Chapter 3Demand Theory

1. Consumer Choice and the Law of Demand

Law of Demand

Law of Demand: There is an inverse relationship between the price of a good and the quantity consumers are willing to purchase.

As price of a good rises, consumers buy less.

The availability of substitutes --goods that do similar functions -- explains this negative relationship.

A market demand schedule is a table that shows the quantity of a good people will demand at varying prices.

Market Demand Schedule

Consider the market for cellular phones. A market demand schedule lays out the amount of cell phones that are demanded in the market for a spectrum of prices.

We can graph these points (price and the respective demand) to make a demand curve for cell phones.

At $3.50 Jones demands 1 pizza . . . and so on . . .

At $3.50 Smith demands 2 pizzas . . . and so on . . .

Jones Smith Two-person marketPrice

Weekly frozen pizza consumption

Price Price

$3.50

$2.50

1 3

$3.50

$2.50

2 3

d

$3.50

$2.50

3 6

Dd

• Consider Jones’s demand for frozen pizza. at $2.50 Jones demands 3 pizzas . . .• Consider Smith’s demand for frozen pizza. at $2.50 Smith demands 3 pizzas . . .• The market demand curve is merely the horizontal sum of the individual demand curves (here Jones and Smith).• The market demand curve will slope downward to the right, just as the individual demand curves do.

Individual and Market Demand Curves

Demand

Market Demand Schedule

Cell Phone Price

(monthly bill)

Millions of Cell Phone Subscribers

$123 2.1 $107 3.5 $ 92 5.3 $ 79 7.6 $ 73 11.0 $ 63 16.0$ 56 24.1

Price(monthly bill)

Quantity(of Cell Phone Subscribers)

140

120

100

80

60

5 10 15 20 25 30

Demand

Market Demand SchedulePrice

(monthly bill)

Quantity(of Cell Phone Subscribers)

140

120

100

80

60

5 10 15 20 25 30

• Notice how the law of demand is reflected by the shape of the demand curve.• As the price of a good rises …• . . . consumers buy less.

Demand

Market Demand SchedulePrice

(monthly bill)

Quantity(of Cell Phone Subscribers)

140

120

100

80

60

5 10 15 20 25 30

• The height of the demand curve at any quantity shows the maximum price that consumers are willing to pay for that additional unit.

• Here, for the 11th unit . . .

• . . . consumers are only willing to pay up to $73 for it.

• While they would be willing to pay up to $92 for the 5.3 (millionth) unit.

Consumer Surplus

Consumer Surplus - the area below the demand curve but above the actual price paid. Consumer surplus is the

difference between the amount consumers are willing to pay and the amount they have to pay for a good.

Lower market prices will increase consumer surplus.

Consumer Surplus• Lets consider the market for cellular phones again. This time we will assume that the demand for cell phones is more linear and that the market price is $100.

Quantity(of Cell Phone Subscribers)

140

120

100

80

60

5 10 15 20 25 30

Demand

• If the market price is $100, then the 25th unit will not sell because those who demand it are only willing to pay $60 for cellular phone service.• At $100, the 15th unit will sell because those who demand it are willing to pay up to $100 for cellular phone service.• At $100, the 10th unit will sell because those who demand it are

willing to pay up to $120 for cellular phone service.

MarketPrice = $100

Price(monthly bill)

Consumer Surplus

• For all those goods under 15 units, people are willing to pay more than $100 for service.

Price(monthly bill)

Quantity(of Cell Phone Subscribers)

140

120

100

80

60

5 10 15 20 25 30

Demand

• The area, represented by the distance above the actual price paid and below the demand curve, is called consumer surplus.• This area represents the net gains to buyers from market exchange.

MarketPrice = $100

2. Changes in Demand Versus Changes in Quantity Demanded

Changes in Demand and Quantity Demanded

Change in Demand - shift in entire demand curve.

Change in Quantity Demanded - movement along the same demand curve in response to a price change.

Change in DemandPrice

(dollars)

Quantity(of Compact Disks per yr)

25

20

15

10

5

5 10 15 20 25 30

• If CDs cost $15 each, the CD

demand curve D1 shows that 10 units would be demanded.

