2.4 multiproduct monopoly

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1 2.4 Multiproduct Monopoly Matilde Machado Slides available from: http://www.eco.uc3m.es/ OI-I-MEI/

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2.4 Multiproduct Monopoly. Matilde Machado Slides available from: http://www.eco.uc3m.es/OI-I-MEI/. 2.4 Multiproduct Monopoly. The firm is a monopoly in all markets where it operates i=1,….n goods sold by the monopolist p=(p 1 ,….p n ) prices charged for each good (uniform) - PowerPoint PPT Presentation

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Page 1: 2.4 Multiproduct Monopoly

1

2.4 Multiproduct Monopoly

Matilde MachadoSlides available from:

http://www.eco.uc3m.es/OI-I-MEI/

Page 2: 2.4 Multiproduct Monopoly

Industrial Organization- Matilde Machado 2.4. Multiproduct Monopoly 2

2.4 Multiproduct Monopoly The firm is a monopoly in all markets where it operates i=1,….n goods sold by the monopolist p=(p1,….pn) prices charged for each good (uniform) q=(q1,….qn) quantities sold of each good qi=Di(p) = demand of good i – Note that what is

important here is that demand for good i may depend on the full price vector not only of pi

C(q1,…qn)= Cost function, depends on the quantities produced of all goods. Note, quantities here

may not be added because the monopolist is producing different goods.

Page 3: 2.4 Multiproduct Monopoly

Industrial Organization- Matilde Machado 2.4. Multiproduct Monopoly 3

2.4 Multiproduct Monopoly

Examples:Example 1: Launching Prices – e.g.: “imagénio” by

Telefónica, CNN plus (initial prices very cheap), ING 1st deposit; cable TV (some extra channels at very low prices).

Example 2: Learning-by-doing –

Example 3: New Product lines – Kmart, gas stations at certain supermarkets.

Page 4: 2.4 Multiproduct Monopoly

Industrial Organization- Matilde Machado 2.4. Multiproduct Monopoly 4

2.4 Multiproduct Monopoly

A special case (theory) Suppose demands are independent i.e. they

only depend on their own price pi: qi=Di(pi). Separability in the Cost function :

C(q1,….qn)=C1(q1)+…Cn(qn)

In this case the monopolist’s maximization problem may be written as n separate problems since the n markets are independent.

Page 5: 2.4 Multiproduct Monopoly

Industrial Organization- Matilde Machado 2.4. Multiproduct Monopoly 5

2.4 Multiproduct Monopoly

A special case(cont.)

1 ,... 1 1

( ) ( ( ))

FOC: 0 for 1,...,

( ) ( ) ( ( )) ( )

( ( )) 1

n

n n

i i i i i ip p i i

i

i i i i i i i i i i

i i i i

i i

D p p C D p

i np

D p D p p C D p D p

p C D p

p

Max

Lerner Index

That is, the optimal pricing strategy is to have a higher

margin in those markets in which demand is less elastic. This is

the same result obtained in third-degree price discrimination,

except that here the goods are different while in third-degree price discrimination we were dealing with the same good

Page 6: 2.4 Multiproduct Monopoly

Industrial Organization- Matilde Machado 2.4. Multiproduct Monopoly 6

2.4 Multiproduct Monopoly

More General case – w.l.o.g. assume n=2

1 2

1 1 2 1 2 1 2 2 1 1 2 2 1 2,

1 2 1 21 1 2

1 1 1 1 1 2 1

2 1 12 2 1

2 2 2 1 2 2

( , ) ( , ) ( ( , ), ( , ))

( ) ( ) ( ) ( )FOC: 0 ( )

( ) ( ) ( ) ( ) 0 ( )

p p

D p p p D p p p C D p p D p p

D p D p D DC CD p p p

p p p D p D p

D p D p DC CD p p p

p p p D p D

Max

2

2

D

p

Page 7: 2.4 Multiproduct Monopoly

Industrial Organization- Matilde Machado 2.4. Multiproduct Monopoly 7

2.4 Multiproduct MonopolyAssume additive costs

Hence, the first FOC simplifies to:

1 2 1 1 2 2( , ) ( ) ( )C q q C q C q

1 2 1 21 1 2 1 2

1 1 1 1

1 1 2 2 11 1 2

1 1 1 2 1

1 1 1 2 2 11 2

1 1 1 1 2 1

( ) ( )( ) ( ) ( )

( ) ( )( )

( ) ( )

D p D p D DD p p p C C

p p p p

D p D D p D pD p p p

p D p D p

D D p D D pC C

p D p p D p

Page 8: 2.4 Multiproduct Monopoly

Industrial Organization- Matilde Machado 2.4. Multiproduct Monopoly 8

2.4 Multiproduct Monopoly

The first FOC simplifies further to:

1 1 2 1 21 1 2

1 1 1 2 1

1 1 1 2 1 21 2

1 1 1 1 2 1

( ) ( )( )

( ) ( )

D p p D p p pD p D D

p D p D p

D p D D p DC C

p D p p D p

11 12

11 12

2 1 21 11 1 12 2 1 11 2 12

1 1 1

( ) ( ) ( )p D D

D p D D C Cp p p

A

Page 9: 2.4 Multiproduct Monopoly

Industrial Organization- Matilde Machado 2.4. Multiproduct Monopoly 9

2.4 Multiproduct Monopoly

Multiply both sides by p1/D1:

2 1 21 11 1 12 2 1 11 2 12

1 1 1

( ) ( ) ( )p D D

D p D D C Cp p p

A

2 21 1 11 2 12 1 11 2 12

1 1

2 21 1 11 1 2 12 2 12

1 1

21 1 1 2 2 12

11 1 11

2 2 12 21 1

1 11 1 11 1

( ) ( )

