externality: outside the price system pollution from a factory, envy felt by individuals inefficiency

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1 7 Externality( 外部性 ) 1

2 7.1 Introduction externality: outside the price system pollution from a factory, envy felt by individuals inefficiency control of externalities is practically important global warming( 地球温暖化 ) destruction of ozone layer( オゾン層の破壊 ) government intervention ---> internalization( 内部化 ) Pigouvian taxes( ピグー税 ) tradable licenses( 取引可能な許可証 ) Coase theorem( コースの定理 ) 2

3 7.2 Externalities Defined Definition 4 (Externality 外部性 ) An externality is present whenever some economic agent s welfare is directly affected by the action of another agent in the economy. directly = exclude effects mediated by prices (pecuniary externality 金銭的外部性 ) production externality consumption externality 3

4 consumption x={x 1,x 2,...,x H } production y={y 1,y 2,...,y m } U h =U h (x,y), h=1,...,h Y j =Y j (x,y), j=1,...,m utility fns and production sets are possibly dependent on the entire arrays actions of the agents in the economy will no longer be independent( 独立 ) or determined solely by prices competition will generally not achieve efficiency in an economy with externalities 4

5 7.3 Market Inefficiency presence of externalities Pareto-inefficient = never max welfare incorrect quantities of goods in the market two-consumer, two-good economy utility fns: U 1 =x 1 +u 1 (z 1 )+v 1 (z 2 ) U 2 =x 2 +u 2 (z 2 )+v 2 (z 1 ) positive externality if v h ( ) is increasing negative externality if v h ( ) is decreasing assume: supply of x <--- endowment w h z=x z is produced from x by a competitive industry normalize: price of x =1, so in eq. price of z =1 5

6 max decision of consumers u h (z h )=1, h=1,2 private marginal benefit = private marginal cost x h +z h =w h, h=1,2 x 1 +z 1 +x 2 +z 2 =w 1 +w 2 Pareto-efficient allocation max U 1 +U 2 =[x 1 +u 1 (z 1 )+v 1 (z 2 )]+[x 2 +u 2 (z 2 )+v 2 (z 1 )] s.t. w 1 +w 2 -x 1 -z 1 -x 2 -z 2 0 solution: u 1 (z 1 )+v 2 (z 1 )=1 u 2 (z 2 )+v 1 (z 2 )=1 externalities affect the optimal allocation( 最適配分 ) v h >0: positive externality, v h <0: negative 6

7 individual consumer s maximization max U 1 =x 1 +u 1 (z 1 )+v 1 (z 2 ) s.t. x 1 +z 1 =w 1 max U 2 =x 2 +u 2 (z 2 )+v 2 (z 1 ) s.t. x 2 +z 2 =w 2 substitute the constraints into utility functions U 1 =w 1 -z 1 +u 1 (z 1 )+v 1 (z 2 ) U 2 =w 2 -z 2 +u 2 (z 2 )+v 2 (z 1 ) du 1 /dz 1 =-1+u 1 (z 1 )=0 u 1 (z 1 )=1 du 2 /dz 2 =-1+u 2 (z 2 )=0 u 2 (z 2 )=1 7

8 Pareto efficiency max W=U 1 +U 2 =x 1 +x 2 +u 1 (z 1 )+u 2 (z 2 )+v 1 (z 2 )+v 2 (z 1 ) s.t. x 1 +x 2 +z 1 +z 2 =w 1 +w 2 substitute the constraints into welfare function W=w 1 +w 2 -z 1 -z 2 +u 1 (z 1 )+u 2 (z 2 )+v 2 (z 1 )+v 1 (z 2 ) W/ z 1 =-1+u 1 (z 1 )+v 2 (z 1 )=0 u 1 (z 1 )+v 2 (z 1 )=1 W/ z 2 =-1+u 2 (z 2 )+v 1 (z 2 )=0 u 2 (z 2 )+v 1 (z 2 )=1 8

9 Another way to find Pareto efficiency max U 1 =x 1 +u 1 (z 1 )+v 1 (z 2 ) s.t. x 2 +u 2 (z 2 )+v 2 (z 1 ) U 2, x 1 +x 2 +z 1 +z 2 =w 1 +w 2 substitute the constraints into welfare function L=x 1 +u 1 (z 1 )+v 1 (z 2 )+λ[x 2 +u 2 (z 2 )+v 2 (z 1 ) U 2 ] +μ[w 1 +w 2 -x 1 -x 2 -z 1 -z 2 ] L/ x 1 =1-μ=0 μ=1 L/ λ=0 L/ x 2 = λ-μ=0 λ=μ=1 L/ μ=0 L/ z 1 =u 1 (z 1 )+λv 2 (z 1 )-μ=0 u 1 (z 1 )+v 2 (z 1 )=1 L/ z 2 =λu 2 (z 2 )+v 1 (z 2 )-μ=0 u 2 (z 2 )+v 1 (z 2 )=1 9