• If, somehow, the preferences for CDs changed then the demand for CDs may change. • Here we will assume that consumer income increases, increasing demand for CDs at all price levels. At $15 15 units are now demanded.

• If the price of CDs changed to $7.50, the quantity demanded for CDs would increase to 20 units.

D1D2

10 15 20

Demand Curve Shifters

Change in the Number of Consumers

Change in Price of Related Good

Changes in ExpectationsDemographic ChangesChanges in Consumer Tastes

and Preferences

Changes in Consumer Income

1. Which of the following do you think would lead to an increase in the current demand for beef: (a) higher pork prices, (b) higher incomes, (c) higher prices of grains used to feed cows, (d) good weather conditions leading to a bumper (very good) corn crop, (e) an increase in the price of beef?

Questions for Thought:

2. What is being held constant when a demand curve for a specific product (like shoes or apples, for example) is constructed? Explain why the demand curve for a product slopes downward and to the right.

The Market Demand Curve

Shows the total quantity of the good that would be purchased at each price

MARKET DEMAND FOR PERSONAL COMPUTERS, 1996

QD PER YEAR PRICE/COMPUTER(thousands) (dollars)

800 3000975 2750

1150 25001325 22501500 2000

Market Demand for Personal Computers, 1996

2000

2200

2400

2600

2800

3000

3200

0 500 1000 1500 2000

quantity

Pri

ce

The Market Demand Curve

Other Determinants of Market Demand

Consumer tastes and preferences.Consumer incomes.Level of other prices.

Size of consumer population.

Demand Functions

Q of good X = f ( Price of X,

Incomes of consumers,

Prices of other goods,

Population,

Advertising expenditures,

Etc.)

3. Elasticity of Demand

Elastic and Inelastic Demand Curves

Elastic demand - quantity demanded is sensitive to small price changes. Easy to substitute away from

good.Inelastic demand - quantity

demanded is not sensitive to price changes. Difficult to substitute away

from good.

Elastic and Inelastic Demand Curves

2.00

1.25

2.00

1.25

Gasoline

Tacos

1 2 3 4 5 6 7 8 9 10

1 2 3 4 5 6 7 8 9 10

• If the market price for gasoline was to rise from $1.25 to $2.00, the quantity demanded in the market decreases insignificantly (from 8 to 7 units).• If the market price for tacos rises from $1.25 to $2.00, the quantity demanded in the market decreases significantly (from 8 to 1 unit).• Taco demand is highly sensitive to price changes and can be described as elastic; gasoline demand is relatively insensitive to price changes and can be described as inelastic.

Price elasticity reveals the responsiveness of the amount purchased to a change in price.

Elasticity of Demand

Price Elasticityof demand = =

% Q

% P

% Change in quantity demanded% Change in Price

- or put simply -)()(

)()(

1010

1010

PPPP

QQQQ

(c)

Price

Quantity/time

(b)

Price

Quantity/time

(a)

Price

Quantity/time

Demand curve of unitary elasticity

Mythicaldemandcurve

Demandfor Cigarettes

• Perfectly inelastic: Despite an increase in price, consumers still purchase the same amount. In fact, the substitution and income effects prevent this from happening in the real world.

• Relatively inelastic: A percent increase in price results in a smaller % reduction in sales. The demand for cigarettes has been estimated to be highly inelastic.

• Unitary elasticity: The % change in quantity demanded is equal to the % change in price. A curve of decreasing slope results. Sales revenue (price times quantity sold) is constant.

Elasticity of Demand

(e)

Price

Quantity/time

(d)

Price

Quantity/time

Demand for Farmer Jones’s wheat

Demandfor Apples

• Relatively elastic: A percent increase in price leads to a larger % reduction in purchases. When good substitutes are available for a product (as is the case for apples), the amount purchased will be highly sensitive to a change in price.

• Perfectly elastic: Consumers will buy all of Farmer Jones’s wheat at the market price, but none will be sold above the market price.

Elasticity of Demand

DQuantity Demanded

/Time

1

2

100 110

Price ($)

Elasticity (– ) 0.14=

= ( - ) 0.14

)()(

)()(

1010

1010

PPPP

QQQQ

Recall -

• With this straight-line (constant-slope) demand curve, demand varies across a range of prices.

