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Economics of the Firm
Competitive Pricing Techniques
Every business has a goal. What’s the goal of your business?
“To Make Money!!!”
Maximize Profits
Increase Market Share
Maximize Shareholder Value
Maximize return on investment
To be a leader in technology
To be “Green”
Optimal decision making (for example, pricing) depends crucially on what your goal is!
TCPQ
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)
TCPQ
Lets take this piece by piece
We will treat costs as a given. Every firm has a total cost function.
Q
TC
)(QTCTC
Total costs of production are a function of quantity produced
$300
56
TC For pricing decisions, we focus on marginal cost
101
10
Q
TCMC
57
$310
1Q
10TC
Q
P
Q
P
For every price I could charge, my demand curve tells me what my sales will be.
)(PQQ
For any sales goal that I set, my demand curve will tell me what price I can charge to obtain that goal
)(QPP
D
Next, we need to know something about the consumer the firm faces. Every firm should have an estimated demand curve. We can think about a demand curve in one of two ways
So, we can get firm revenues one of two ways:
I select a sales target
My demand curve will tell me the sales I will achieve at that target
TQ )( TQPP
Revenues equal price times quantity
TPQTR
I select a price target
My demand curve will tell me the price I can charge to hit that target
TP )( TPQQ
Revenues equal price times quantity
QPTR T
In either case, higher sales will be associated with a lower price
TPQTR QPTR T
If I want to increase my sales target, I need to lower my price to all my existing customers
OR
I need to drop my target price if I want to reach new customers
Q
p
Q
p
D
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?
Q
p
Q
p
D
Your demand curve will tell you how much you need to lower your price to reach one more customer
Q
P
Q
p
1
P
This area represents the revenues
that you lose because you have to lower your price to existing customers
pThis area represents the revenues that you gain from attracting a new customer
pQQ
PMR
If we are maximizing profits, we want marginal revenues to equal marginal costs:
MCpQQ
P
MCMR
MCpPP
Q
Q
P
1
1MC
pMCpp
Firm’s will be charging a markup over marginal cost where the markup is related to the elasticity of demand
Market Structure Spectrum
Perfect Competition Monopoly
One Producer Supplies the entire Market
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
QTC 10
PQ 2100
Suppose there is a monopolist that faces the following demand
Further, the monopoly has a linear cost function
Q
p
D
$40
20
60020102040
Can this firm do better?
PQ 2100
First, to increase sales by one, by how much does this firm have to lower it’s price?
Q
p
D
$40
20
QP 5.50 A $0.50 price drop would increase sales by one
21
$39.50
-$.50*20 = -$10 Again, this is a loss because we lowered our price to our existing customers!
(1)($39.50) The additional sale!
MR = $29.50MC = $10
We should lower price!
p
D
QMR = 50-Q
MC=$10
40
30
QP 5.50
MCpQQ
P
30
40
1050
105.505.
P
Q
Q
QP 5.50
QTC 10
10
80040104030
p
D
Q
MC=$10
40
30
10
QP 5.50 Let’s check…
$30.50
$29.50
4139
50.79939103950.30
50.79941104150.29
p
D
QMR
MC
40
30
PQ 2100
5.140
302
Q
P
P
Q
10 30
5.11
1
10
p
The markup formula works!
Now, suppose this market is serviced by a large number of identical firms – each with marginal costs equal to $10
iQ
iP
Q
P
D
DP~
PQ 2100
Industry Firm Level
Lowest price among firm i’s competitorsTCQP ~
iQ
Is it possible for
iQ
iP
Q
P
D
DP~
PQ 2100
Industry Firm Level
iQ
MCP ~
$10
Profit > 0
As long as price is above marginal cost, there is an incentive for each firm to undercut its rivals. This incentive disappears when price equals marginal cost.
Competitive Market equilibrium
iQ
iP
Q
P
D
D10$~ P
PQ 2100
Industry Firm Level
iQ
Profit = 0
As long as price is above marginal cost, there is an incentive for each firm to undercut its rivals. This incentive disappears when price equals marginal cost.
S
80
$10
1
1
MCp Perfectly competitive firms face demand curves that
are perfectly elastic (infinite elasticity. Hence, the markup (and profits) are zero)
i
iQ
iP
D
Firm Level
iQ
10$
Q
10$
p
D
MC
80
Industry
25.
Note: Industry elasticities in competitive industries are always less than 1 (industry profits could be increased by raising price!)
Measuring Market Structure – Concentration Ratios
Suppose that we take all the firms in an industry and raked them by size. Then calculate the cumulative market share of the n largest firms.
