Model

Monopoly

Duopoly

Nash Equilibrium

Oligopoly



Econ 460 Urban Economics

Lecture 1F: Hotelling’s Model Instructor: Hiroki Watanabe

Spring 2012

© 2012 Hiroki Watanabe

Model

Monopoly

1 / 64

Duopoly

1

Hotelling’s Model

2

Monopoly (N = 1)

3

Duopoly (N = 2)

4

Nash Equilibrium

5

Oligopoly (N ≥ 2)

6

Now We Know

Nash Equilibrium

Oligopoly

© 2012 Hiroki Watanabe

Model

Monopoly

2 / 64

Duopoly

Nash Equilibrium

1

Hotelling’s Model Hot Dog Vendors in Rockefeller Plaza

2

Monopoly (N = 1)

3

Duopoly (N = 2)

4

Nash Equilibrium

5

Oligopoly (N ≥ 2)

6

Now We Know

© 2012 Hiroki Watanabe



Oligopoly



3 / 64

Model

Monopoly

Duopoly

Nash Equilibrium

Oligopoly



Hot Dog Vendors in Rockefeller Plaza

Firm’s location choice (Lecture 1D): Firm A’s location choice affects Firm B via bid rent. Production level y¯ was given.

What if y¯ is endogenous and firm’s location choice affects profit of other firms?

© 2012 Hiroki Watanabe

Model

4 / 64

Monopoly

Duopoly

Nash Equilibrium

Oligopoly



Hot Dog Vendors in Rockefeller Plaza

Hotelling’s model (c.f. Varian Chpt 25 [Var05]). Think of a region in which consumers are uniformly located along a line segment [0, 1]. Each consumer prefers to travel a shorter distance to a hot dog vendor (homogeneous good). There are N sellers. Where would we expect these sellers to choose their locations?

© 2012 Hiroki Watanabe

Model

5 / 64

Monopoly

Duopoly

Nash Equilibrium

Oligopoly



Population Denisty (people/mi)

Hot Dog Vendors in Rockefeller Plaza

1

0

−0.2 © 2012 Hiroki Watanabe

0

0.2

0.4 0.6 Location (miles)

0.8

1

1.2 6 / 64

Model

Monopoly

Duopoly

Nash Equilibrium

Oligopoly



Hot Dog Vendors in Rockefeller Plaza

Consumer location is given by  (0 ≤  ≤ 1). n-th vendor’s location is given by n (0 ≤ n ≤ 1). Definition 1.1 (Mill & Delivered Price) 1

is the on-site price of a hot dog. The mill price of the n-th vendor is given by pn .

2

is the overall cost that a consumer pays for a hot dog, including trip cost. A consumer at  pays . pn + | − n | | {z } |{z} distance to vendor n mill price of vendor n

© 2012 Hiroki Watanabe

Model

Monopoly

7 / 64

Duopoly

Nash Equilibrium

Oligopoly



Hot Dog Vendors in Rockefeller Plaza

Each consumer buys one hot dog. Normalize pn = 1 for all n. Demand faced by Liz is DL (L , K , · · · ) hot dogs. Demand faced by Kenneth is DK (L , K , · · · ) hot dogs. (Assume the cost is sunk, i.e., the vendor has already made enough hot dogs). Liz’s profit is 1 · DL (L , K , · · · ) = DL (L , K , · · · ) dollars. Kenneth’s profit is 1 · DK (L , K , · · · ) = DK (L , K , · · · ) dollars.

© 2012 Hiroki Watanabe

Model

Monopoly

8 / 64

Duopoly

1

Hotelling’s Model

2

Monopoly (N = 1)

3

Duopoly (N = 2)

4

Nash Equilibrium

5

Oligopoly (N ≥ 2)

6

Now We Know

© 2012 Hiroki Watanabe

Nash Equilibrium

Oligopoly



9 / 64

Model

Monopoly

Duopoly

Nash Equilibrium

Oligopoly



Suppose there is a single vendor (monopolist). Question 2.1 (Location of the Monopolist) 1

What is the demand that the monopolist faces?

2

What is the monopolist’s profit when she locates  = 0, .25 and .5?

3

Which location maximizes the vendor’s profit?

4

Which location minimizes total delivered price payed by the customers?