• Using the equation for elasticity from before, the formula for arc elasticity shows that, when price rises from $1 to $2 . . . and quantity demanded falls from 110 to 100 . . . the elasticity for that region of the demand curve is ( - .14 ) (inelastic).

(110 - 100) (110 + 100)

($1 - $2) ($1 + $2)

Elasticity of Demand

DQuantity Demanded

/Time

Price ($)

Elasticity (– ) 7. 0=

= ( - ) 7.0

)()(

)()(

1010

1010

PPPP

QQQQ

Recall -

• A price increase of the same magnitude (but a smaller %) from $10 to $11 . . . leads to a decline in quantity demanded from 20 to 10. Even though the change in price here was smaller than before (as a %) the same change in quantity demanded occurred.

(20 - 10) (20 + 10)

($10 - $11) ($10 + $11)

Elasticity of Demand

• Using the same equation to calculate elasticity as before, the elasticity amounts to - 7.0 (greater than - .14 from before).

• Thus the price-elasticity of a straight-line demand curve increases as price rises.

10

11

10 20

Availability of substitutes

Determinants of Price Elasticity of Demand

When good substitutes for a product are available, a rise in price induces many consumers to switch to other products causing demand to be elastic.

Share of total budget expended on product As the share of the total budget

expended on the product rises, demand is more elastic.

25

$1.50

(a) Ballpoint pens per week (in thousands)

$1.00

100

D

90

$1.50

(b) Cigarette packs per week (in millions)

$1.00

100

D

PricePrice

• As the price of ballpoint pens (a) rises from $1.00 to $1.50 (a 50% increase in price) . . . quantity demanded plunges from 100,000 to 25,000 (a 75% decrease in quantity demanded).

• The % reduction in quantity demanded is larger than the % increase in price, thus the demand for ballpoint pens is elastic.• As the price of cigarettes (b) rises from $1.00 to $1.50 (a 50% increase in price) . . . quantity demanded plunges from 100 mil. to 90 mil. (a 10% decrease in quantity demanded).• The % reduction in quantity demanded is smaller than the % increase in price, thus the demand for cigarettes is inelastic.

Elastic and Inelastic Demand

If the price of a product increases, consumers will reduce their consumption by a larger amount in the long run than in the short run.

Time and Demand Elasticity

Thus, the demand for most products will be more elastic in the long run than in the short run.

This relationship is often referred to as the second law of demand.

Elasticity of Demand

0.9 1.2

0.9

1.1

1.1 0.9 1.2 1.2

2.3 4.0 2.4 2.8

1.2–1.5 4.0 4.6

0.1 0.1 0.1 0.1 0.2 0.7 0.1

0.5

0.25 0.5

0.45

0.4 0.6 0.6 0.2

INELASTIC

Salt Matches Toothpicks Airline travel (short run) Gasoline (short run) Gasoline (long run) Residential natural gas (short run) Residential natural gas (long run) Coffee Fish (cod), consumed at home Tobacco products (short run)

Legal services (short run) Physician services Taxi (short run) Automobiles (long run)

APPROXIMATELY UNITARY ELASTICITY

Movies Housing, owner occupied (long run) Shellfish (consumed at home) Oysters (consumed at home) Private education Tires (short run

Tires (long run) Radio and television receivers

ELASTIC

Restaurant meals Foreign travel (long run) Airline travel (long run) Fresh green peas Automobiles (short run Chevrolet automobiles Fresh tomatoes

• Can you explain why the demand for some goods is highly inelastic while that for others is elastic.

Price elasticity of demand

The percentage change in quantity demanded resulting from a 1 percent change in price.

= - Q x P

P Q

Arc elasticities

uses average values of Q and P as reference points

Q x (P1 + P2)/2

P (Q1 + Q2)/2

5. Total Revenue, Total Expenditure, and the Price Elasticity of Demand

-- unchanged --

increase decrease

Price ElasticityOf Demand

NumericalElasticity

Coefficient(In Absolute Value)

Elastic

Unitary Elastic

Inelastic

1 to

1

0 to 1

Impact of Raising Price on Total Consumer

Expenditures or a Firm’sTotal Revenue

decrease

Impact of Lowering Priceon Total Consumer

Expenditures or a Firm’sTotal Revenue

increase -- unchanged --

Total Expenditures and Demand Elasticity

• The table above summarizes the relationship between changes in price and total expenditures for demand curves of varying elasticity.

