Finance 30210: Managerial Economics

Competitive Pricing Techniques

Once production decisions have been made, a firm can be represented by it’s cost function

)(QTCTC

Total costs of production are a function of quantity produced

An increase in production from 55 to 56 increased total costs by $1.50

For pricing decisions, we focus on marginal cost

We will be assuming that pricing decisions are being made to maximize current period profits

Total Revenues equal price times quantity

Total Costs (note that total costs here are economic costs. That is, we have already included a reasonable rate of return on invested capital given the risk in the industry)

Profits

As with any economic decision, profit maximization involves evaluating every potential sale at the margin

How do my profits change if I increase my sales by 1?

How do my revenues change if I increase my sales by 1? (Marginal Revenues)

How do my costs change if I increase my sales by 1? (Marginal Costs)

As with any economic decision, profit maximization involves evaluating every potential sale at the margin

MR>MC: Profits are increasing

MR>MC: Profits are Decreasing

MR=MC: Profits are Maximized

Profit = Producer Surplus – Fixed Costs

Producer Surplus

Recall that in a perfectly competitive world, price equals marginal revenue

The market determines the equilibrium price

Market

Dollars

Demand

Supply

Dollars

Firm Level

The prevailing price (treated as a constant by each firm) becomes that firms marginal revenue

Producer Surplus

Recall the characteristics we laid out for a competitive market

#1: Many buyers and sellers – no individual buyer/firm has any real market power

#2: Homogeneous products – no variation in product across firms

#3: No barriers to entry – it’s costless for new firms to enter the marketplace

#4: Perfect information – prices and quality of products are assumed to be known to all producers/consumers

Can you think of situations where all these assumptions hold?

Market Structure Spectrum

Perfect Competition Monopoly

One Producer With 100% market share

The market is supplied by many producers – each with zero market share

Firm Level Demand DOES NOT equal industry demand

Firm Level Demand EQUALS industry demand

When making pricing decisions, you need to be aware of what your market structure is

Measuring Market Structure – Concentration Ratios

Suppose that we have the following three industries…

Industry A• 10 Firms in the

industry, each with an equal 10% market share

Industry B• 22 Firms in the

industry• The two largest

firms have 20% market share each

• The remaining 20 Firms have 3% market share each

Industry C• 8 Firms in the

industry• The 4 largest firms

have 15% market share each

• The remaining 4 Firms have 10% market share each

Which industry is the most competitive? Which is the least?

# of Firms

01 32 4 5 60 7 2210

Cumulative Market Share

Let’s plot out the three industries and take a look…

Concentration ratios look at the cumulative market share of the N largest firms

# of Firms

01 32 4 5 60 7 2210

2CR 4CR 8CR 10CR 22CR

Concentration Ratios in US manufacturing; 1947 - 1997

Year1947 17 23 30

1958 23 30 38

1967 25 33 42

1977 24 33 44

1987 25 33 43

1992 24 32 42

1997 24 32 40

100CR 200CR50CR

Aggregate manufacturing in the US hasn’t really changed since WWII

Industry CR(4)

Breakfast Cereals 83

Automobiles 80

Aircraft 80

Telephone Equipment 55

Women’s Footwear 50

Soft Drinks 47

Computers & Peripherals 37

Pharmaceuticals 32

Petroleum Refineries 28

Textile Mills 13

Concentration Ratios in US by Industry

Concentration ratios vary significantly by industry!!

Measuring Market Structure: The Herfindahl-Hirschman Index (HHI)

iisHHI

is = Market share of firm i

Rank Market Share

1 25 6252 25 6253 25 6254 5 255 5 256 5 257 5 258 5 25

HHI = 2,000

01 32 4 5 60 7 2010

AB HHI = 500

HHI = 1,000

The HHI index penalizes a small number of total firms

01 32 4 5 60 7 2010

HHI = 500HHI = 555

The HHI index also penalizes an unequal distribution of firms

# of Firms

01 32 4 5 60 7 2210

iisHHI

2is = Market share of firm i

10001010 2 HHI

980320202 22 HHI

1300104154 22 HHI

HHI Index in For Selected Industries

Industry HHIBreakfast Cereals 2446Automobiles 2862Aircraft 2562Telephone Equipment 1061Women’s Footwear 795Soft Drinks 800Computers & Peripherals 464Pharmaceuticals 446Petroleum Refineries 422Textile Mills 94

