Academic journal article American Economist

Coase Theorems 1-2-3

Academic journal article American Economist

Coase Theorems 1-2-3

Article excerpt

Joseph Felder [*]

Abstract

Develops a pedagogical model so simple and powerful that students practically discover the three Coase Theorems for themselves. Three Theorems? Yes. Theorem One: In the absence of transaction costs, the initial allocation of rights between parties does not matter. Theorem Two: In the presence of transaction costs, the initial allocation of rights may matter; one initial allocation may be superior to another. Theorem Three: In the presence of transaction costs, some distributions of limited rights may be superior to any that the parties could arrive at themselves through trade.

"The Problem of Social Cost" [1] by Ronald Coase is a very famous article and is among the most cited economics articles of all time. [2] Coase's main arguments are ones every economics student and law student should be familiar with.

This paper uses simple graphical techniques to bring Out those main points. The approach taken here, as in Coase's original article, is thoroughly Marshallian, complete with all the weaknesses of that approach. One well known weakness is the omission of income effects. Another is a disregard for the distribution of costs and benefits. It is assumed that social welfare is increased by an action if the benefits exceed the costs, even when the benefits go to one party and the costs are borne by others. It is assumed that social welfare is increased by an action if the gains to the gainer are so great that the gainer could compensate the losers and still come out ahead. There is no requirement that the gainer actually compensate the losers. Thus, the losers might well be left worse off.

As in Coase's original article, we assume that all markets are perfectly competitive or, at least, behave as if they were perfectly competitive. In our reworking of this material, we benefited greatly from Coase's follow-up article, "Notes on the Problem of Social Cost." [3]

I. The Problem to be Examined

There are many firms in the neighborhood. They have a choice of product mixes, production techniques, and levels of output. Some are cleaner than others, but the cleaner product mixes, production techniques, and output levels are more costly. The firms want to avoid any added cost, if possible. Suppose the dirtiest strategy dirties 12 cubic feet of air per production period and the cleanest is perfectly clean.

Look at Figure 1. The 12 cubic feet of air the firms would befoul are shown along the horizontal axis. Those 12 cubic feet of air are the focus of this paper. They are there throughout. The only question is: How many of these 12 cubic feet are dirty and how many are clean?

The horizontal axis answers that question. Twelve dirty cubic feet of air means zero clean cubic feet; 4 dirty cubic feet means 8 clean cubic feet; and zero dirty cubic feet means 12 clean cubic feet.

The curve labeled DEMAND shows the firms' demand for dirty air. The area under DEMAND shows the profit added by dirtying various amounts of air. Dirtying 4 cubic feet, as a byproduct of their other activities, adds BC dollars to the firms' profits, and dirtying 12 cubic feet adds BCD dollars to the firms' profits.

Starting with the profit maximizing amount of dirty air, 12 cubic feet, and reading from right to left, DEMAND shows the firms' marginal cost of abatement or abstention. The area under DEMAND shows the profit foregone when a cleaner strategy is chosen. Dirtying only 4 cubic feet of air means foregoing D dollars in potential profit, and dirtying no air at all means foregoing BCD dollars in profit.

Many people are subjected to the air dirtied by the firms. We call them the firms' "neighbors." The curve labeled MC shows the marginal cost dirty air imposes on the neighbors. The area under MC shows the total cost, or welfare loss, imposed on the neighbors by various amount of dirty air. When the firms dirty 4 of the 12 cubic feet, they impose a cost of C dollars on the neighbors, and when the firms dirty all 12 cubic feet, they impose a cost of CDE dollars on the neighbors. …

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