(a) The Firm’s Price, Quantity Sold, Total Revenue, and Price Elasticity

Price Quantity

Sold Total

Revenue Price Elasticity of Demand

((0-1) / (0+1)) / ((9-8) / (9+8)) = 17.00

((1-2) / (1+2)) / ((8-7) / (8+7)) = 5.00

((2-3) / (2+3)) / ((7-6) / (7+6)) = 2.60

((3-4) / (3+4)) / ((6-5) / (6+5)) = 1.57

((4-5) / (4+5)) / ((5-4) / (5+4)) = 1.00

((5-6) / (5+6)) / ((4-3) / (4+3)) = 0.64

((6-7) / (6+7)) / ((3-2) / (3+2)) = 0.38

((7-8) / (7+8)) / ((2-1) / (2+1)) = 0.20

((8-9) / (8+9)) / ((1-0) / (1+0)) = 0.06

$9 0 $0x =

$8 1 $8x =

$7 2 $14 x =

$6 3 $18 x =

$5 4 $20 x =

$4 5 $20 x =

$3 6 $18 x =

$2 7 $14 x =

$1 8 $8 x =

$0 9 $0x =

(b) The Firm’s Demand Curve, Total Revenue, and Elasticity

Quantity

$9$8$7$6

$010 2 3 4 5 6 7 8 9

Price

$5$4$3$2$1

$9 x 0 = $0

Price Elasticity

$8 x 1 = $8$7 x 2 = $14

$6 x 3 = $18$5 x 4 = $20

$4 x 5 = $20$3 x 6 = $18

$2 x 7 = $14$1 x 8 = $8

$0 x 9 = $0

P X Q = TRe = 17.00

e = 5.00e = 2.60

e = 1.57e = 1.00

e = 0.64e = 0.38

e = 0.20e = 0.06

Here demand is inelastic so lower prices result in less revenue and higher prices result in more revenue

Here demand is elastic so lower prices result in more revenue and higher prices result in less revenue

Total revenue unchanged by price when demand is unitary elastic

• By tracing out the demand curve, one can follow how changes in price (through changes in quantity demanded) change total revenue collected.• By calculating the price elasticity of demand at different points along the demand curve, one can follow how and where total revenue is maximized.

Total Revenues and Demand Elasticity

Total Revenues and Demand Elasticity

$5$0

$9$8$7$6$5$4$3$2$1$0

$10 $15 $20Total Revenue

Price

(c) Price versus Total Revenue

20

$20

$15

$10

$5

$04 6 8 91 3 5 7

Quantity

Total Revenue

(d) Quantity versus Total Revenue

(a) The Firm’s Price, Quantity Sold, & Total Revenue

Price Quantity

Sold Total

Revenue

$9 0 $0x =

$8 1 $8x =

$7 2 $14 x =

$6 3 $18 x =

$5 4 $20 x =

$4 5 $20 x =

$3 6 $18 x =

$2 7 $14 x =

$1 8 $8 x =

$0 9 $0x =

Elasticity

17.00

5.00

2.60

1.57

1.00

.64

.38

.20

.06

• The firm maximizes its revenue at the price (or quantity) where demand is unitary elastic.

Total Revenue ismaximized somewherebetween $4 and $5 (where demand isunitary elastic).

Total Revenue ismaximized somewherebetween $4 and $5 (where demand isunitary elastic).

Total Revenue ismaximized somewherebetween 4 and 5 units (again, where demand is unitary elastic).

Total Revenue ismaximized somewherebetween 4 and 5 units (again, where demand is unitary elastic).

Price Elasticity of Demand and Total Expenditures

> 1 ==> an inverse relationship between price changes and total expenditures.

< 1 ==> a direct relationship between price changes and total expenditures.

= 1 ==> no change in total expenditures as price changes.