© 2012 Hiroki Watanabe

Model

Monopoly

10 / 64

Duopoly

Nash Equilibrium

Oligopoly



Liz solves: max0≤L ≤1 π L (L ) = 1 · DL (L ). DL (L ) = 1. π L (L ) = 1 · DL (L ) = 1. Liz’s profit is 1 regardless of the location L .

© 2012 Hiroki Watanabe

Model

Monopoly

11 / 64

Duopoly

Nash Equilibrium

Oligopoly



Mill Price and Delivered Price ($)

2

1.5

1

0.5 Mill(x)=1 Delivered(x)=|x−0| 0 0

© 2012 Hiroki Watanabe

0.25

0.5 Location (miles)

0.75

1 12 / 64

Model

Monopoly

Duopoly

Nash Equilibrium

Oligopoly



Mill Price and Delivered Price ($)

2

1.5

1

0.5 Mill(x)=1 Delivered(x)=|x−.25| 0 0

0.25

© 2012 Hiroki Watanabe

Model

Monopoly

0.5 Location (miles)

Duopoly

0.75

1 13 / 64

Nash Equilibrium

Oligopoly



Mill Price and Delivered Price ($)

2

1.5

1

0.5 Mill(x)=1 Delivered(x)=|x−.5| 0 0

0.25

© 2012 Hiroki Watanabe

Model

Monopoly

0.5 Location (miles)

Duopoly

0.75

Nash Equilibrium

1 14 / 64

Oligopoly



Delivered price is location-variant. Definition 2.2 (Total Delivered Price (TDP)) Total delivered price measures the overall price that consumers paid to purchase their hot dogs. It is equivalent to vendor’s profit and the aggregate sum of | − L | from  = 0 to  = 1. TDP(L = 0) = 1 + .5 = 1.5 = TDP(L = .25) = 1 + TDP(L

© 2012 Hiroki Watanabe

= .5) = 1 +

1 4

5 16

=

=

5 4

24 . 16

21 . 16 = 20 . 16

15 / 64

Model

Monopoly

Duopoly

Nash Equilibrium

Oligopoly



1.5

Total Delivered Price ($)

1.4 1.3 Total Profit TDP(xL)

1.2 1.1 1 0.9 0

0.25

© 2012 Hiroki Watanabe

Model

Monopoly

0.5 0.75 Vendor Location (xL)

Duopoly

Nash Equilibrium

1 16 / 64

Oligopoly



What is socially optimal for the economy as a whole is L = .5 (minimizes total cost of trip while maintaining the profitability). What is privately optimal for the vendor is any L in [0, 1]. Question 2.3 (Profit Maximization and Social Welfare) Is there any way that Liz chooses L = .5 by herself? Is political intervention necessary to realize L = .5?

© 2012 Hiroki Watanabe

Model

Monopoly

17 / 64

Duopoly

1

Hotelling’s Model

2

Monopoly (N = 1)

3

Duopoly (N = 2) Duopoly Isoprofit

4

Nash Equilibrium

5

Oligopoly (N ≥ 2)

6

Now We Know

© 2012 Hiroki Watanabe

Nash Equilibrium

Oligopoly



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Model

Monopoly

Duopoly

Nash Equilibrium

Oligopoly



Duopoly Suppose there are two vendors (N = 2). Liz solves: max0≤L ≤1 π L (L , K ) = 1 · DL (L , K ). Kenneth solves: max0≤K ≤1 π K (L , K ) = 1 · DK (L , K ). Note Liz does not solve: max0≤L ≤1,0≤K ≤1 π L (L , K ) = 1 · DL (L , K ). (why?) What do DL (L , K ), DK (L , K ) look like? Start with (L , K ) = (0, 1). © 2012 Hiroki Watanabe

Model

Monopoly

19 / 64

Duopoly

Nash Equilibrium

Oligopoly



Duopoly

Mill Price and Delivered Price ($)

2

1.5

1

0.5

Mill(x)=1 L

Delivered (x)=|x−0| DeliveredK(x)=|x−1| 0 0

0.25

© 2012 Hiroki Watanabe

Model

Monopoly

Duopoly

0.5 Location (miles)

0.75

Nash Equilibrium

1 20 / 64

Oligopoly



Duopoly

DL (0, 1) = .5 ⇒ π L (0, 1) = .5. DK (0, 1) = .5 ⇒ π K (0, 1) = .5. Does Liz improve her profit by moving to the east?

