Externalities © Allen C. Goodman 2009

Ideal Market Processes are desirable if … We accept the value judgment that “personal wants of individuals should guide the use of society’s resources.” Three structural characteristics are necessary: –All markets are competitive. –All participants are fully informed. –All valuable assets can be individually owned and managed without violating the competition assumption. If these hold, government’s best role involves determining an income distribution, providing rules of property and exchange and enforcing competition.

Markets If markets behave properly, COST of item equals the PRICE that buyers are willing to pay. Value to consumer = Value to producer With competition, in the short run, the firm produces to where: MC = MR = P Value of resources in production = MR = Value to consumer We can do a little bit of geometry to show this:

Typical Firm Diagram Mkt.Firm Firm qEconomy Q P P* D S MC AC MR

Pareto Efficiency Context of trade. One can’t make oneself better off, without making someone else worse off. We usually do this with an exchange Edgeworth Box. Abner Belinda Abner’s Preferences Belinda’s Preferences

Pareto Efficiency Start at Point A. Is this an Equilibrium? Abner Belinda No, they can trade Belinda can be better off. A So can Abner. B

Pareto Efficiency We can plot similar points, which we recognize as a “contract curve” Abner Belinda And so on. A B

Pareto Efficiency We must recognize that point X is Pareto Optimal. Abner Belinda So is point Y. A B X Y

Utility Possibility Frontier We can plot Abner’s utility against Belinda’s Utility. Why do we draw it this way? Abner’s Utility Belinda’s Utility X Y What if we want a perfectly egalitarian society? Does equal utility mean equal allocations?

So, are markets always great? Externality – A cost or benefit in production or consumption that does NOT accrue to the producer or the consumer of the commodity. No single person can own or manage air or water. Consider a person who wants to heat a house with a wood fire. 1.More wood  more heat. 2.W/ more heat, willingness to pay for additional heat . 3.More wood and more heat  more smoke

Heat and smoke Individual sees price of wood as P 1. Compares price to marginal benefit (demand curve). Individual purchases quantity A of wood. BUT… Heat, smoke $ MC MSC D = WTP P1P1 A Wood  Smoke. Assume that more burning  more smoke. We get MSC curve B

Heat and smoke If we go past B the marginal benefits are: Heat, smoke $ MC MSC D = WTP P1 A Wood  Smoke. Assume that more burning  more smoke. We get MSC curve B Inc. Ben. Inc. Costs If we go past B the marginal costs are:

Heat and smoke If we go past B we get societal losses. Heat, smoke $ MC MSC D = WTP P0P0 P1P1 AB Inc. Ben. Losses This is a NEGATIVE externality. How to remedy? A tax of P 0 – P 1. Called a Pigovian Tax, after, Arthur Pigou early 20 th century economist Arthur Pigou

Tax Heat and smoke Tax of P 0 – P 1. Heat, smoke $ MC MSC D = WTP P0P0 P1P1 AB Inc. Ben. Losses Tax Has nothing (necessarily) to do with cleaning up the air. We must set up a market for a resource that no one specifically owns. Think of it as taking revenues and refunding it back to population. Who gains? Who loses?

A general problem – the Lake Externalities Equations n industrial firms Y i = output P i = price x i units of labor at wage W Production Function Y i = Y i (z i, x i, q), where: z i = waste discharges q = quality of lake L = assimilative capacity of Lake q = Q (z 1, z 2,..., z n, L)

Society’s Objective Societal Objective: Max U =  P i Y i (x i, z i, q) -  W x i - C (L) - [q - Q (z 1, z 2,..., z n, L)] P i is the willingness to pay (related to utility of goods). P i Y i is the amount spent (related to utility of goods). is the valuation of the extra unit of environmental quality. First Order Conditions:  U /  x i = P i Y i xi - W = 0.(a)  U /  z i = P i Y i z i + Q zi = 0(b)  U /  q =  P j Y j q - = 0(c)  U /  L = Q L - C' = 0(d) Public Good

Society’s Objective First Order Conditions:  U /  x i = P i Y i xi - W = 0.(a)  U /  z i = P i Y i z i + Q zi = 0(b)  U /  q =  P j Y j q - = 0(c)  U /  L = Q L - C' = 0(d) For Firm 1: P 1 Y 1 x1 = W P 1 Y 1 z1 = - Q z1 P 1 Y 1 q = Eq'm: P 1 Y 1 z1 = [P 1 Y 1 q ] [- Q z1 ] z1z1 $ P 1 Y 1 z1 [P 1 Y 1 q ] [- Q z1 ] z* 1

Amount Collected Society’s Objective First Order Conditions:  U /  x i = P i Y i xi - W = 0.(a)  U /  z i = P i Y i z i + Q zi = 0(b)  U /  q =  P j Y j q - = 0(c)  U /  L = Q L - C' = 0(d) For Firm 1: P 1 Y 1 x1 = W P 1 Y 1 z1 = - Q z1 P 1 Y 1 q = z1z1 $ P 1 Y 1 z1 [P 1 Y 1 q ] [- Q z1 ] z* 1 For Society: P 1 Y 1 x1 = W P 1 Y 1 z1 = - Q z1  P j Y j q = Optimum: P 1 Y 1 z1 = [P 1 Y 1 q +  2,n P j Y j q ] [- Q z 1 ] > [P 1 Y 1 q ] [- Q z 1 ] z* 1 TAX

So … Societal optimum dictates that each firm produce less than in an autarkical system. Remedy, again, would be a tax. Once again, a situation where ownership is not well-defined and one’s actions affect others.

Coase Theorem The output mix of an economy is identical, irrespective of the assignment of property rights, as long as there are zero transactions costs. Does this mean that we don’t have to do pollution taxes, that the market will take care of things? Some argue that it’s not really a theorem. It does set out the importance of transactions costs. Let’s analyze.

Externalities and the Coase Theorem Production of Y decreases production of X, or F Y < If we maximize U (X, Y) we get:

Planning Optimum If we maximize U (X, Y) we get: If we maximize U (X, Y) w.r.t. L x and K x, we get: Does a market get us there?

Planning optimum  Market Optimum Does a market get us there? If firms maximize conventionally, we get:

So? Society’s optimum Market optimum Since F Y < 0, p Y /p X is too low by that factor. Y is underpriced.

Coase Theorem The output mix of an economy is identical, irrespective of the assignment of property rights, as long as there are zero transactions costs. Suppose that the firm producing Y owns the right to use water for pollution (e.g. waste disposal). For a price q, it will sell these rights to producers of X. Profits for the firm producing X are: Reduced by paying to pollute

Coase Theorem We know that q = -p X F Y α  1 gets to Y; Like the iceberg model

Coase Theorem We know that q = -p X F Y

Change the ownership - X owns We know that q = -p X F Y / 

If  = 1 We are at a Pareto optimum We are at same P O. If  is close to 1 We may be Pareto superior We are not necessarily at same place. Where we are depends on ownership of prop. rights.

Remarks These are efficiency arguments. Clearly, equity depends on who owns the rights. We are looking at one-consumer economy. If firm owners have different utility functions, the price-output mixes may differ depending on who has property rights.

If X holds, Y pays this muchIf Y holds, X pays this much Graphically T = T x + T y q Y’s supply (if Y holds) X’s demand (if Y holds) -p x F Y P y -r/G K = P y -w/G L T*

If X holds, Y pays this muchIf Y holds, X pays this much But, with transactions costs  T = T x + T y q Y’s supply (if Y holds) X’s demand (if Y holds) -p x F Y P y -r/G K = P y -w/G L T* Y gets this much qq X gets this much qq The equilibria are not the same!