Total Revenue, Marginal Revenue, and Price Elasticity

Suppose P = a - bQ, then TR = aQ - bQ2

MR = dTR/dQ = a - 2bQ

Since = -(dQ/dP) x (P/Q)

= 1/b x (a - bQ)/Q

Quantity

Price

Quantity

Dollars

a

a/ba/2b

Total Revenue

Demand and MR

MR = P [ 1 - (1/)]

Marginal Revenue, Price and Price Elasticity

Determinants of Price Elasticity of Demand

Elasticity is greater when:there are more substitutes for the product.the product is a more important part of a

consumer’s budget.the time period under consideration is

greater.

6. Income Elasticity

Income elasticity indicates the responsiveness of the demand for a product to a change in income.

Income Elasticity

Income Elasticityof demand

=% Change in

quantity demanded% Change in Income

Income Elasticity of Demand

Income Elasticity of Demand: This is measure of the responsiveness of the demand for a good to changes in consumer income. It is measured by the percentage change in quantity demanded divided by the percentage change in buyer income

Normal Good: Positive income elasticity Inferior Good: Negative income elasticity

A normal good is any good with a positive income elasticity of demand.

Income Elasticity

As income expands, the demand for normal goods will rise.

Goods with a negative income elasticity are inferior goods. As income expands, the demand for

inferior goods will decline.

Income Elasticity

The percentage change in quantity demanded resulting from a 1 percent change in consumer income

Q x I

I Q

Cross Price Elasticity of Demand

Cross Price Elasticity of Demand: This is a measure of the responsiveness of the demand for a good to changes in the price of a related good. It is measured by the percentage change in the quantity demanded one one good (say, Coke) divided by the percentage change in the price of a related good (say, Pepsi)

C = {QX/QX}/{PY/PY}

Cross Elasticity

The percentage change in quantity demanded of good X resulting from a 1 percent change in the price of good Y

X,YQx x PY

Py Qx

Cross Price Elasticity of Demand (cont.)

Substitutes: Goods that have a positive cross price elasticity of demand are substitutes

Complements: Goods that have a negative cross price elasticity of demand are complements

Other Elasticities

Own Advertising Elasticity of Demand: Defines the percentage change in the consumption of a good that results from a given percentage change in the advertising expenditure on that good

Cross Advertising Elasticity of Demand: Measures the percentage change in the consumption of a good that results from a given percentage change in advertising for another good

Advertising Elasticity

The percentage change in quantity demanded resulting from a 1 percent change in advertising expenditure

Q x A

A Q

EXAMPLE

Q = 100 - .2Px + .5PY + .04I

px = -.2 (Px/Q) I = +.04 (I/Q)

pY = +.5 (PY/Q)

Point versus Arc Elasticities

Arc Elasticity of Demand: This measures the elasticity of demand when the changes being considered are discrete along, or an arc of, the demand curve

Point Price Elasticity of Demand: This measures the elasticity of demand when the the changes in price and quantity are infinitesimally small, at a point on the demand curve

Elasticity and Pricing

Since TR = MR x Q and TC = MC x Q, therefore = (MR-MC) x Q. If Max. is objective, If MR>MC, the firm can increase by selling

more (Q>0), and to do so, it must lower P If MR<MC, the firm can increase by selling

less (Q<0), and to do so, it must raise P If MR=MC, the firm cannot increase by

increasing or decreasing output=>P&Q are optimal

Elasticity and Pricing

Since MR = MC, then P (1-1/) = MC If the firm’s total variable costs are

directly proportional to output, so that MC=c, then the percentage contribution margin on additional units sold is the ratio of profit per unit to revenue per unit or PCM=(P-c)/P

Elasticity and Pricing (cont.)

Then,MR-MC>0 as >1/PCMMR-MC<0 as <1/PCMThis implies that

a firm should lower P whenever exceeds 1/PCM on the additional units it will sell by P

a firm should raise P whenever is lower than 1/PCM of the units it would not sell by P

The Value of Elasticities

Information on elasticities can be very useful to managers as they contemplate pricing decisions. If demand is inelastic at the current price, a price decrease will result in a decrease in total revenue, etc.

Elasticities are useful summary measures which impart information about the impact of variable changes on firm’s qty demanded

The Value of Elasticities (cont.)

