5. Externalities (2016)Apunte Inglés
Positive and negatve externalities.
Vista previa del texto
- Externalities defined and classified: When you produce, you may produce some negative
externalities (M), pollution. This affect to other people, as the fisherman who can’t get any fishes
because they are all death.
- Market failure: Qm > Q* - Correct negative externalities: - Pigouvian Taxes: If you produce externalities, you pay for them.
- Pigouvian Subsidies: If you reduce you’re externalities, you’ll be paid for.
- Auctioning Pollution Permits.
- Bargaining (Coase theorem): Qm=Q* - Merges.
“Market mechanism” Qm M=M(Q,T) (fixed technology case).
max π(Q)=B(Q)-PC(Q) Q Qm so that MB(Qm)=MPC(Qm) “Social Optimum” Q* max NSW(Q)=B(Q)-[PC(Q)+EC(Q)] Q GSW(Q) SC(Q) * * * Q such that MB(Q )=MPC(Q ) + MEC(Q*) MSC NSW=Net Social Wage EC=External Cost MEC:Marginal External Cost MPC:Marginal Private Cost MSC:Marginal Social Cost.
When you introduce the government to solve this problem, you’ll have a Utility Possibility Surface, with 3 agents (Firm, Fisherman and Government [tax payers]).
So now, you’ll not be sure all the agents will be better off. If you put taxes to the firm, you’ll achieve a Pareto Efficient point, but the firm will be worse of.
The other way round, if you subsidize the firm, the tax payers will be worse off.
- Pigouvian taxes (τ): If the rights are well defined, the tax will work. If the river belongs to the firm, the tax will be paid by the fisherman. And the other way round. If the river is of the fisherman, the firm will pay the tax, interiorizing the externality. So now: π(Q)=B(Q) - PC(Q) - τQ Qmτ* so that MB(Qmτ*)=MPC(Qmτ*) + τ* So, the MPC of the firm will move. The correct tax will be the tax that make Qm=Q*.
τ* = MEC(Q*).
R= τ* Q* - Pigouvian Subsidies (Θ): Subsidies encourage to produce more. But a Pigouvian Subsidy is a subsidy design to produce less. The firm receive a subsidy equivalent to a fixed number the production of last year, and this subsidy is reduced in this fixed number for an increased of your production. In other words, the subsidy is Θ times the difference between the past production and your new production.
s= ΘQm - ΘQmΘ = Θ(Qm - QmΘ)= Θ∆Q π(Q)=B(Q) - PC(Q) + Θ*(Qm - QmΘ*) QmΘ* so that MB(QmΘ*) -Θ* =MPC(QmΘ*) - Auctioning Pollution Permits: Only those who pay the permits, can pollute the river. With this, you create a market for the externality, leading it to a market equilibrium. This point will be efficient.
- Regulation: The government decides a fixed amount of M, and decides that all the firms will consume the same amount of M (MA=MB=M/2).MA=MB=M=2M/2=M/2 + M/2. MB - M/2=M/2 - MA.
If you allow the firms to buy the permits in a market system, the social welfare gain will be positive. So, the regulation system is not efficient.
As we can see: if we transfer part of the firm A permits to firm B (MA/2), 4 will be the lost of firm A, and 2+3 the gain of firm B.
Geometrically, 4 is the same as (2+3)/2, so the lost of firm A is compensated by part of the gain of firm B. Now, the other part of (2+3)/2 is the same as 1, so finally, 1+ +3 is the total social gain.
A system with regulation + permits exchange will be efficient, as the auctioning pollution permits, and the pollution effect will be the same, but distributional effects will be completely different.
- Mergers: In the other case, we have the pollute firm and the fisherman, affected by the externality. Now, let’s see in an only firm. It sells chemical products and fishes, so doesn’t want to pollute the river more than necessary, or its fishes would die. The externality is internalized.
max π (Q,F)=B(Q) - PC(Q) + B(F) - PC(F) - EC(Q).
- Coase Theorem: Consider property rights (the river belongs to the firm owner or to the fisherman) and the engage in bargaining. If they can engage in bargaining at 0 cost, the Coase theorem says they will achieve a Pareto efficient point. This happens and don’t matter if the owner of the river is the firm owner or the fisherman.
In other words: If: - Property rights are well defined and can be legally executed.
- Parties can bargain at a small (zero!) transaction cost.
Then: - Qmb,firm will be Pareto-efficient.
- Qmb,fisherman will be Pareto-efficient.
And if “income effects can be assumed away” then Qmb,firm=Qmb,fisherman =Q* However, distributive effects remains indeterminate.
The river belonging to the fisherman: Q*=Qmb,fisherman such that MB(Qmb,fisherman) - MPC(Qmb,fisherman)=MEC(Qmb,fisherman) MB(Qmb,fisherman) = MPC(Qmb,fisherman) + MEC(Qmb,fisherman) = MSC (Qmb,fisherman).
MB-MPC=maximum amount of money is willing to pay.
MEC-Q exe=minimum amount of money the fisherman is willing to accept.
The river belonging to the firm: Q*=Qmb,fish such that MB(Qmb,fish) - MPC(Qmb,fish)=MEC(Qmb,fish) MB(Qmb,fish)=MPC(Qmb,fish)+MEC(Qmb,fish)=MSC (Qmb,fish).
MB-MPC=minimum amount of money the firm is willing to accept.
MEC-Q exe=maximum amount of money the fisherman is willing to pay.
2<side payment from the fisherman to the firm<4 In the case were the river belongs to the fisherman, we can divide the cost in a Monetary Cost (the fishes which die) and a No-Monetary Cost (the fisherman betraying their ancestors).
- Variable Technology Case: M=M(Q,T) (abatement/reduction in pollution)A=M-M M=with T, perhaps 0.
max NSW(Q)=B(Q) - [PC(Q,A) + EC(Q,A)] Q,A SC(Q) MPCQ=∂PC/∂Q ≥0 MPCA=∂PC/∂A >0 MECQ=∂EC/∂Q ≥0 MECA=∂EC/∂A <0 F.O.C. Q –> MBQ(Q*)=MPCQ (Q*,A*) + MECQ(Q*,A*) A –> MPCA(Q+,A*) - MECA (Q*,A*)=0 -MECA(Q*,A*)=MPCA(Q*,A*) =MB of Abatement!!!! EC(Q,A)=\PC(Q,A)\ MEC()=MPC() Positive Externalities - The Coase theorem can be completely apply to positive externalities.
- Pigouvian Subsidy: ∆Q –> ∆S.
Qmø, MPB(Q) + Ø = MC (Qmø).
Ø*=MPB(Q*) => Optimal Pigouvian Subsidy.
Can we achieve Q* paying a smaller subsidy? Yes, but it would be difficult to implement.
Qm parents are sending their children to school without any subsidy, so we’re only interested in increasing a small amount of school places (between Qm and Q*).
We will design a subsidy focused on this amount of school places. S=Ø*(Q-Qm).
But the parents who doesn’t receive the subsidy will be angry, so this will not be incentive compatible.