© 2012 Hiroki Watanabe

21 / 64

Model

Monopoly

Duopoly

Nash Equilibrium

Oligopoly



Duopoly

Mill Price and Delivered Price ($)

2

1.5

1

0.5

Mill(x)=1 L

Delivered (x)=|x−.1| DeliveredK(x)=|x−.8| 0 0

0.1

0.450.5 Location (miles)

© 2012 Hiroki Watanabe

Model

Monopoly

Duopoly

0.8

1 22 / 64

Nash Equilibrium

Oligopoly



Duopoly

DL (.1, 1) = DK (.1, 1)

1+.1 2

= .55

= 1 − .55 = .45.

Does Kenneth improve his profit by moving to the west?

© 2012 Hiroki Watanabe

Model

23 / 64

Monopoly

Duopoly

Nash Equilibrium

Oligopoly



Duopoly

Mill Price and Delivered Price ($)

2

1.5

1

0.5

Mill(x)=1 L

Delivered (x)=|x−.1| DeliveredK(x)=|x−.8| 0 0

© 2012 Hiroki Watanabe

0.1

0.450.5 Location (miles)

0.8

1 24 / 64

Model

Monopoly

Duopoly

Nash Equilibrium

Oligopoly



Duopoly

DL (.1, .8) = DK (.1, .8)

.1+.8 2

= .45.

= 1 − .45 = .55.

© 2012 Hiroki Watanabe

Model

25 / 64

Monopoly

Duopoly

Nash Equilibrium

Oligopoly



Duopoly

1

If L < K , Liz takes the consumers from 0 to the midpoint between L and K : DL (L , K ) =

L + K

.

2

Kenneth takes the rest: DK (L , K ) = 1 − DL (L , K ) = 1 −

L + K

.

2

© 2012 Hiroki Watanabe

Model

26 / 64

Monopoly

Duopoly

Nash Equilibrium

Oligopoly



Duopoly 2

If L > K , Kenneth takes the consumers from 0 to the midpoint between L and K : DK (L , K ) =

L + K

.

2

Liz takes the rest: DL (L , K ) = 1 − DK (L , K ) = 1 −

3

L + K

.

2

If L = K , they split the market even: DL (L , K ) = DK (L , K ) = .5.

© 2012 Hiroki Watanabe

27 / 64

Model

Monopoly

Duopoly

Nash Equilibrium

Oligopoly



Isoprofit

© 2012 Hiroki Watanabe

Model

28 / 64

Monopoly

Duopoly

Nash Equilibrium

Oligopoly



Isoprofit

An isoprofit curve of Liz indicates the set of location (L , K ) that results in the same profit.

© 2012 Hiroki Watanabe

Model

29 / 64

Monopoly

Duopoly

Nash Equilibrium

Oligopoly



Isoprofit For Liz, isoprofit at .4 is a set of location (L , K ) that results in π L (L , K ) = .4. 1

If L < K (region above 45◦ line) π L (L , K ) =

2

L + K

= .4 ⇒ K = −L + .8.

If L > K (region below 45◦ line) π L (L , K ) = 1 −

3

2

L + K 2

= .4 ⇒ K = −L + 1.2.

If L = K (45◦ line) π L (L , K ) = .5 , .4

© 2012 Hiroki Watanabe

30 / 64

Model

Monopoly

Duopoly

Nash Equilibrium

Oligopoly



Isoprofit Liz′s Isoprofit 1

0.

0.

0.

7

0.

5

6

0. 9

8

8 0.

0.8

0.

4

0.6

0. 5

0. 2

0.

3

x

K

0. 4

0.

5 0.

0.4

0.

2

0.2

5

0.

0.

1

.63 0.70.89. 000.

0

0

0. 3

0.

5

4

0.

4 0.

3 .6 07 0.

0.

6

0.

0.

5

0.

2

8

0.

7

0.2

0.4

0.6

0.8

1

xL

© 2012 Hiroki Watanabe

Model

.6 0. 3 0 7 .045. 00.

0. 6

.23 7.0.04.5.1 000.0

Monopoly

31 / 64

Duopoly

Nash Equilibrium

Oligopoly



Isoprofit For Liz, isoprofit at .5 is a set of location (L , K ) that results in π L (L , K ) = .5. 1

If L < K (region above 45◦ line) π L (L , K ) =

2

L + K 2

If L > K (region below 45◦ line) π L (L , K ) = 1 −

3

= .5 ⇒ K = −L + 1.