In a monopolized market, the single firm in the market faces the industry demand curve

Given the chosen quantity, industry demand determines price

Market

Dollars

Demand

Dollars

Individual

The single firm in the market has profit maximized based off of where MR = MC

Producer Surplus

In a world where firms have market power, they control their level of sales by setting their price. Suppose that you have the following demand curve (A relationship between price and quantity):

PQ 2100 Total Sales

Your listed price

60202100 Q

For example: If you were to set a price of $20, you can expect 60 sales

We could also talk about inverse demand (a relationship between quantity and price):

PQ 2100

210040

For example: If you wanted to make 40 sales, you could set a $30 price

QP 5.50 A price that will hit that target

Your target for sales

Either way, if we know price and total sales, we can calculate revenues

QP 5.50

Total Revenues =($30)(40) = $1200

Total Revenues = Price*Quantity

Can we increase revenues past $1200 and, if so, how?

Either way, if we know price and total sales, we can calculate revenues

QP 5.50

Turns out lowering price was the right thing to do to raise revenues.

50Q30Q

Total Revenues =($35)(30) = $1050

Total Revenues =($25)(50) = $1250

Initially, you have chosen a price (P) to charge and are making Q sales.

Total Revenues = PQ

Suppose that you want to increase your sales. What do you need to do?

Your demand curve will tell you how much you need to lower your price to reach one more customer

This area represents the revenues that you lose because you have to lower your price to existing customers

This area represents the revenues that you gain from attracting a new customerp

Your demand curve will tell you how much you need to lower your price to reach one more customer

Revenues =($30)(40) = $1200

50.29$p($.50)(40) =$20

($29.50)(1) =$29.50

$29.50 From additional sale- $20 loss from lowering price$9.50 increase in revenues

Revenues =($29.50)(41) = $1209.50

QP 5.50

An elasticity of demand that is greater than 1 in absolute value indicates that lowering price will increase revenues

50.29$P

Total Revenues =($29.50)(41) = $1209.5

Total Revenues =($30)(40) = $1200

% Change in revenues = .80%

QPTR %%%

7.1% P

5.2% Q

.80% -1.70% 2.5%

47.17.1

An elasticity of demand that is less than 1 in absolute value indicates that raising price will increase revenues

50.10$P

00.10$P25.

Total Revenues =($10)(80) = $800

Total Revenues =($10.50)(79) = $829.50

% Change in revenues = 3 .75%

QPTR %%%

25.1% Q

3.75% 5.00% -1.25%

25.0.525.1

10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90 95

Elasticity

1 9 17 25 33 41 49 57 65 73 81 89 970

Total Revenues

Revenues are maximized when the elasticity of demand equals -1

Max RevenuesQuantity = 50Price =$25Revenues = $1,250

Quantity = 50Price =$25Elasticity = -1

Elasticity is less than -1: raise price

Elasticity is greater than -1: lower price

0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90 95100

P = $30

MR = $9.50

Q = 40P = $30Revenues = ($30)(40) = $1200

Q = 41P = $29.50Revenues = ($29.50)(41) = $1209.50

Marginal Revenues = $9.50

Because you must lower your price to existing customers to attract new customers, marginal revenue will always be less than price

QP 5.50

QMR 50

25.50 QQPQTR

0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90 95100

P = $25

MR = MC = $0

Note that because we have ignored the cost side, we are assuming marginal costs are equal to zero!

Revenues = $1250

Now, let’s bring in the cost side. For simplicity, lets assume that you face a constant marginal cost equal to $20 per unit.

