Chapter 34 Externalities 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. Hence the market equilibrium is not efficient. Government intervention is not the only solution. Private bargaining may work. Key is in defining the property right.

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. The Edgeworth is only different that we measure the amount of smoke in one direction.

Look at the case where the smoker has the legal right to smoke and another extreme where non-smoker has the legal right of clean air. Externalities do not cause inefficiency when there is a well-defined property right. Moreover, with the property right defined, bargaining may lead to efficiency.

Fig. 34.1

In the example above, the amount of externality will depend on the assignment of property rights. There is a special case where the outcome of externalities is independent of the assignment of property rights. 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. 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.

Fig. 34.2

Consider a situation involving production externalities. A steel firm produces s and some pollutants x. A fishery produces f and is adversely affected. Suppose S’s cost is c s (s,x) and F’s cost is c f (f,x). Assume that ∆c f /∆x>0 and ∆c s /∆x≤0. In the market equilibrium, S max p s s- c s (s,x), F max p f f-c f (f,x). FOC:p s = ∆c s (s*,x*)/∆s, 0= ∆c s (s*,x*)/∆x and p f = ∆c f (f*,x*)/∆f. ∆c f (f*,x*)/∆x>0, but S fails to consider this.

Fig. 34.3

Ways to get efficient levels of pollution. Internalizing the externalities: Consider the case where S and F merge. Then they max p s s-c s (s,x)+p f f-c f (f,x) and by definition, there is no externality anymore. FOC: p s = ∆c s (s’,x’)/∆s, 0= ∆c s (s’,x’)/∆x+ ∆c f (f’,x’)/∆x and p f = ∆c f (f’,x’)/∆f. Taxing: Key is to make pollution tax t (p s s-c s (s,x)-tx) so that t=∆c f (f’,x’)/∆x.

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. 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 c 1 (x) and c 2 (x’). Hence we need to solve:

Min x,x’ c 1 (x)+c 2 (x’) s.t. x+x’=X. So at optimum, the marginal cost of each firm should equal. 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 |c 1 ’(y)|>|c 2 ’(y’)|, then increasing one unit of emission saves the cost of firm 1 by |c 1 ’(y)| while reducing one unit of emission costs firm 2 by |c 2 ’(y’)|.

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