1 Externe Effekte 32. Kapitel: Externe Effekte MarktEffizienz Konsum / Produkt der andere Aufgaben...

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32. Kapitel: Externe EffekteExterne Effekte32. Kapitel: Externe EffekteExterne Effekte

32. Kapitel: Externe EffekteExterne Effekte32. Kapitel: Externe EffekteExterne Effekte)(),( xfycu Markt Effizienz

),(),,( YxfyCcu

Konsum / Produkt der andere

Aufgaben (1-5)

zu Kapitel 32Click hier

2


),(),,( smusmu BA

Geld & Rauch

Raucher & Nichtraucher

),( fmuB

),( fmuB

m

f

Bm

s

A

3


Geld & Rauch


m

f

B

m

s

A m

f

B

m

f

B

4


Geld & Rauch


m

s

A

m

f

B

5


Geld & Rauch


m

s

A

B

f

0 Rauch

1 Rauch

m1 + m2

6


Geld & Rauch


m

s

A

B

m1 + m2

f

0 Rauch

1 Rauch

7


Geld & Rauch


m

s

A

B

m1 + m2

f

0 Rauch

1 Rauch

gesetzliche RechteEigentumsrecht

Legal rightsproperty rights

8


Geld & Rauch


m

s

A

B

f

0 Rauch

1 Rauch

9


Geld & Rauch


m

s

A

B

f

0 Rauch

1 Rauch

10


Geld & Rauch


m

s

A

B

f

0 Rauch

1 Rauch

Quasilineare Nutzenfunktion )(),( svmsmu

Coase Theorem

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32. Kapitel: Externe EffekteExterne Effekte32. Kapitel: Externe EffekteExterne EffekteExterne Effekte in Produktion

S --- Stahl s + Verschmutzung x

xscS ,

x

xscS ,

xscsp SSxs

,max,

(Kostenfunkton)

12


Flussabwärts (down river)F --- Fischprodukt f

xfcF ,

xfcfp FFf

,max

x

xfcF ,

(Kostenfunkton)

13


xfcfp FFf

,max

xscsp SSxs

,max,

x

xscs

xscp

S

SS

**,0

**,

xfcfp FFf

,max

f

xfcp FF

**,

14


x

xscs

xscp

S

SS

**,0

**,

f

xfcp FF

**,

x

xfcF ,

x

xscS ,

X*

0

**,

x

xfcF

15


xfcxscfpsp FSFSxfs

,,max,,

x

xfc

x

xsc

f

xfcp

s

xscp

FS

FF

SS

**,**,0

**,

**,

Merger - fusionierte Firmen

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x

xsc

x

xfc SF

**,**,

x

xfc

x

xsc FS

**,**,0

0

0

**,

x

xscS

x

xscS *,

X*

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x

xscS ,

x

xfcF ,

x

SMCFMC

sozial optimale x

privat optimale x

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Steuer t

txxscsp SSxs

,max,

x

xsct

s

xscp

S

SS

**,

**,

x

xfc

x

xsc FS

**,**,0

x

xfct F

**,

wenn:

Besteuereung der Verschmutzung

sozial optimale x*

19


Steuer t

x

xfct F

**,

Pigou - Steuer

Arthur Pigou

1877-1959

? ?

20


Wenn F ein Recht auf sauberes Wasser hat.

xfcqxfp FFxf

,max,

xscqxsp SSxs

,max,

Nachfrage für x:

Angebot von x:

x

xfc

x

xsc FS

**,**,0

x

xsc

x

xfcq SF

**,**,

Optimales Verschmutzungsniveau

21


Wenn S das Recht auf Verschmutzung hat.(bis zu einer Menge X.)

xfcxXqfp FFxf

,max,

xscxXqsp SSxs

,max,

Nachfrage für x:

Angebot von x:

x

xfc

x

xsc FS

**,**,0

x

xsc

x

xfcq SF

**,**,

Optimales Verschmutzungsniveau

22

32. Kapitel: Externe EffekteExterne Effekte32. Kapitel: Externe EffekteExterne EffekteDie Tragödie der Allmende

The Tragedy of the CommonsThe Tragedy of the Commons

c Kühe

f(c) der Wert der Milch

a Kosten einer Kuh

Gesamtwohlfahrt: accfc

)(max

acf )(

acMP )(Grenzprodukt = Kosten

c

)(cf

23


Private Entscheidung

ac

cf

1

)1()(cf

cc

c

cf )( c

a

ac

cf

)(aAP

C

24


c

cf )(

c

)(cf )(

)(cf

c

cf

MPAP

c

AP

MP

25


a

c

AP

MP

Gesamtwohlfahrt: acMP )(

Private Entscheidung acAP )(

26

32. Kapitel: Externe EffekteExterne Effekte32. Kapitel: Externe EffekteExterne EffekteVerschmutzungszertifikate - Vouchers

X Emissionsziel

2 firmenci(xi) -- Die Kosten der Erreichung einer Emissionsquote xi

Xxxds

xcxcxx

21

2211,

..

min21

*22

*11 xcxc

xi

ci(xi)

12111

min xXcxcx

27

32. Kapitel: Externe EffekteExterne Effekte32. Kapitel: Externe EffekteExterne EffekteVerschmutzungszertifikate - Vouchers

Zertifikate: Q1 , Q2

iiiix

pQpxxci

min

pxc ii *

*22

*11 xcxc

28

1. A village owns a common green where villagers graze their goats. The cost to a goatowner of owning and caring for a goat is $4. The total revenue from all goats on thecommon pasture is f(g)=48g-2g2, where g is the number of goats on the pasture. Thecouncil decides to allow a goat to use the common pasture only if its owner buys it agoat license. To maximize total profit (of villagers and council), how many Dollarsper goat should the council charge?

2. The 130 campers at a Campground like their own campfires, but hate the smoke fromtheir neighbors' campfires. Each camper's utility function is U= 22f-f 2-s where f isthe number of hours her own campfire burns per day and where s is the amount ofsmoke in the air, this is defined as 12 times the average amount of hours that campersuse their fires. The campground authority could make all campers better off bylimiting the number of hours of campfire per day for everyone. How many hours ofcampfires per day should the authority allow each camper in order to make the typicalcamper as well off as possible?

3. Two neighboring stores attract customers to each other and to themselves byadvertising. Where x1 and x2 are the advertising expenditures of stores 1 and 2, theprofits of the firms are (48+x2)x1-2(x1)

2 for store 1 and (54+x1)x2-2(x2)2 for store 2.

Knowing these functions, one investor buys both stores. In order to maximize histotal profits, how much should he spend on advertising for store 1?

Aufgaben (1-5) für Kapitel 32

29

Aufgaben für Kapitel 32

4. An airport is located next to a housing development. Where X is the number ofplanes that land per day and Y is the number of houses in the housingdevelopment, profits of the airport are 30X-X2 and profits of the developer are36Y-Y2-XY. Let H1 be the number of houses built if a single profit-maximizingcompany owns the airport and the housing development. Let H2 be the number ofhouses built if the airport and the housing development are operatedindependently and the airport has to pay the developer the total "damages" XYdone by the planes to the profits of the developer.

5. An apiary (Bienenhaus) is located next to an apple orchard. The apiary produceshoney and the apple orchard produces apples. The cost function of the apiary isCH(H,A)=H2/100-2A and the cost function of the apple orchard isCA(H,A)=A2/100 where H and A are the number of units of honey and applesproduced respectively. The price of honey is 4 and the price of apples is 1 per unit.Let A1 be the output of apples if the firms operate independently, and let A2 be theoutput of apples if the firms are operated by a single owner so as to maximize totalprofit.

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