Quantity Price Total Revenue

Marginal Revenue

Total Cost

Marginal Cost

Profit

1 $49.50 $49.50 $49.50 $20 $20 $29.50

2 $49 $98 $48.50 $40 $20 $58

3 $48.50 $145.50 $47.50 $60 $20 $85.50

4 $48 $192 $46.50 $80 $20 $112

5 $47.50 $237.50 $45.50 $100 $20 $137.50

6 $47 $282 $44.50 $120 $20 $162

7 $46.50 $325.50 $43.50 $140 $20 $185.50

Continuing on down…

29 $35.50 $1029.50 $21.50 $580 $20 $449.50

30 $35 $1050 $20.50 $600 $20 $450

31 $34.50 $1069.50 $19.50 $620 $20 $449.50

1 5 9 13 17 21 25 29 33 37 41 45 49 53 57 61 65 69

Total Revenue Total CostProfit

Slope = 20

Profits = $450

A profit maximizing price sets marginal revenue equal to marginal cost. Marginal revenue is the change in total revenue (i.e. the slope)

1 5 9 13 17 21 25 29 33 37 41 45 49 53 57 61 65 69

Price Marginal CostMarginal Revenue

P = $35

Profit = ($35-$20)*30 = $450

Price = $35Quantity = 30Elasticity = -2.36

A profit maximizing price sets marginal revenue equal to marginal cost

QP 5.50

QMR 50

25.50 QQPQTR

MCQMR 205030Q

A profit maximizing strategy equates marginal revenues with marginal costs…

MCpQQP

Marginal Revenue

MCpppQ

Firm’s will be charging a markup over marginal cost where the markup is related to the elasticity of demand

1 5 9 13 17 21 25 29 33 37 41 45 49 53 57 61 65 69

Price Marginal CostMarginal Revenue

P = $35

Profit = ($35-$20)*30 = $450

Price = $35Quantity = 30Elasticity = -2.36

42.35$

20$35$

42.36.211

A profit maximizing price sets marginal revenue equal to marginal cost

This is not a coincidence. A monopoly sets a markup that is inversely proportional to the elasticity of demand!

Markups for Selected Industries

Industry LICommunication .972Paper & Allied Products .930Electric, Gas & Sanitary Services .921Food Products .880General Manufacturing .777Furniture .731Tobacco .638Apparel .444Motor Vehicles .433Machinery .300

Suppose that we assumed the automobile industry were monopolized…

433.PMCP

3.2433.1

So, a 1% increase in automobile prices will lower sales by 2.3%

MCp Perfectly competitive firms face demand curves that are perfectly elastic (infinite elasticity. Hence, the markup (and profits) are zero)

Firm Level

Industry

Note: Industry elasticities in competitive industries are always less than 1 (industry profits could be increased by raising price!)

Loss from charging existing customers a lower price

Gain from attracting new customers

Is it possible to attract new customers without lowering your price to everybody?

You need to be able to identify customer types and prevent resale!!

Dollars

40,000

Let’s suppose that Notre dame has identified three different consumer types for Notre Dame football tickets. Further, assume that Notre Dame has a marginal cost of $20 per ticket.

70,000 80,000

Alumni

Faculty

Students

If Notre Dame had to set one uniform price to everybody, what price would it set?

Dollars

40,000

Let’s suppose that Notre dame has identified three different consumer types for Notre Dame football tickets. Further, assume that Notre Dame has a marginal cost of $20 per ticket.

70,000 80,000

Alumni

Faculty

Students

Price Quantity Total Revenue

Total Cost Profit

$120 40,000 $4.8M $800,000 $4.0M

$80 70,000 $5.6M $1.4M $4.2M

$40 80,000 $3.2M $1.6M $1.6M

$20 MC

Dollars

40,000

Now, suppose that Notre Dame can set up differential pricing.

70,000 80,000

Alumni

Faculty

Students

Price Quantity Total Revenue

Total Cost Profit

$120 40,000 $4.8M $400,000 $4.4M

$80 30,000 $2.4M $300,000 $2.1M

$40 10,000 $400,000 $200,000 $200,000

Total 80,000 $7.6M $900,000 $6.7M

$20 MC

Pricing Schedule• Regular Price: $120• Faculty/Staff: $80• Student: $40

What would Notre Dame need to do to accomplish this?