Size Rank
Cumulative Market Share
100
80
40
20
01 32 4 5 60 7 2010
A
BC
Measuring Market Structure – Concentration Ratios
Size Rank
Cumulative Market Share
100
80
40
20
01 32 4 5 60 7 2010
A
B
C
4CR Measures the cumulative market share of the top four firms
Concentration Ratios in US manufacturing; 1947 - 1997
Year
1947 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
Measuring Market Structure: The Herfindahl-Hirschman Index (HHI)
N
iisHHI
1
2
is = Market share of firm i
Rank Market Share
1 25 625
2 25 625
3 25 625
4 5 25
5 5 25
6 5 25
7 5 25
8 5 25
2is
HHI = 2,000
Cumulative Market Share
100
80
40
20
01 32 4 5 60 7 2010
A
B HHI = 500
HHI = 1,000
The HHI index penalizes a small number of total firms
Cumulative Market Share
100
80
40
20
01 32 4 5 60 7 2010
A
B
HHI = 500HHI = 555
The HHI index also penalizes an unequal distribution of firms
Concentration Ratios in For Selected Industries
Industry CR(4) HHI
Breakfast Cereals 83 2446
Automobiles 80 2862
Aircraft 80 2562
Telephone Equipment 55 1061
Women’s Footwear 50 795
Soft Drinks 47 800
Computers & Peripherals 37 464
Pharmaceuticals 32 446
Petroleum Refineries 28 422
Textile Mills 13 94
Another way to measure competition is by the outcome.
P
MCPLI
The Lerner index measures the percentage of a
product’s price that is due to the markup
Perfect Competition Monopoly
MCp
0LI
1
1
MCp
1
LI
Lerner index in For Selected Industries
Industry LI
Communication .972
Paper & Allied Products .930
Electric, Gas & Sanitary Services .921
Food Products .880
General Manufacturing .777
Furniture .731
Tobacco .638
Apparel .444
Motor Vehicles .433
Machinery .300
P
MCPLI
An industry’s cost structure will influence an industry’s competitive nature
Q
Costs
MC
AC
If market size is small, this industry experiences decreasing costs (big firms have an advantage over small firms)
However, if the industry gets big enough, costs start to increase and the size advantage becomes a disadvantage!
Costs
MC
AC
Costs
MCAC
Industries with globally scale economies tend to develop as natural monopolies (the market should – and will – be serviced by one producer). This can happen if production exhibits increasing marginal productivity, or if there are large fixed costs.
Monopoly Market Characteristics
Small market size
Scale economies (Network Externalities, Learning by Doing, Large Fixed Costs)
Government Policy (Protected Monopolies)
Any one of these characteristics suggest that the market structure could be monopolistic.
Long Run Industry Dynamics
As an industry ages, three things happen….
Q
p
D
Short Run
Q
p
D
Long Run
25. 5.1
As more alternatives become available, consumer demand becomes much more price responsive
Long Run Industry Dynamics
As an industry ages, three things happen….
Q
pMC
Short Run
Q
p
MC
Long Run
As production techniques become more flexible, marginal costs drop and become much less sensitive to input prices
Long Run Industry Dynamics
As an industry ages, three things happen….
Market Structure Spectrum
Perfect Competition (Long Run)
Monopoly (Short Run)
As new firms enter the industry (i.e. no artificial or natural barriers), the industry becomes more competitive and markups fall
Most firms face the a downward sloping market demand and therefore must lower its price to increase sales.
Q
p
Q
p
D
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?
Price Discrimination
Q
p
D
$15
$12
20 21
If this monopolist could lower its price to the 21st customer while continuing to charge the 20th customer $15, it could increase profits.
Requirements:
Identification
No Arbitrage
Price Discrimination (Group Pricing)
Suppose that you are the publisher for JK Rowling’s newest book “Harry Potter and the Deathly Hallows”
Your marginal costs are constant at $4 per book and you have the following demand curves:
PQUS 25.9
PQE 25.6
US Sales
European Sales
PQUS 25.9
QD
$36
p
9Q
D
$24
p
6Q
D
$36
p
15
$24
3
European MarketUS Market Worldwide
PQE 25.6
24 ,5.15
24 ,25.9
PP
PPQ
$24
3
If you don’t have the ability to sell at different prices to the two markets, then we need to aggregate these demands into a world demand.