L + K 2

= .5 ⇒ K = −L + 1.

If L = K (45◦ line) π L (L , K ) = .5

A crossbuck shape. © 2012 Hiroki Watanabe

Model

32 / 64

Monopoly

Duopoly

Nash Equilibrium

Oligopoly



Isoprofit For Kenneth, isoprofit at .4 is a set of location (L , K ) that results in π K (L , K ) = .4. 1

If L < K (region below 45◦ line) π K (L , K ) = 1 −

2

2

= .4 ⇒ K = −L + 1.2.

If L > K (region above 45◦ line) π K (L , K ) =

3

L + K

L + K 2

= .4 ⇒ K = −L + .8.

If L = K (45◦ line) π K (L , K ) = .5 , .4

© 2012 Hiroki Watanabe

33 / 64

Model

Monopoly

Duopoly

Nash Equilibrium

Oligopoly



Isoprofit

Question: where is Kenneth’s isoprofit at .5 located?

© 2012 Hiroki Watanabe

Model

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Monopoly

Duopoly

Nash Equilibrium

Oligopoly



Isoprofit Kenneth′s Isoprofit 1

0. 5

0. 3

0.

4

0. 2

0. 1

2 0. 5

0.8

0.

6

0.

K

x © 2012 Hiroki Watanabe

Model

0. 5

0. 7 ..54 03 00.

0. 9

0

Monopoly

0. 8

4

0.

8 0.

2

0. 7

0. 6

0.

6 0.

.47 0.30.21.5 000.

0.

5

0. 8

0.2

0.

0.

0. 6

0

3 06.7 0.

0. 7

0.4

4

0.

0. 4

5

0.6

.87 3.006..9 00.0

0. 5

0.

3

0.2

0.4

0.6

0.8

1

xL

Duopoly

Nash Equilibrium

Oligopoly

35 / 64



Isoprofit

How does Liz react to Kenneth’s location? If Kenneth is at K = 0, Liz maximizes its profit by locating slightly to the east of K . (L , 0) ⇒ L = 0 + ε (ε = an infinitesimally small distance). If Kenneth is at K = .2, Liz maximizes its profit by locating slightly to the east of K . (L , .2) ⇒ L = .2 + ε. If Kenneth is at K = .4, Liz maximizes its profit by locating slightly to the east of K . (L , .4) ⇒ L = .4 + ε.

© 2012 Hiroki Watanabe

36 / 64

Model

Monopoly

Duopoly

Nash Equilibrium

Oligopoly



Isoprofit

(L , .5) ⇒ L = .5. (L , .6) ⇒ L = .6 − ε. (L , .8) ⇒ L = .8 − ε. (L , 1) ⇒ L = 1 − ε.

© 2012 Hiroki Watanabe

Model

Monopoly

37 / 64

Duopoly

Nash Equilibrium

Oligopoly



Isoprofit

How does Kenneth react to Liz’s location? (0, K ) ⇒ K = 0 + ε. (.2, K ) ⇒ K = .2 + ε. (.4, K ) ⇒ K = .4 + ε. (.5, K ) ⇒ K = .5. (.6, K ) ⇒ K = .6 − ε. (.8, K ) ⇒ K = .8 − ε. (1, K ) ⇒ K = 1 − ε.

© 2012 Hiroki Watanabe

Model

Monopoly

38 / 64

Duopoly

Nash Equilibrium

Oligopoly



Isoprofit

© 2012 Hiroki Watanabe

Turn

L

K

Initial Liz Kenneth Liz .. .

0 .99 .99 .97

1 1 .98 .98

Kenneth Liz Kenneth Liz Kenneth

.52 .50 .50 .50 .50

.51 .51 .50 .50 .50

39 / 64

Model

Monopoly

Duopoly

Nash Equilibrium

Oligopoly

1

Hotelling’s Model

2

Monopoly (N = 1)

3

Duopoly (N = 2)

4

Nash Equilibrium Nash Equilibrium & Socially Efficient Location

5

Oligopoly (N ≥ 2)

6

Now We Know

© 2012 Hiroki Watanabe

Model

Monopoly



40 / 64

Duopoly

Nash Equilibrium

Oligopoly



Nash Equilibrium & Socially Efficient Location

Definition 4.1 (Nash Equilibrium) Nash equilibrium is the location (LNE , KNE ) such that none of the vendor can profit by unilaterally changing its location. For duopoly, the Nash equilibrium (LNE , KNE ) = (.5, .5).