Example: DVD codes are a digital rights management technique that allows film distributors to control content, release date, and price according to region.

DVD coding allows for distributors to price discriminate by region.

Suppose that you are the pricing for the DVD release of Avatar

Your marginal costs are constant at $4 and you have the following demand curves:

PQUS 25.9 PQE 25.6

US Sales

European Sales+

PQ 5.15 Total Sales

Here is what our aggregate demand looks like

QuantityD

$24PQUS 25.9

PQE 25.6

At a price above $24, Europeans aren’t buying. You only have the American market

At a price below $24, we now have both markets.

PQ 5.15

PQUS 25.9

Option #1: We could charge a common price to everyone…

QuantityD

QP 230

PQ 5.15 Solve for inverse demand

2230 QQPQTR

Calculate total revenues

MCQMR 4430

Equate marginal revenues to marginal costs

17$5.6

5.84$5.6417$ MC

Option #2: Why don’t we just charge them different prices?

QuantityD

4Quantity

4836436

43625.9

QMRQQTR

America Europe

$24$80,000

14$5.2

4824424

42425.6

QMRQQTR

Why is movie theatre popcorn so expensive?

Dollars

General Public

Senior Citizens

This would be an easy price discrimination problem…

Pricing Schedule• Regular Price: $15• Senior Citizens: $8

Now, suppose that the identities are unknown? How can the theatre extract more money out of the avid moviegoer?

Dollars

Avid Moviegoer

Occasional Moviegoer

Ticket Price Popcorn Price Total

Option #1 $14 $1 $15

Option #2 $8 $7 $15

Option #3 $2 $13 $15

As long as the total price (popcorn + ticket) is $15 or less, avid moviegoers will still go

Which pricing option would you choose?

PQ 100100

Suppose that Disneyworld knows something about the average consumer’s demand for amusement park rides. Disneyworld has a constant marginal cost of $.02 per ride

Dollars

Demand

Price (per ride) Quantity (rides)

$.99 1

$.98 2

$0 100

PQ 100100

As a first pass, we could solve for a profit maximizing price per ride

Dollars

Demand

Price (per ride)

Quantity (rides)

Total Revenues

MarginalRevenues

Marginal Cost

$1 0 $0

$.99 1 $.99 $.99 $.02

$.98 2 $1.96 $.97 $.02

$.52 48 $24.96 $.05 $.02

$.51 49 $24.99 $.03 $.02

$.50 50 $25 $.01 $.02MC

Profit = $24.01

PQ 100100

If all Disney does is charge a price per ride, they are leaving some money on the table

Dollars

Demand

Profit = $24.01

$1CS = (1/2)($1-.51)*49 = $12.00

We are charging this person $24.01 for 49 rides when they would’ve $36.01!

PQ 100100

Like the movie theatre, Disney has two prices to play with. We have a price per ride as well as an entry fee. For any price per ride, we can set the entry fee equal to the consumer surplus generated.

Dollars

Demand

Profit = (P-.02)*Q

$1 Fee = (1/2)($1-P)*Q

Price (per ride)

Quantity (rides)

Ride Revenue

Fee Revenue

Total Revenues

MarginalRevenues

Marginal Cost

$1 0 $0 $0 $0 --- ---

$.99 1 $.99 $.005 $.995 $.995 $.02

$.98 2 $1.96 $.02 $1.98 $.985 $.02

$.03 97 $2.91 $47.05 $49.96 $.03 $.02

$.02 98 $1.96 $48.02 $49.98 $.02 $.02

$.01 99 $.99 $49 $49.99 $.01 $.02

Total Profit = $48.02

We are still looking to where marginal revenues equal marginal costs.

PQ 100100

The optimal pricing scheme here is to set a price per ride equal to marginal cost. We then set the entry fee equal to the consumer surplus generated.