42 ,5.15
24 ,25.9
PP
PPQ
3Q ,230
3Q ,436
Q
QP
Q
$36
p
15
$24
3
$12
3Q ,430
3Q ,836
Q
QMR
$18
DMR
Q
$36
p
153
43Q ,430
3Q ,836MC
Q
QMR
DMR
MC
17$P
6.5
$17
5.6Q
5.84$5.64$5.617$
$4
If you can distinguish between the two markets (and resale is not a problem), then you can treat them separately.
PQUS 25.9
D
p
9
US Market
USUS QP 436
MCQMR USUS 4836
20$
4
P
QMC
MR
4
$20
If you can distinguish between the two markets (and resale is not a problem), then you can treat them separately.
EE PQ 25.6
D
p
6
European Market
EE QP 424
MCQMR EE 4824
14$
5.2
P
QMC
MR
2.5
$14
D
p
9
MC
MR
4
D
p
6
MC
MR
2.5
$14
European Market
US Market
Price Discrimination (Group Pricing)
89$5.64$)5.2(14$420$
$20
Suppose you operate an amusement park. You know that you face two types of customers (Young and Old). You have estimated their demands as follows:
Oo PQ 80
YY PQ 100
Old
Young
You have a a constant marginal cost of $2 per ride
Can you distinguish low demanders from high demanders?
Can you prevent resale?
D
p
49
D
p
39
$41
OldYoung
$51
$100
$80
Oo PQ 80YY PQ 100
If you could distinguish each group and prevent resale, you could charge different prices
02Q ,5.90
20Q ,100
Q
QP
Q
$100
p
180
$80
20
$60
02Q ,90
02Q ,2100
Q
QMR
$70
DMR
First, lets calculate a uniform price for both consumers
90
Two Part Pricing
Q
$100
p
180
DMR
MC
46$P
88
$46
88Q
$2
202Q ,90
02Q ,2100MC
Q
QMR
D
p
54
D
p
34
$46
OldYoung
First, you set a price for everyone equal to $46. Young people choose 54 rides while old people choose 34 rides.
$46
$100
$80
Can we do better than this?
Q Q
Q
p
D
Note that young consumer was willing to pay exactly $46 for the 54th ride. However, she was willing to pay more than $46 for all the previous rides. We call this consumer surplus.
YY PQ 100
$46
54
$55
45
This consumer would have paid up to $55 for the 45th ride. If the going market price was $46, consumer surplus for the 45th ride would have been $9.
D
p
54
$46
$100
The young person paid a total of $2,484 for the 54 rides. However, this consumer was willing to pay $3942.
YY PQ 100
458,1$46$100$)54)(2/1( YCS
$2,484
$1,458
484,2$5446$ Sales
942,3$
How can we extract this extra money?
Q
D
p
54
D
p
34
$46
OldYoung
Two Part pricing involves setting an “entry fee” as well as a per unit price. In this case, you could set a common per ride fee of $46, but then extract any remaining surplus from the consumers by setting the following entry fees.
$46
$100
$80$1458
$578
Entry Fee =$1458 Young
$578 Old
Could you do better than this?
P = $46/Ride
$2484 $1564
Q Q
D
p
98
D
p
78
$2
OldYoung
Suppose that you set the cost of the rides at their marginal cost ($2). Both old and young people would use more rides and, hence, have even more surplus to extract via the fee.
$2
$100
$80$4802
$3042
Entry Fee =$4802 Young
$3042 OldP = $2/Ride
Q Q
D
p
98
D
p
78
$2
OldYoung
$2
$100
$80$4802
$3042
Block Pricing involves offering “packages”. For example:
“Geezer Pleaser”: Entry + 78 Ride Coupons (1 coupon per ride): $3198
“Standard” Admission: Entry + 98 Ride Coupons (1 coupon per ride): $4998
$2(98) = $196 $2(78) = $156
($4802 +$196)
($3042 +$156)
Suppose that you couldn’t distinguish High value customers from low value customers: Would this work?
1 Ticket Per Ride78 Ride Coupons: $3198
98 Ride Coupons: $4998
D
p
98
D
p
78
$2
OldYoung
$2
$100
$80$4802
$3042
$2(98) = $196 $2(78) = $156
p
78
$22
$100
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?
$3042
$1716
If the high value customer buys the 78 ride package, she keeps $1560 of her surplus!