10 marginal utilities at the optimum positive externality: below those in market outcome negative: above those in market outcome market outcome is not Pareto-efficient in general positive: more of z is consumed at the optimum than under the market outcome negative: converse Fig. 7.1 market outcome: PMB=MC Pareto-efficient outcome: SMB=MC SMB= u h (z h h )+ v h ~'( z ) 10

11 marginal h benefit and cost SMB( ~ ' 0 ) v h v~' 0 u h '( z h ) u h '(ˆ z h ) PBM MC SMB( ~ ' 0) v h h ẑ z h z h 11

12 7.4 Externality Examples River Pollution( 汚染 ) example of Louis Gevers two firms: located along the same river upstream( 上流 ) firm u pollutes the river reduces the production of downstream( 下流 ) firm d both produce the same output sell at the constant unit price of 1 (same revenue) inputs: labor (market price w) and water (free) technologies: F u (L u ), F d (L d,l u ), F d / L u <0 profit: p i =F i ( )-wl i i=u, d 12

13 equilibrium 0 u 0 d total stock of labor is allocated between u and d labor input of u: from the left, d: from the right u s profit max: upper part of the diagram ---> L u* given L u* d s profit max: lower part ---> L d* profits: p u, p d inefficiency of competitive equilibrium small reduction in L to u no effect on p u since choice is optimal p u / L u =0 outward shift of d s production function ---> p d this change raises the aggregate profit( 集計利潤 ) externality ---> u uses too much of labor 13

14 upstream revenue p u cost w 0 u 0 w d L u*,l d* cost revenue p d downstream 14

15 7.4.2 Traffic Jams( 交通渋滞 ) externalities imposed by drivers on each other N: commuters( 通勤者 ) choice of commuting by train or by car train: 40 minutes car: commuting time increases as the number of car users increases ---> externality minimization of transportation time( 輸送時間 ) equilibrium travel time by car = travel time by train ---> 40% optimum = max of aggregate time saving( 時間の節約 ) 20% ---> overusing of cars 15

16 minutes commuting maximum time saving car train % car users 16

17 7.4.3 Pecuniary Externality( 金銭的外部性 ) set of students: economist or lawyer being economist is great when there are few economists, but not when there are many price competition students choose the profession with the best earning prospects( 所得見込み ) pecuniary externality: decision to become a economist lowers all other economists incomes equilibrium: % of economists earnings of economist = earnings of lawyer laissez-faire( 自由放任 ) equilibrium ---> efficient 17

18 income of lawyers income of economists lawyer economist 0 E

19 7.4.4 The Rat Race Problem contest for relative position (George Akerlof) students work too hard when the ranking is given intense competition for a promotion in workplace classroom example ( 相対評価 ) performance is judged in relative term (not absolute) advantage over other students can only be gained by working harder than they do all must work harder ---> all extra effort cancels out inefficient rat race( 出世争い ) if all agree less work, the same grades are obtained agreement of less work is not self-supporting 19

20 cost of effort c, 0<c<½ Prisoners Dilemma( 囚人のジレンマ ) player 2 low high player 1 low high 1/2 1-c 1/2 0 1-c 0 1/2 -c 1/2 -c 20

21 performance-enhancing drugs by athletes no effective drug regulation( 薬物規制 ) ---> enhance performance by using anabolic steroid steroid( ステロイド ) ---> increase the chance to win unregulated contests: more and more drugs ---> substantial risks (cancer, health problems) voluntary restraint is not an effective solution public intervention( 公的介入 ) of strict drug testing rat race problem <--- relative( 相対的 ) position electoral competition ---> too much advertising ban on cigarette advertising ---> beneficial to cigarette companies 21

22 7.4.5 The Tragedy of the Commons ( 共有地の悲劇 ) common right of access to a resource inefficiency <--- divergence between individual and social incentives fishermen s problem lake used by fishermen from a village in its bank fishermen do not own boats but can rent them for daily use at a cost c B boats ---> F(B): number of fish caught by each boat, decreasing in B w: wage (opportunity cost) p=1: price of fish 22

