own price elasticity of soda sales
What will happen to firm’s total revenue if it
reduced the price of hamburgers by 1 percent?
∆R = $20+$80 = 100
$20 from increased burger revenue; $80 from
Additional soda revenues