Externalities and Efficiency: Market Inefficiencies and Private Bargaining

1. Chapter 35 Externalities • Key Concept: Market equilibrium may not be efficient. • Private bargaining when property right is defined may lead to efficiency.

2. Chapter 35 Externalities • Positive externality: I get pleasure from observing my neighbor’s flower garden. • Negative externality: I cannot sleep when my neighbor plays loud music at 3 am. • These are consumption externality if a consumer cares directly about another agent’s consumption or production.

3. Production externality arises when the production possibility of a firm is influenced by another firm or consumer. • Positive:an apple orchard located next to a beekeeper • Negative:a fishery is affected by the pollutants dumped into its fishing area

4. Key is that there are goods people care about that are not sold on markets. • There is no market for loud music at 3 am, or for the flower garden your neighbor keeps.

5. Earlier we see market is efficient. Now market may not be efficient. • However, other institutions such as the legal system or governemtn intervention may mimic the market mechanism to some degree and achieve efficiency.

6. To see the inefficiency of markets: • Typically, demand only reflects private marginal benefits of consumers and supply private marginal costs of producers. • These could differ from social marginal benefits and social marginal costs.

7. Hence the market equilibrium is not efficient. • Efficiency = zero pollution?

9. Government intervention is not the only solution. • Private bargaining may work. • Key is in defining the property right.

10. Start with an example to illustrate the main considerations. • A smoker and a non-smoker who have preferences over money and smoke. • A smoker would like to smoke as much as he could while a non-smoker would like the air to be as clean as possible.

11. The Edgeworth box is only different that we measure the amount of smoke in one direction. • Money can be divided between the two consumers, so there will be two amounts of money to measure. • But there is only one amount of smoke they must both consume.

12. B is better off when A reduces smoke, not because B gets to consume more smoke, but because both consumes the same amount of smoke and it is a bad for B.

13. Look at the case where both have the same amount of money. • Possible endowments will on the vertical line EE’.

14. One extreme case is where the smoker has the legal right to smoke. • Another extreme is where non-smoker has the legal right of clean air.

15. Fig. 34.1

16. If we start from E, just like before, the endowment point may not be efficient. • X is a Pareto improvement. • How do we achieve that?

17. Market mechanism will do. • U Max? • Market clears?

18. The only problem arises if the property rights are not well-defined. • The practical problems with externalities generally arise because of poorly defined property rights.

19. Externalities do not cause inefficiency when there is a well-defined property right. • Moreover, with the property right defined and mechanisms are in place to allow for negotiations between people, people can trade their rights to produce externalities in the same way that they trade rights to produce and consume ordinary goods.

20. In the example above, the amount of externality will depend on the assignment of property rights. • Compare X with X’. • A is happier with X’ and B is happier with X. Having different distributional consequences, but on the ground of efficiency, they are both satisfactory.

21. There is a special case where the outcome of externalities is independent of the assignment of property rights.

22. This is the case of quasilinear preferences. • Since preferences take the form of m+v(smoke), indifferent curves are parallel to each other along the m axis. • Hence if we have an efficient allocation, moving along the m axis, we get another efficient allocation.

23. Fig. 34.2

24. Coase Theorem: When parties can bargain without cost and to their mutual advantage, the resulting outcome will be efficient, regardless of how the property rights are specified. • Astronger version implies that the efficient amount of the good involved in the externality is independent of the distribution of property rights.

25. Consider a situation involving production externalities. • A steel firm produces s and some pollutants x. • A fishery produces f and is adversely affected.

26. Suppose S’s cost is cs(s, x). • F’s cost is cf(f, x). • Assume that ∆cf/∆x>0 and ∆cs/∆x≤0.

27. In the market equilibrium: • S max pss-cs(s,x) • F max pff-cf(f,x) • FOC • ps= ∆cs(s*,x*)/∆s, 0= ∆cs(s*,x*)/∆x • pf= ∆cf(f*,x*)/∆f. ∆cf(f*,x*)/∆x>0, but S fails to consider this.

28. Fig. 34.3

29. Ways to get efficient levels of pollution. • Internalizing the externalities. • Consider the case where S and F merge. • Then they max pss-cs(s,x)+pff-cf(f,x) and by definition, there is no externality anymore.

30. Then they max pss-cs(s,x)+pff-cf(f,x). • FOC: • ps= ∆cs(s’,x’)/∆s, • 0= ∆cs(s’,x’)/∆x+ ∆cf(f’,x’)/∆x • pf= ∆cf(f’,x’)/∆f.

31. 0= ∆cs(s*,x*)/∆x • -∆cs(s*,x*)/∆x=0 • 0= ∆cs(s’,x’)/∆x+ ∆cf(f’,x’)/∆x • -∆cs(s’,x’)/∆x= ∆cf(f’,x’)/∆x>0

32. Taxing: Key is to make pollution tax t max pss-cs(s,x)-tx so that t=∆cf(f’,x’)/∆x. • -∆cs(s’,x’)/∆x – t = 0 or • ∆cs(s’,x’)/∆x + t = 0 • 0= ∆cs(s’,x’)/∆x+ ∆cf(f’,x’)/∆x • But we have to know the correct t.

33. Another interpretation is there is a missing market. • Suppose the fishery has the right to clean water.

34. S max pss-cs(s,x)-qx • F max pff-cf(f,x)+qx • FOC • -∆cs(s’,x’)/∆s=q= ∆cf(f’,x’)/∆f.

35. Sometimes if the government has a pretty good idea about how much pollution to reduce, then the problem becomes to find the most cost effective way to achieve the targeted reduction.

36. A practical measure is the pollution vouchers. • Suppose two polluting firms, each having emission quotas x and x’. • The cost of achieving the quota is c1(x) and c2(x’).

37. Hence we need to solve: • Minx,x’ c1(x)+c2(x’) s.t. x+x’=X. • So at optimum, the marginal cost of each firm should equal.

38. If we allow firms to trade pollution vouchers. • Suppose we first assign some quotas y and y’ where y+y’=X to each firm. • If |c1’(y)|>|c2’(y’)|, then increasing one unit of emission saves the cost of firm 1 by |c1’(y)| while reducing one unit of emission costs firm 2 by |c2’(y’)|.

39. Alternatively, if there is a market for the emission quota (say the price is p), then 1 should compare |c1’(y)| to p. • If |c1’(y)|> p, then buying one unit of quota costs only p but saves the emission cost by |c1’(y)|. Hence worthwhile doing.

40. So 1 will be the buyer and 2 will be the seller. • If market clears, then what 1 is willing to buy must equal what 2 must be willing to supply. • Moreover, their MCs both equal to the common price.

41. Tragedy of the commons • c is number of cows • f(c) is the milk produced if c cows grazed on the commons. • a is the cost to buy a cow

42. Tragedy of the commons • c is number of cows • f(c) is the milk produced if c cows grazed on the commons. • a is the cost to buy a cow

43. To maximize the total wealth of the village, we should • max f(c) – ac Marginal • But each individual villager • considers f(c)/c – a, so as long as f(c)>ac, it is worth doing… Average • Overfishing is another example.

45. Chapter 35 Externalities • Key Concept: Market equilibrium may not be efficient. • Private bargaining when property right is defined may lead to efficiency.