© 2012 Hiroki Watanabe

Model

Monopoly

41 / 64

Duopoly

Nash Equilibrium

Oligopoly



Nash Equilibrium & Socially Efficient Location

Is the Nash equilibrium (LNE , KNE ) = (.5, .5) socially efficient? Fact: the socially efficient allocation is (L∗ , K∗ ) = (1/ 4, 3/ 4) or (3/ 4, 1/ 4).

© 2012 Hiroki Watanabe

42 / 64

Model

Monopoly

Duopoly

Nash Equilibrium

Oligopoly



Nash Equilibrium & Socially Efficient Location Nash Equilibrium Location

Mill Price and Delivered Price ($)

2

1.5

1

0.5

Mill(x)=1 L

Delivered (x)=|x−.5| DeliveredK(x)=|x−.5| 0 0

0.25

0.5 Location (miles)

© 2012 Hiroki Watanabe

Model

Monopoly

Duopoly

0.75

1 43 / 64

Nash Equilibrium

Oligopoly



Nash Equilibrium & Socially Efficient Location Efficient Location

Mill Price and Delivered Price ($)

2

1.5

1

0.5

Mill(x)=1 L

Delivered (x)=|x−.25| DeliveredK(x)=|x−.75| 0 0

0.25

© 2012 Hiroki Watanabe

Model

Monopoly

Duopoly

0.5 Location (miles)

0.75

1 44 / 64

Nash Equilibrium

Oligopoly



Nash Equilibrium & Socially Efficient Location

Compare:

Nash Socially Efficient Socially Efficient

© 2012 Hiroki Watanabe

Location

Profit

TDP

(.5, .5) (.25, .75) (.75, .25)

(.5, .5) (.5, .5) (.5, .5)

1+1/4 1+1/8 1+1/8

45 / 64

Model

Monopoly

Duopoly

Nash Equilibrium

Oligopoly



Nash Equilibrium & Socially Efficient Location Liz′s Isoprofit 1

x

K

0.75

0.5

0.25

0

0

0.25

© 2012 Hiroki Watanabe

Model

Monopoly

Duopoly

0.5 xL

0.75

1 46 / 64

Nash Equilibrium

Oligopoly



Nash Equilibrium & Socially Efficient Location

Question 4.2 (Socially Inefficient Equilibrium) Why can’t vendors choose the socially optimal location, when both Nash equilibrium location and socially efficient location yield the same profits?

© 2012 Hiroki Watanabe

Model

Monopoly

47 / 64

Duopoly

Nash Equilibrium

Oligopoly



Nash Equilibrium & Socially Efficient Location

They are indifferent between (LNE , KNE ) and (L∗ , K∗ ). Given (L , K ) = (.25, .75), Liz will move to a location slightly to the west of K = .75. (L , K ) = (.74, .75) → (.74, .73) → (.72, .73) → · · · → (.5, .5).

© 2012 Hiroki Watanabe

48 / 64

Model

Monopoly

Duopoly

1

Hotelling’s Model

2

Monopoly (N = 1)

3

Duopoly (N = 2)

4

Nash Equilibrium

5

Oligopoly (N ≥ 2) N=3 N≥4

6

Now We Know

Nash Equilibrium

Oligopoly

© 2012 Hiroki Watanabe

Model



49 / 64

Monopoly

Duopoly

Nash Equilibrium

Oligopoly



N=3

If there are 3 vendors, Liz solves max0≤L ≤1 π L (L , K , J ) = 1 · DL (L , K , J ). For N = 3, there is no Nash equilibrium. Consider 1 2 3

All the vendors locate at different place. L = K = J . L = K , J .