Dollars

Demand

$1 Fee = (1/2)($1-.02)*98 = $48.02

Total Profit = $48.02

Pricing Schedule• Entry Fee: $48.02• Price Per Ride: $.02

Or, we could combine the two

Entry Fee: $48.02+ Ride Charges: $1.9698 Ride Package = $49.98Ride Revenue = .02*98 = $1.96

Dollars

Demand

Profit = $24.01

Now, suppose that we introduced two different clientele. Say, senior citizens and Non-seniors. We could discriminate based on price per ride (assume there is one of each type)

PQ 100100 Non-Seniors

Dollars

Demand

Profit = $15.21

PQ 10080 Seniors

Total Profit = $24.01 + $15.21 = $39.22

Alternatively, you set the cost of the rides at their marginal cost ($.02) for everybody and discriminate on the entry fee.

Entry Fee =$48.02 Young

$30.42 OldP = $.02/Ride

Dollars

Demand

Total Profit = $48.02 + $30.42 = $78.44

Fee = (1/2)($1-.02)*98 = $48.02 Fee = (1/2)($.80-.02)*78 = $30.42

Ride Revenue = .02*98 = $1.96 Ride Revenue = .02*78 = $1.56

PQ 10080 Seniors

Or, you could establish different package prices.

Pricing Schedule=Regular Admission (98 rides): $49.98

Senior Citizen Special (78 Rides): $31.98

Dollars

Demand

Total Price = $48.02 + $1.96 = $49.98

Fee = (1/2)($1-.02)*98 = $48.02 Fee = (1/2)($.80-.02)*78 = $30.42

Total Price = $30.42 + $1.56 = $31.98

PQ 10080 Seniors

Suppose that you couldn’t distinguish High value customers from low value customers: Would this work?

Dollars

Demand

$.80Fee = (1/2)($1-.02)*98 = $48.02 Fee = (1/2)($.80-.02)*78 = $30.42

PQ 10080 PQ 100100

Pricing Schedule=Regular Admission (98 rides): $49.98

“Early Bird” Special (78 Rides): $31.98

We know that is the high value consumer buys 98 ticket package, all her surplus is extracted by the amusement park. How about if she buys the 78 Ride package?

$30.42

$17.16

If the high value customer buys the 78 ride package, she keeps $15.60 of her surplus!

78 Ride Coupons: $31.98

Total Willingness to pay for 78 Rides: $47.58

$15.60

PQ 100100

You need to set a price for the 98 ride package that is incentive compatible. That is, you need to set a price that the high value customer will self select. (i.e., a package that generates $15.60 of surplus)

$48.02

Total Willingness = $49.98 - Required Surplus = $15.60

Package Price = $34.38

78 Ride Coupons: $31.9898 Ride Coupons: $34.38

84.62$17602$.38.34$98.31$

Bundling

Suppose that you are selling two products. Marginal costs for these products are $100 (Product 1) and $150 (Product 2). You have 4 potential consumers that will either buy one unit or none of each product (they buy if the price is below their reservation value)

Consumer Product 1 Product 2 Sum

A $50 $450 $500

B $250 $275 $525

C $300 $220 $520

D $450 $50 $500

If you sold each of these products separately, you would choose prices as follows

P Q TR Profit

$450 1 $450 $350

$300 2 $600 $400

$250 3 $750 $450

$50 4 $200 -$200

P Q TR Profit

$450 1 $450 $300

$275 2 $550 $250

$220 3 $660 $210

$50 4 $200 -$400

Product 1 (MC = $100) Product 2 (MC = $150)

Profits = $450 + $300 = $750

A $50 $450 $500

B $250 $275 $525

C $300 $220 $520

D $450 $50 $500

Pure Bundling does not allow the products to be sold separately

Product 2 (MC = $150)

With a bundled price of $500, all four consumers buy both goods:

