20. Common Property

7/25/2019 20. Common Property

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Externalities & Common Property

Common Properties Resources

• “Tragedy of the Commons” Hardin, Lloyd

• common property resource: communal ownership can work as long as community is “small” (“shame

operates)

• use of resource y ! indi"id can reduce ene#ts a"ailale to others

o there is an external cost imposed on other users of common property resource

Tragedy of the Commons

gra$ing area owned “in common” y all memers of a "illage

"illagers gra$e cows on the common

o %c& cows are gra$ed

o total milk production is f(c) f&' and f&&

production rises with * of animal, ut rises at a decreasing rate

set price of milk + !relati"e cost of gra$ing a cow + -c

o pro#t function:

o prolem is to:

income.ma/imi$ing * of cows to gra$e c* satis#es:

o Marginal income gaine from last cow gra$ed + marginal cost of gra$ing it

For c = c* a"erage gain per cow gra$ed:

f’! & f’’"!

o 0t optimum a"erage gain: f(c1)2c1 ' a"erage cost -c

o 3conomic pro#t from introducing ! more cow + 4"e

o 5o one owns the common entry no restricted 6 continues until economic pro#t of gra$ing

another cow + :

#ndi$idual Maximi%ation eads to '$er()se

• 3ach animal.owner adds more cows as long as a$erage gain ' a$erage cost

• 7ree entry in commons continues as lons as gain per co cost per co

• “8pen 0cess” * of cows gain per co = cost per co (net gain + )

• free entry leads to pro#t

Tragedy of the Commons Open Access: Avg Benet = Avg Cos



Common Property Example+ Fishery

• -eriodic 9ield (catch) of #sh from entire lake (9) depends on (is a function of):

o * of #shing oats operating %5&

9 + yield of #sh caught

5 + * of oats #shing during the period

• -eriodic Cost of operating ! #shing oat + , units of #sh per one period

• Compare cost 6 yield (ene#t

o Total yield as f(/) of * of oats #shing

o Total cost + straight line with slope . (periodic cost)

o ;ant to compare surplus (pro#t) under pro#t.ma/imi$ing *

of oats w2 the “common property” result (all #shers decideindi"idually whether or not to operate oat)

• How many oats do we e/pect to see operating<

o 9ield2oat ' cost2oat continue of entry

o 9ield2oat + 9(5)25 + =!5 > ?@A5B@25 + -! . !/012

0s long as !! . !/012 , operation of another

#shing oat will e D5EDFDEG0LL9 pro#taleo Cuto of * of oats, where yield2oat +

! > ?@A5 + I + ?@A5 5B(80) + @

• at eJuilirium pro#t +

3ol$ing a Common Property Pro4lem

• if Ko"&t nationali$es the #shery and operated is as a Crown Corp?o is #shery owned y single entity optimum * of oats to operate<

• 0ssume goal is ma/ pro#t each period

• !st deri"ati"e w?r?t 5 +

o 2* = -0 H0L7 of * of oats we e/pect with open access

(5B(80) + @)

• total pro#t when open access is +

• total pro#t when #shery owned y go"t& (! entity)

dierence<

Common Property+ 'pen 5ccess

• 'pen 5ccess6

o #ndi$id #shers additional gain is yield from operating another oat

o #ndi$id #sher&s additional cost + cost of operating another oat + ,

o as long as:

57ER58E 9per 4oat: 85#2 57ER58E 9per 4oat: C'3T

• Dt is pro#tale for an indi"idual to add a oat to the #shing ground

o The addition of another oat will reduce the #sh stock decreasing amount caught y 0LL

8TH3 M80TNo This cost (smaller stock, less yield to other oats) is an E;TER25 C'3T to the indi"idual #sh

ignored



• 3ole 'nership6

o 3ntire pro#t from all #sh caught accrues to a single owner

o Df owner ass another oat more #sh from new oat feer #sh caught y all of the othe

boatso Malances gain from one more 4oat with reduction in catch2yield from all other boats

o ;ill add another oat only if T8T0L amount of catch2yield increases (enough to oset cost of

operating another oat)o Malances M5R8#25 85#2 from another oat with M5R8#25 C'3T of operating it

• Nole owner:

o 3Juates M5R8#25 <#E per oat + M5R8#25 C'3T per oat

• Gnder common property, open acces

o 578 <#E = 578 C'3T

3ol$ing

• if ha"e perfect info 6 know that we want !@ oats operating pass a law allowing only that many

oats to operateo prolem:

@ want to ut only allowed !@

which get right to operating #shing oat<

;hen there are !@ oats

• Total pro#t + OI (O per oat)

;hom should go"&t grant licenses<

• -rolem e/ternal cost is eing ignored (thinner #sh stock)

o 5eed to force indi"id potential #shers, oat >operators,

to take ownership of eect To take cost of fewer #sh into account when making decision whether or not to operate

another oat

• -rolem optimal * of oats, pro#ts + O per oatP pro#t encourages entry, entry stops when pro#t p

oat + o How to make pro#t per oat + , 6 still get right * of oats operating<

Nystem of licenses (can operate 85L9 if they ought a license)

License fee per oat + eJui" of O #sh units per period



• pro#t per oat + when 377DCD35T * operating

• entry as long as pro#t + 4"e

o pro#t per oat now

5$g<ield92: . C . icense Fee= <92:>2 . , . ?= @-! . !/012A . B = ? . !/012

o 5 !@ pro#t per oat (net license) + 4"e =encouraging entry

o 5 ' !@ net license + ."e =inducing e/it

o 5 + !@ neither e/it2entry

8Qection no pro#t eing made

o There is y go"&t has appropriated ito (no pro#t under open accessR too many oats)

o pri$ate pro#t N8CD0L surplus 6 right * oats operating

characteri$es common property prolems:

o e/istence of pri"ate pro#t (due to 3ST350L cost) e/cessi"e entry (too many operators)

o go"t dealt with it using regulation (laws) eliminate pro#ts y increasing cost

sol"es o"er.entry ut eliminates surplus

o license schemes are etter still generate surplus (how is it distriuted)

Tragedy of the Commons

• reason for tragedy when "illager adds one more cow P his income rises (y f(c)2c > -c))

o ut e"ery other "illagers income falls

• the "illager who ass the e/tra cow takes no account of the cost imposed upon the rest of the "illage

• modern >day “tragedies of commons”

o o"er.#shing

o o"er.logging

o o"er.intensi"e use of pulic parks

o uran trac congestion

Documents

20. Common Property