Coase Theorem and the Tragedy of the commons

Transcription

1 Coase Theorem and the Tragedy of the commons

2 Coase Theorem Introduction Ronald Coase s seminal essay, The Problem of Social Cost (1960), is one of the most cited articles in the economics and legal literatures, and much of this attention is owed to a proposition that has come to be known as the Coase Theorem. He noted that negotiations among a ected parties would result in an e cient outcome under the standard assumptions of competitive markets (especially, that the costs of transacting are zero), as long as rights are well-de ned. Speci cally, it is necessary to know whether the damaging business is liable or not for damage caused.

3 Information and the Coase Theorem Introduction What are the causes of imperfections in bargaining? We cannot assume that all mutually bene cial contracts are signed, unless we assume perfect information. Transaction Costs

4 Problem A chemical producer dumps toxic waste into a river. The waste reduces the population of sh, reducing pro ts for the local shing industry by $100, 000 per year. The rm could eliminate the waste at a cost of $60, 000 per year. The local shing industry consists of many small rms. Using the Coase Theorem, explain how costless bargaining will lead to a socially e cient outcome, regardless of whether the property rights are owned by the chemical rm or the shing industry. Why bargaining not be costless? How would your answer to part (a) change if the waste reduces the pro ts for the shing industry by $40, 000? (Assume, as before, that the rm could eliminate the waste at a cost of $60, 000 per year)

5 Solution Assume property rights are owned by the Chemical rm, the local shing industry has two options 1 Pay to the chemical producer $60, 000 to eliminate the toxic waste or 2 Accept the loss in pro ts $100, 000 per year 3 The local shing industry will eliminate the toxic waste ($60, 000) Assume property rights are owned by the local shing industry, the Chemical rm has two options 1 Compensate the local shing industry by $100, 000 per year or 2 Clean up the waste, the cost is $60, Hence the Chemical rm will also choose to eliminate the toxic waste

6 Why bargaining not be costless? Because the waste harms many shermen, it may not be easy to organize them to bargain about compensation. Organizing the shermen may be costly. In addition, if shermen and the rm have di erent perception regarding the cost of the externality, they might not reach an e cient solution

7 The Tragedy of the Commons The Tragedy of the Commons (Garrett Hardin, 1968) rst published in the journal Science. Is a dilemma arising from the situation in which multiple individuals, acting independently, will ultimately deplete a shared limited resource, even when it is clear that it is not in anyone s long-term interest for this to happen. Consider an agricultural-village in which the villagers graze their cows on a common eld. We want to compare two allocations.

8 The Tragedy of the Commons Two allocations: 1 The rst is the private ownership solution where someone owns the eld and decides how many cows should graze there 2 The second is the case in which the eld is owned in common by the villagers and access to it is Assumptions of the model: $a cost of a cow f (c) is the value of milk produced by c cows c is the number of cows

9 First Case: Well de ned Property Rights In this case the villager wants to maximize her total wealth or total net bene ts π(total net bene ts) = f (c) c a Therefore, in order to maximize the total amount of wealth we will set up the following problem: maxπ(total net bene ts) c = f (c) c a dπ() da = f 0 (c) a = 0 f 0 (c) = a where f 0 (c) is the marginal product of an additional cow and c is the marginal cost Villager would pay to put another cow on if : f 0 (c) a Villager would pay to take one o if : f 0 (c) < a

10 Second Case: No Property Rights! Each villager has a choice of grazing a cow or not grazing on. Therefore, it will be pro table to graze a cow as long as: Output generated by the cow is greater than the Cost of a Cow or f (c) > c a Suppose there are c cows currently being grazed, so that the current output per cow will be: f (c) c hence from our above inequality, we need that the average product is greater than the cost of a cow f (c) c > a

11 Second Case: No Property Rights! Another way to derive this result is to appeal to free entry. If it is pro table to graze a cow on the common eld, villagers will purchase a cow. They will stop adding cows to the common only when the pro ts have been driven to zero, that is π(total net bene ts) = f (c) c a = 0 Hence solving for a f (c) = a c Therefore, unlimited access destroys the incentives to conserve.

12 The Tragedy of the Commons