By categorizing the relationship in terms of a single number, we are able to reduce a variety of relationships between products to a common denominator, such that we may rank the values of elasticity for comparison purposes, e.g. ranking products by the magnitude of their cross elasticities can tell us which are the strongest substitutes, etc.

The Value of Elasticities (cont.)

The income elasticity of demand of a firm’s product is an important determinant of the firm’s success during fluctuations in economic activity. Sellers of luxury items such as gourmet foods will find demand rise during booms and fall rapidly during recessions, while necessities will be stable

Knowledge of income elasticities can be used in targeting marketing efforts

The Value of Elasticities (cont.)

Information regarding cross elasticities can assist firms in assessing the impact of price changes among related goods on a particular product including its own related products

Cross elasticities are also useful in establishing boundaries between industries, such as in deciding antitrust cases. Goods with high cross elasticities are considered to be in the same market

Defining Economic Value

Understanding Value is key to developing effective pricing strategy

While in common usage, the term value refers to the total savings or satisfaction that a customer receives from the product, this is the use value, or what economists refer to as the utility gained from the product

What is crucial for developing pricing strategy is what marketers call economic value-to-the-customer or what economists call exchange value

Defining Economic Value(cont.)

Exchange value depends first and foremost on what alternatives the customer has

Total economic value is the maximum price that a “smart shopper”, fully informed about all market alternatives and seeking the best value, would pay.

A product’s “economic value” is the price of the consumer’s best alternative (called reference value) plus the value of whatever differentiates the product from the alternative (called the differentiation value)

Defining Economic Value(cont.)

Reference value is the cost (adjusted for differences in units) of the competing product that the customer views as the best alternative for the one being considered

Differentiation value is the value to the customer (both positive and negative) of any differences between the product being considered and the reference product

Economic Value Analysis

Economic value analysis is a analytical tool to determine the value that consumers place on a good in terms of their “maximum willingness-to-pay” and is very helpful to the manager wanting to set a price such that she/he can extract the maximum value from the consumer

It is an especially good sales tool when buyers are facing extreme cost pressures and are very price sensitive

Steps in Economic Value Analysis

Step 1: Review the cost of the competitive product or process that the customer views as the best alternative (Restate the cost of the alternative in terms of the units of the product for which you are calculating economic value. This is the products reference value)

Step 2: Identify all factors that differentiate your product from the competitive product or process in terms of superior(inferior) performance, better(poorer) reliability, additional(reduced) features,lower(higher) maint. costs, faster(slower) service, higher(lower)costs, etc

Steps in Economic Value Analysis(cont.)

Determine the value to the customer of these differentiating factors. Sources of value may be subjective(e.g., greater pleasure in consuming the product) or objective(e.g., cost savings, profit gains). These positive and negative values associated with the differentiating attributes comprise the differentiation value

Warning:Consider only the value of the difference between your product and alternative in terms of either costs saved to achieve a particular benefit or as extra benefits received for a given cost

Steps in Economic Value Analysis(cont.)

Step 4: Sum the reference value and the differentiation value to determine the total economic value, the value that someone would pay who was fully informed about all market alternatives and was economically rational when making the purchase decision

Step 5: Determine the selling price to extract the maximum value, recognizing that new products must usually be priced below economic value to induce adoption(see example in handout in binder)

Defining Value Added

Value added is the difference between the cost of the materials/inputs that the producer or service-provider and the value of the product or service when she/he sells it

Value added is a tool for understanding where economic value is created within a firm’s value chain

Value-added analysis determines the incremental profit that each of the activities of the firm creates

What Are Managers Worth? An Application of Value-Added Analysis

Management value added measures what managers add to the firm’s value. It is the difference between what they cost the firm and what they bring in to the firm

Management value added is that part of overall business value added that is not attributable to a business’s workers or shareholder capital

Business value added is equal to the firm’s total revenues minus all taxes and purchases

Shareholder value added is equal to the total value of shareholder capital multiplied by the cost of that capital

Management Value Added at Sony

Sales revenue $ 9.5 billion- Purchases and taxes - $ 8.5 billion

---------------------------------------------= Business value added $ 1.0 billion- Shareholder value added -$ 0.5 billion

- Operations costs -$ 0.3 billion- Management costs -$ 0.4 billion

----------------------------------------------= Management value added -$ 0.2 billion