Profits = 4($500 -$100 - $150) = $1,000

A $50 $450 $500

B $250 $275 $525

C $300 $220 $520

D $450 $50 $500

Mixed Bundling allows the products to be sold separately

Price 1 = $250Price 2 = $450Bundle = $500

Consumer A: Buys Product 2 (Profit = $300) or Bundle (Profit = $250)Consumer B: Buys Bundle (Profit = $250)Consumer C: Buys Product 1 (Profit = $150)Consumer D: Buys Only Product 1 (Profit = $150)

Profit = $850

or $800

A $50 $450 $500

B $250 $275 $525

C $300 $220 $520

D $450 $50 $500

Mixed Bundling allows the products to be sold separately

Price 1 = $450Price 2 = $450Bundle = $520

Consumer A: Buys Only Product 2 (Profit = $300)Consumer B: Buys Bundle (Profit = $270)Consumer C: Buys Bundle (Profit = $270)Consumer D: Buys Only Product 1 (Profit = $350)

Profit = $1,190

A $300 $200 $500

B $300 $200 $500

C $300 $200 $500

D $300 $200 $500

Bundling is only Useful When there is variation over individual consumers with respect to the individual goods, but little variation with respect to the sum!?

Individually Priced: P1 = $300, P2 = $200, Profit = $1,000

Pure Bundling: PB = $500, Profit = $1,000

Mixed Bundling: P1 = $300, P2 = $200, PB = $500, Profit = $1,000

Suppose that you sell laser printers. To create printed pages, you need both a printer and an ink cartridge. For now, assume that the toner cartridges are sold in a competitive market and sell for $2 each. An ink cartridge is good for 1,000 printed pages.

Dollars

Demand

Quantity of printed pages (000s)

Toner cartridge price

You can set the price of the printer equal to the customer’s consumer surplus ?

CS = ½*($16 - $2)(14) = $98

Now, suppose that you design a printer that requires a special cartridge that only you produce. What would you do if you could choose a printer price and a cartridge price?

Dollars

Demand

CS = ½*($9 - $2)(7) = $24.50

Q P TR TC MR MC Profit

1 $15 $15 $2 $15 $2 $13

2 $14 $28 $4 $13 $2 $24

3 $13 $39 $6 $11 $2 $33

4 $12 $48 $8 $9 $2 $40

5 $11 $55 $10 $7 $2 $45

6 $10 $60 $12 $5 $2 $48

7 $9 $63 $14 $3 $2 $49

8 $8 $64 $16 $1 $2 $48

We could make our money on the cartridges and sell the printers cheap…

Profit = $49 + $24.50 = $73.50

Alternatively, we could do something like the amusement park. We maximize profits combining cartridge revenue AND printer revenue

Dollars

Demand

CS = ½*($16 - $2)(14) = $98

Q P TR CS Total TC MR MC Profit

1 $15 $15 $.5 $15.5 $2 $15.5 $2 $13.5

2 $14 $28 $2 $30 $4 $14.5 $2 $26

3 $13 $39 $4.5 $43.5 $6 $13.5 $2 $37.5

4 $12 $48 $8 $56 $8 $12.5 $2 $48

5 $11 $55 $12.5 $67.5 $10 $11.5 $2 $57.5

13 $3 $39 $84.5 $123.5 $26 $3.5 $2 $97.5

14 $2 $28 $98 $126 $28 $2.5 $2 $98

15 $1 $15 $112.5 $127.5 $30 $1.50 $2 $97.5

We are back to a low cartridge price and a high printer price

Now, suppose that you have two customers. Call them high value and low value. Suppose that you can easily identify them and prevent resale. We could discriminate on both the printer price and the cartridge price.

Dollars

Demand

$16CS = ½*($16 - $9)(7) = $24.50

Dollars

Demand

$12CS = ½*($12 - $2)(5) = $12.50

PQ 12PQ 16

Profit = ($9-$2)7 +$24.50 = $73.50 Profit = ($7-$2)5 +$12.50 = $37.50

Total Profit = $111

Alternatively, we could essentially give the cartridges away and discriminate on the printer (like Disneyworld).