( ) ( )

1 1( ) ( )

( )( ) 1

D Dp p p C C

D D

D Dp C p p C

D D

Dp C p p C

D

p C Dp C

p p D

Page 10: 2.4 Multiproduct Monopoly

Industrial Organization- Matilde Machado 2.4. Multiproduct Monopoly 10

2.4 Multiproduct Monopoly

Case 1: Independent goods 12=0,

Case 2: Substitutes:

1 1

1 11

( ) 1p C

p

2 2 112 12

1 1 2

0 0 because 0D D p

p p D

2 2 12 21 1

1 11 1 11 1 11

( )( ) 1 1p C Dp C

p p D

The monopolist’s margin is higher

than with independent goods

Page 11: 2.4 Multiproduct Monopoly

Industrial Organization- Matilde Machado 2.4. Multiproduct Monopoly 11

2.4 Multiproduct MonopolyCase 2 (cont.): intuition:

↑p1 ↑D2 gives incentives to the monopolist to ↑p2

When maximizing the joint profit, the monopolist internalizes the effects that the sale of one good has on the demand of the others. In the case of 2 substitute goods this implies that the monopolist should increase the prices of both goods relative to a situation where he treated the two goods separately.

Page 12: 2.4 Multiproduct Monopoly

Industrial Organization- Matilde Machado 2.4. Multiproduct Monopoly 12

2.4 Multiproduct Monopoly

Case 3: Complements

↑p1 ↓D2 (because ↓D1 ) then we may guess that the price of good 1 is lower than in the case in which the monopolist would treat the two goods independently.

2 2 12 21 1

1 11 1 11 1 11

( )( ) 1 1p C Dp C

p p D

212

1

0 0D

p

Page 13: 2.4 Multiproduct Monopoly

Industrial Organization- Matilde Machado 2.4. Multiproduct Monopoly 13

2.4 Multiproduct MonopolyCase 3 (cont.): Complements

↑p1 ↓D2 (and so does ↓D1 ) therefore this gives incentives to the monopolist to ↓p2

Note: If there is strong complementarity between the two goods the monopolist sells, it may be optimal for the monopolist to sell one of the goods, say good 1, below its marginal cost in order to increase the demand for good 2.

Example: Price of the mobile phone with and without contract with the company

Page 14: 2.4 Multiproduct Monopoly

Industrial Organization- Matilde Machado 2.4. Multiproduct Monopoly 14

2.4 Multiproduct Monopoly

Example 1: Launching prices, inter-temporal production and imperfect information:

The Monopoly produces a single good The good is sold in 2 consecutive periods The first period’s demand is D1(p1) and costs

C1(q1)

Period 2: q2=D2(p2,p1) and C2(q2)

↓p1 ↑D1

↑D2 then (complements) 2

1

0D

p

For example, because when there are more consumers in

period 1, there is more information about the product

in period 2.

Page 15: 2.4 Multiproduct Monopoly

Industrial Organization- Matilde Machado 2.4. Multiproduct Monopoly 15

2.4 Multiproduct Monopoly

Example1: (cont.):

Note: The profit of the monopolist is:

1

2

0D

p

1 2

1 1 1 1 1 1 2 2 1 2 2 2 1 2,

1

2

2 2

2 2 2

2

1

( ) ( ( )) ( , ) ( ( , ))

given that by definition 0 the problem in the 2nd period is standard:

(.) 1FOC: 0 monopoly price in period 2

since 0

p p

p D p C D p p D p p C D p p

D

p

p C

p p

D

p

Max

1 112

1 1

(.) 1 (complements) 0 (lower launching prices)

p C

p

Page 16: 2.4 Multiproduct Monopoly

Industrial Organization- Matilde Machado 2.4. Multiproduct Monopoly 16

2.4 Multiproduct Monopoly

Example 1: (cont.):Conclusion: The monopolist sacrifices some short-term

profits for higher long-term profits. Ex: launching prices of CNN+, cable TV.

Page 17: 2.4 Multiproduct Monopoly

Industrial Organization- Matilde Machado 2.4. Multiproduct Monopoly 17

2.4 Multiproduct Monopoly

Example 2: Learning by Doing – it is similar to a Multi-product Monopolist with independent demands but interdependent costs, i.e. costs decrease with quantity:

Monopolist produces a single good in two consecutive periods

Demand in period t is qt=Dt(pt) (independent across periods)

C1(q1) 1st period cost function C2(q1,q2) second period cost function

2 2

1 2

0; 0C C

q q

The higher the amount produced in the 1st period, the lower are the costs in the

second period

Page 18: 2.4 Multiproduct Monopoly

Industrial Organization- Matilde Machado 2.4. Multiproduct Monopoly 18

2.4 Multiproduct Monopoly

↑q1

q2

C2

Page 19: 2.4 Multiproduct Monopoly

Industrial Organization- Matilde Machado 2.4. Multiproduct Monopoly 19

2.4 Multiproduct Monopoly

Example 2: (cont.): Monopolist maximizes:

1 2

1 1 1 1 1 1 2 2 2 2 1 1 2 2,

22 2 2 2 2 2 2 2 2

2 2

( ) ( ( )) ( ) ( ( ), ( ))

Again because period 2 does not have an effect in period 1's, the problem is standard:

FOC: 0 ( ) ( ) ( )

p p

p D p C D p p D p C D p D p

CD p p D p D p MR MC

p D

Max

1 21 1 1 1 1 1 1 1 1

1 1 1

1 21 1 1 1 1

1 1

0 ( ) ( ) ( ) ( )

()

C CD p p D p D p D p

p D D

p Cp q MC MR MC

q D

q*1 is larger

than the static

optimal quantity. Short-run profits are sacrificed.