© 2012 Hiroki Watanabe

Model

50 / 64

Monopoly

Duopoly

Nash Equilibrium

Oligopoly



N=3 2 Mill(x)=1 L

Mill Price and Delivered Price ($)

Delivered (x)=|x−.1| K Delivered (x)=|x−.3| DeliveredD(x)=|x−.9|

1 0 © 2012 Hiroki Watanabe

0.2

0.6 Location (miles)

1 51 / 64

Model

Monopoly

Duopoly

Nash Equilibrium

Oligopoly



N=3 2 Mill(x)=1 L

Mill Price and Delivered Price ($)

Delivered (x)=|x−.2| K Delivered (x)=|x−.3| DeliveredD(x)=|x−.8|

1 0

0.25

0.55 Location (miles)

1

© 2012 Hiroki Watanabe

Model

52 / 64

Monopoly

Duopoly

Nash Equilibrium

Oligopoly



N=3 2 Mill(x)=1 L

Mill Price and Delivered Price ($)

Delivered (x)=|x−.2| K Delivered (x)=|x−.2| DeliveredD(x)=|x−.2|

1 0

0.2

1 Location (miles)

© 2012 Hiroki Watanabe

Model

Monopoly

53 / 64

Duopoly

Nash Equilibrium

Oligopoly



N=3 2 Mill(x)=1 L

Mill Price and Delivered Price ($)

Delivered (x)=|x−.2| K Delivered (x)=|x−.2| DeliveredD(x)=|x−.3|

1 0

0.25

1 Location (miles)

© 2012 Hiroki Watanabe

54 / 64

Model

Monopoly

Duopoly

Nash Equilibrium

Oligopoly



N=3 2 Mill(x)=1 L

Mill Price and Delivered Price ($)

Delivered (x)=|x−.2| K Delivered (x)=|x−.2| DeliveredD(x)=|x−.8|

1 0

0.5 Location (miles)

1

© 2012 Hiroki Watanabe

Model

Monopoly

55 / 64

Duopoly

Nash Equilibrium

Oligopoly



N=3 2 Mill(x)=1 L

Mill Price and Delivered Price ($)

Delivered (x)=|x−.2| K Delivered (x)=|x−.3| DeliveredD(x)=|x−.8|

1 0

0.25

0.55 Location (miles)

1

© 2012 Hiroki Watanabe

Model

Monopoly

56 / 64

Duopoly

Nash Equilibrium

Oligopoly



N=3

Fact: socially efficient location is (L , K , J ) = (1/ 6, 3/ 6, 5/ 6) (not necessarily in this order).

© 2012 Hiroki Watanabe

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Model

Monopoly

Duopoly

Nash Equilibrium

Oligopoly



N=3 2 Mill(x)=1 L

Mill Price and Delivered Price ($)

Delivered (x)=|x−1/6| K Delivered (x)=|x−3/6| DeliveredD(x)=|x−5/6|

1 0

1/3 2/3 Location (miles)

1

© 2012 Hiroki Watanabe

Model

Monopoly

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Duopoly

Nash Equilibrium

Oligopoly

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N≥4

There are Nash equilibria for N ≥ 4.

© 2012 Hiroki Watanabe

Model

Monopoly

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Duopoly

1

Hotelling’s Model

2

Monopoly (N = 1)

3

Duopoly (N = 2)

4

Nash Equilibrium

5

Oligopoly (N ≥ 2)

6

Now We Know

© 2012 Hiroki Watanabe

Nash Equilibrium

Oligopoly



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Model

Monopoly

Duopoly

Nash Equilibrium

Oligopoly



Hotelling’s model Social optimality vs individual optimality. Nash equilibrium

© 2012 Hiroki Watanabe

Model

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Monopoly

Duopoly

Nash Equilibrium

Oligopoly



References Hal R. Varian. Intermediate Microeconomics. Norton, seventh edition, 2005.

© 2012 Hiroki Watanabe

Model

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Monopoly

Duopoly

Nash Equilibrium

Oligopoly



Map du Jour

Source

© 2012 Hiroki Watanabe

http://www.worldmapper.org/

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Model

Monopoly

Duopoly

D, demand, 8 Delivered price, 7 duopoly, 19 isoprofit, 29 Mill price, 7 monopoly, 10 N, number of sellers, 5 n, vendor, 7 Nash equilibrium, 41 oligopoly, 50 p, price, 7

© 2012 Hiroki Watanabe

Nash Equilibrium

Oligopoly



π, profit, 11, 19 private optimum, 17 profit, 8 social optimum, 17 socially efficient allocation, 42 TDP, see total delivered price total delivered price, 15 , location, 7

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