Dollars

Demand

$16CS = ½*($16 - $2)(14) = $98

Dollars

Demand

$12CS = ½*($12 - $2)(10) = $50

PQ 12PQ 16

Profit = $98 Profit $50

Total Profit = $148

Suppose that you couldn’t explicitly price discriminate. Let’s say that you know you have a high value and low value demander, but you don’t know who is who. Let’s first try and do this like the amusement park

Dollars

Demand

$16CS = ½*($16 - $2)(14) = $98

Dollars

Demand

$12CS = ½*($12 - $2)(10) = $50

14 Cartridge Package = $98 + $2*14 = $126

10 Cartridge Package = $50 + $2*10 = $70

We need to choose packages so that each demander chooses the “correct” package

Dollars

Demand

$16CS = ½*($16 - $9)(10) = $50

- 10 Cartridge Package = $70

Total Willingness to Pay = $110

Consumer Surplus = $40

14 Cartridge Package = $126

- required consumer surplus = $40

“Discounted Price” = $86

14 Cartridge Package = $8610 Cartridge Package = $70

Profit = $86 + $70 - $2*24 = $108

Let’s try a different strategy. Suppose that you charge a markup on the cartridges and then charge a common price for the printer to each. We would set the price of the printer equal to the consumer surplus of the lower value demander of insure that both groups buy the printer.

Dollars

Demand

$12CS = ½*($12 - $P)(12-P)

PQ 12 Example: Cartridge Price: $3Consumer Surplus = ½*($12 - $3)(9) = $40.50

Charge $40.50 for the printer (Both customers will buy)

Low value customers buy 9 cartridges

High Value customers buy 13 cartridges

Profit = 2*$40.50 + ($3-$2)(21) = $103

We need to find the best cartridge price…

Price Quantity 1 Quantity 2 Total Revenue

Consumer Surplus

Printer Revenue

Total Revenue Total Cost Profit

$0 16 12 $0 $72 $144 $144 $56 $88

$.25 15.75 11.75 $6.875 $69.03 $138.06 $144.93 $55 $89.93

$.50 15.5 11.5 $13.50 $66.135 $132.25 $145.75 $54 $91.75

$3 13 9 $66 $40.5 $81 $147 $44 $103

$4 12 8 $80 $32 $64 $144 $40 $104

$4.25 11.75 7.75 $82.875 $30.03 $60.06 $142.93 $39 $103.93

PQ 16PQ 12

21 QQP

2125. QP CS*2 212$ QQ

Let’s try a different strategy. Suppose that you charge a market on the cartridges and then charge a common price for the printer to each. We would set the price of the printer equal to the consumer surplus of the lower value demander of insure that both groups buy the printer.

Dollars

Demand

$12CS = ½*($12 - $4)(8) = $32

PQ 12 Best Choice:

Charge $32 for the printer (Both customers will buy)

Charge $4 for cartridgesLow value customers buy 8

cartridges (Pay $64 total)High Value customers buy 12

cartridges (Pay $80 total)

Profit = 2*$32 + ($4-$2)(20) = $104

One last example. Consider the market for hot dogs. Most people require a bun for each hot dog they eat (with the exception of the Atkins diet people!)

BH PPQ 12

Price of a Hot Dog Price of a Hot Dog Bun

Hot Dogs and Buns are made by separate companies – each has a monopoly in its own industry. For simplicity, assume that the marginal cost of production for each equals zero.

For simplicity I will assume that marginal costs are zero (i.e. we are maximizing revenues)

PPQ H 102$12

Suppose that you knew that the buns were selling for $2, what should you charge?