23 equilibrium number of boats p =F(B * )-c=w optimal number of boats for the community: B o max {B} B[F(B)-c-w] first order necessary condition F(B o )-c-w+b o F (B o )=0 F (B o ) < 0 ---> B o < B * negative externality: each fisherman is concerned with his profit, they will reduce the quantity of fish caught by other fishermen ---> too many boats public intervention: tax (price-based) 課税, quota (quantity-based) 数量割当 23

24 revenue per boat c-w tax total cost per boat MR AR B o B* number of boats 24

25 7.4.6 Bandwagon Effect( 日和見効果 ) how standards are adopted? Qwerty: reduction of key-jamming problems Dvorak s keyboard ---> not been adopted impossible to switch the better technology? bandwagon effect <--- network externality ( ネットワーク外部性 ) decision to use Qwerty makes it more attractive for manufacturers to produce Qwerty keyboards, and for others to learn Qwerty three equilibrium: 0, 1, p * (0<p * <1, unstable) Qwerty dominates if initial point is to the right of p * 25

26 1 % Qwerty users at time t +1 p * 0 p * 1 % Qwerty users at time t 26

27 7.5 Pigouvian Taxation market inefficiency <--- divergence between social and private benefits (or costs) ---> appropriate taxes or subsidies( 補助金 ) negative consumption externality PMB(SMB): private (social) marginal benefit PMC: private marginal cost equilibrium: x m <--- intersection of PMB and PMC efficiency :x o <--- intersection of SMB and PMC Pigouvian taxation: PMC <--- PMC + t pay tax equal to the marginal damage 27

28 value PMC t PMC compensation PMB benefit for the neighbor SMB x o x m quantity 28

29 two-consumer two-good case utility fns: U 1 =x 1 +u 1 (z 1 )+v 1 (z 2 ) U 2 =x 2 +u 2 (z 2 )+v 2 (z 1 ) social optimum: u 1 (z 1 )+v 2 (z 1 )=1 u 2 (z 2 )+v 1 (z 2 )=1 producer price is equal to 1 utility max: consumer price q 1 =u 1 (z 1 ), q 2 =u 2 (z 2 ) efficiency: q 1 =1- v 2 (z 1 ), q 2 =1-v 1 (z 2 ) Pigouvian taxes or subsidies t 1 =- v 2 (z 1 ), t 2 =- v 2 (z 1 ) positive or negative different tax rates ---> practical difficulty 29

30 consumer s price individual consumer s maximization max U 1 =x 1 +u 1 (z 1 )+v 1 (z 2 ) s.t. x 1 +q 1 z 1 =w 1 max U 2 =x 2 +u 2 (z 2 )+v 2 (z 1 ) s.t. x 2 +q 2 z 2 =w 2 substitute the constraints into utility functions U 1 =w 1 -q 1 z 1 +u 1 (z 1 )+v 1 (z 2 ) U 2 =w 2 -q 2 z 2 +u 2 (z 2 )+v 2 (z 1 ) du 1 /dz 1 =-q 1 +u 1 (z 1 )=0 u 1 (z 1 )=q 1 du 2 /dz 2 =-q 2 +u 2 (z 2 )=0 u 2 (z 2 )=q 2 to attain social optimality (efficiency) u 1 (z 1 )=q 1 =1-v 2 (z 1 ) u 2 (z 2 )=q 2 =1-v 1 (z 2 ) 30

31 individual tax individual consumer s maximization max U 1 =x 1 +u 1 (z 1 )+v 1 (z 2 ) s.t. x 1 +(1+t 1 )z 1 =w 1 max U 2 =x 2 +u 2 (z 2 )+v 2 (z 1 ) s.t. x 2 +(1+t 2 )z 2 =w 2 substitute the constraints into utility functions U 1 =w 1 -(1+t 1 )z 1 +u 1 (z 1 )+v 1 (z 2 ) U 2 =w 2 -(1+t 2 )z 2 +u 2 (z 2 )+v 2 (z 1 ) du 1 /dz 1 = -(1+t 1 )z 1 +u 1 (z 1 )=0 u 1 (z 1 )=1+t 1 du 2 /dz 2 = -(1+t 2 )z 2 +u 2 (z 2 )=0 u 2 (z 2 )=1+t 2 to attain social optimality (efficiency) u 1 (z 1 )=1+t 1 =1-v 2 (z 1 ) t 1 =-v 2 (z 1 ) u 2 (z 2 )=1+t 2 =1-v 1 (z 2 ) t 2 =-v 1 (z 2 ) 31