78 Ride Coupons: $3198
Total Willingness to pay for 78 Rides: $4758
$1560
-
YY PQ 100
D
p
98
$2
$100
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 $1560 of surplus)
$196
$4802
Total Willingness = $4,998
- Required Surplus = $1,560
Package Price = $3,438
q
This is known as Menu Pricing
1 Ticket Per Ride78 Ride: $3198 ($41/Ride)
98 Rides: $3438 ($35/Ride)
Menu Pricing: You can’t distinguish high demand from low demand (2nd Degree Price Discrimination)
Block Pricing: You can distinguish high demand and low demand (1st Degree Price Discrimination)
1 Ticket Per Ride78 Ride: $3198 ( $41/Ride)
98 Rides: $4998 ( $51/Ride)
Group Pricing: You can distinguish high demand from low demand (3rd Degree Price Discrimination)
No Entry FeeLow Demanders: $41/Ride
High Demanders: $51/Ride
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
Consumer Product 1 Product 2 Sum
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)
Product 1 (MC = $100)
With a bundled price of $500, all four consumers buy both goods:
Profits = 4($500 -$100 - $150) = $1,000
Consumer Product 1 Product 2 Sum
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
Product 1 (MC = $100)
Product 2 (MC = $150)
Price 1 = $250
Price 2 = $450
Bundle = $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
Consumer Product 1 Product 2 Sum
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
Product 1 (MC = $100)
Product 2 (MC = $150)
Price 1 = $450
Price 2 = $450
Bundle = $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
Consumer Product 1 Product 2 Sum
A $300 $200 $500
B $300 $200 $500
C $300 $200 $500
D $300 $200 $500
Product 1 (MC = $100)
Product 2 (MC = $150)
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
Tie-in Sales
Suppose that you are the producer of laser printers. You face two types of demanders (high and low). You can’t distinguish high from low.
D
p
12
D
p
16
$12
$16PQ 12 PQ 16
You have a monopoly in the printer market, but the toner cartridge market is perfectly competitive. The price of cartridges is $2 (equal to MC) – a toner cartridge is good for 1,000 printed pages.
Quantity of printed pages (in thousands)
Price for 1,000 printed pages
Tie-in Sales
You have already built 1,000 printers (the production cost is sunk and can be ignored). You are planning on leasing the printers. What price should you charge?
D
p
12
D
p
16
$12
$16
PQ 12 PQ 16
QQ10
$2$2
14
$50$98
A monthly fee of $50 will allow you to sell to both consumers. Can you do better than this? Profit = $50*1000 = $50,000
Tie-in Sales
Suppose that you started producing toner cartridges and insisted that your lessees used your cartridges. Your marginal cost for the cartridges is also $2. How would you set up your pricing schedule?
D
p
$12
Qcp
cp12
2125. cP 2122 cc pQp
4$cp
cp228 (Aggregate Demand)
Tie-in Sales
D
p
12
D
p
16
$12
$16
PQ 12 PQ 16
QQ8
$4$4
12
$32$72
By forcing tie-in sales. You can charge $4 per cartridge and then a monthly fee of $32.
Profit = ($4 - $2)*(8 + 12) + 2($32) = $104*500 = $52,000
Complementary Goods
Suppose that the demand for Hot Dogs is given as follows:
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.
Each firm must price their own product based on their expectation of the other firm
BHB QPP 12
Bun Company Hot Dog Company
HBH QPP 12
0212 BH QPMR 0212 HB QPMR
2
12 HB
PQ
2
12 BH
PQ
Complementary Goods
Each firm must price their own product based on their expectation of the other firm
Bun Company Hot Dog Company
2
12 HB
PQ
2
12 BH
PQ
Substitute these quantities back into the demand curve to get the associated prices. This gives us each firm’s reaction function.
2
12 HB
PP
2
12 BH
PP
Complementary Goods
Any equilibrium with the two firms must have each of them acting optimally in response to the other.
Bp
Hp
2
12 HB
PP
2
12 BH
PP
$4
$4
$12
$6 $12
$6
8$
4$
HB
HB
PP
PP
Bun Company
Hot Dog Company
Now, suppose that these companies merged into one monopoly
QPP BH 12
0212 QMR
6$
6
BH PP
Q
Complementary Goods
Case Study: 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?
Case Study: Microsoft vs. Netscape
Suppose that the demand for browsers/operating systems is as follows (look familiar?). Again, Assume MC=0
BOS PPQ 12
Case #1: Suppose that Microsoft never entered the browser market – leaving Netscape as a monopolist.
8$
4$
BOS
BOS
PP
PP
Case Study: Microsoft vs. Netscape
Case #2: Now, suppose that Microsoft competes in the Browser market
With competition (and no collusion) in the browser market, Microsoft and Netscape continue to undercut one another until the price of the browser equals MC ( =$0)
Given the browser’s price of zero, Microsoft will sell its operating system for $6
QPOS 120
0212 QMR 6$
6
OSP
Q