Quantity Price Total Revenue Marginal Revenue

1 $9 $9 $9

2 $8 $16 $7

3 $7 $21 $5

4 $6 $24 $3

5 $5 $25 $1

6 $4 $24 -$1

You charge $5

But, if the bun guy sees you charging $5, he needs to react to that…

PPQ B 75$12

1 $6 $6 $6

2 $5 $10 $4

3 $4 $12 $2

4 $3 $12 $0

5 $2 $10 -$2

6 $1 $6 -$4

Bun Guy charge $4

But, if the bun guy is charging $4, you need to react to that…

PPQ B 84$12

1 $7 $7 $7

2 $6 $12 $5

3 $5 $15 $3

4 $4 $16 $1

5 $3 $15 -$1

6 $2 $12 -$3

You charge $4

Each firm must price their own product based on their expectation of the other firm

BHB QPP 12Bun Company Hot Dog Company

HBH QPP 12

0212 BH QPMR 0212 HB QPMR

Complementary Goods

Each firm must price their own product based on their expectation of the other firm

Bun Company Hot Dog Company

Substitute these quantities back into the demand curve to get the associated prices. This gives us each firm’s reaction function.

Complementary Goods

Any equilibrium with the two firms must have each of them acting optimally in response to the other.

$6 $12

Bun Company

Hot Dog Company

Now, suppose that these companies merged into one monopoly

PPPQ HB 1212

Quantity Combined Price

Total Revenue Marginal Revenue

1 $11 $11 $11

2 $10 $20 $9

3 $9 $27 $7

4 $8 $32 $5

5 $7 $35 -$3

6 $6 $36 $1

7 $5 $35 -$1

8 $4 $32 -$3

9 $3 $27 -$5

You charge $6 for hot dog/bun

Now, suppose that these companies merged into one monopoly

QPP BH 12

0212 QMR

BH PPQ

Complementary Goods

HB PPQ 12

Look at what happened here…

Separate Hot Dog/Bun Suppliers

Consumer Pays $8 for a hot dog/bun pair

Single Hot Dog/Bun Suppliers

6$ BH PP

Consumer Pays $6 for a hot dog/bun pair

Eliminating a company benefits consumers!!!

Example: Microsoft vs. Netscape

The argument against Microsoft was using its monopoly power in the operating system market to force its way into the browser market by “bundling” Internet Explorer with Windows 95.

To prove its claim, the government needed to show:• Microsoft did, in fact, possess monopoly power• The browser and the operating system were, in fact, two distinct

products that did not need to be integrated• Microsoft’s behavior was an abuse of power that hurt

consumers

What should Microsoft’s defense be?

Spatial Competition – Location Preferences

When you purchase a product, you pay more than just the dollar cost. The total purchase cost is called your opportunity cost

Consider two customers shopping for wine. One lives close to the store while the other lives far away.

20 miles

2 miles

The opportunity cost is higher for the consumer that is further away. Therefore, if both customers have the same demand for wine, the distant customer would require a lower price.

Spatial Competition – Location Preferences

Starbucks currently has 12,937 locations in the US

Gucci currently has 31 locations in the US

How can we explain this difference?

Consider a market with N identical consumers. Each has a demand given by

otherwise

,0 if ,1

We must include their travel time in the total price they pay for the product. The firm can’t distinguish consumers and, hence, can’t price discriminate.

txpp ~

Dollar Price

Distance to Store

Travel Costs

There is one street of length one. Suppose that you build one store in the middle. For simplicity, assume that MC = 0

X = 1/2 X = 1/2

With a price

Vtxp ~ This is the “marginal customer”

p~ What fraction of the market will you capture?

To capture the whole market, set x = 1/2 2

Now, suppose you build two stores…

X = 1/4 X = 1/4

With a price

X = 1/4 X = 1/4

Now, suppose you build three stores…

X = 1/6 X = 1/6

With a price

X = 1/6 X = 1/6 X = 1/6X = 1/6

Do you see the pattern??

With ‘n’ stores, the price you can charge is

nFntVN

2~ As n gets arbitrarily large, p

approaches V

Further, profits are equal to

Total Sales PriceTotal Costs

n 2max

Maximizing Profits

Number of locations is based on: • Size of the market (N)• Fixed costs of establishing a new location (F)• “Moving Costs” (t)

Horizontal Differentiation

Baskin Robbins has 31 Flavors…how did they decide on 31?

t = Consumer “Pickiness”N = Market sizeF = R&D costs of finding a new flavor

Finance 30210: Managerial Economics

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