32 7.6 Licenses( 許可証 ) licenses ---> direct control of externality tradable licenses ---> greatest benefit require information on the aggregate quantity of externality that is optimal comparison between taxes and licenses information for calculation: equivalent Pigouvian taxes: preferences, production technology licenses: total to the optimal level of externality ---> precise knowledge is needed to determine optimum 32

33 information known when decisions are made when all costs and benefits are known with certainty by gvn and individuals, licenses and taxation are equivalent in their effects Fig 7.8: optimal x o is achieved by tax t or issuing x o licenses If not, no equivalence. gvn must take decisions before the actual costs and benefits are known for sure timing: who chooses what and when gvn DM --> costs and benefits --> individual DM 33

34 pollution abatement( 汚染削減 ) problem PMC: PMC L, PMC H with equal prob benefits are known for sure gvn chooses its policy without knowing PMC ---> act on expected value PMC E ---> z*, t* license scheme: abatement is z* for sure tax: abatement depends on realized cost PMC L ---> z L, PMC H ---> z H licenses and taxation are not equivalent taxation: PMC L ---> excess abatement PMC H ---> underabatement( 過少削減 ) no answer which is better 34

35 value PMC H PMC E PMC L t* SMB z H z* quantity z L 35

36 7.7 Internalization( 内部化 )Merger forming single units out of the parties affected private and social costs become the same industry with production externality internalization ---> single monopolist ---> welfare loss (greater than initial loss) always implies construction of larger agents and a consequent increase in market power agents may not wish to become a single unit c.f. household s consumption externality 36

37 7.8 The Coase Theorem Theorem 3 (Coase theorem) In a competitive economy with complete information and zero transaction costs, the allocation of resources will be efficient and invariant w.r.t. legal rules of entitlement ( 資格 )(property rights 所有権 ). legal rules of entitlement or property rights ownership compensation payments no need for policy intervention except prop. rights private agreements( 合意 ) ---> Pareto efficiency 37

38 implication of Coase theorem equilib. is invariant to how prop. rights are assigned factory polluting the atmosphere of a neighboring house firm has the right to pollute --> house pay compensation C G: cost to the householder of the pollution G>C ---> willing to compensate the firm, externality cease G<C ---> externality is left to continue polluter-pays principle( 汚染者負担原則 ) cost to the firm: C compensation required by the household: G C>G ---> firm is willing to compensate the household C<G ---> firm stops externality outcome is determined by the value G relative to C differences in the final distribution of income 38

39 value pollutee has right compensation by polluter = net loss of pollutee PMC net benefit for polluter PMB SMB x o x m quantity 39

40 value polluter has right compensation by pollutee = net loss of polluter PMC net benefit for pollutee PMB SMB x o x m quantity 40

41 practical relevance of Coase theorem assignment of prop. rights ---> who should pay? transaction costs( 取引費用 ) ---> nonexistence of markets in externalities pollution caused by car emissions( 排出 ) driver must purchase pollution rights from agents affected by car emissions each time that the car is used welfare loss due to waste of resources in organizing the market outweigh any gain from having the market thinness of the market one agent on each side of the market non-competitive behavior bargaining between the two agents 41

42 bargaining by two agents: polluter & pollutee pollutee cannot observe the benefit of pollution B but knows that it is drawn from a distribution F(B) polluter cannot observe the cost of pollution C but knows that it is drawn from a distribution G(C) prop. rights to the pollutee Pareto-efficiency ---> pollution is allowed if B>C pollutee makes a take-it-or-leave-it offer to polluter pollutee requires compensation T>0 polluter only accepts T if B>T ---> prob 1-F(T) max {T} [1-F(T)][T-C] ---> T*>C C<B<T* ---> offer is rejected ---> Pareto-inefficient 42

43 7.9 Nonconvexity( 非凸性 ) externality = source of nonconvexity Fig 7.10: output is driven to zero by an externality regardless of the level of other inputs economy may fail to have an equilibrium with personalized taxes suppose firm receives a subsidy for accepting ext. output level = zero, offer to accept ext. ---> unlimited profits price of accepting ext. =zero ---> not accept any demand for ext. is discontinuous constant returns to scale( 規模に関する収穫一定 ) all inputs including ext. <---> constant level of ext. 43

44 output output externality externality 44

45 45

46 46

Chapter 10: Externalities Chapter 11: Public Goods and Common Resources

Chapter 10: Externalities Chapter 11: Public Goods and Common Resources Econ 23 Introduction to Economics: Micro Chapter : Externalities Chapter 11: Public Goods and Common Resources Instructor: Hiroki Watanabe Spring 213 Watanabe Econ 23 Externality & 11 Public Goods 1 /