Coase Theorem Explained: Bargaining, Property Rights, and Transaction Costs

The Coase theorem says that if property rights are clearly defined and transaction costs are low, the people involved in an externality will bargain their way to the efficient outcome, and they reach that same outcome no matter who holds the right at the start. The assignment of rights changes who pays whom, but it does not change how much of the harmful activity takes place.

The idea comes from the economist Ronald Coase, and it reframes the problem of externalities. Instead of asking "how should the government stop the polluter?", it asks "what is stopping the two sides from making a deal?" When bargaining is too costly, as it usually is when many people are affected, governments turn to taxes or permits instead.

The conditions behind the theorem

The Coase result needs two conditions, and the third point below is what usually makes the second one true:

1. Clear property rights. Someone must own the right in question: either the right to pollute or the right to be free from pollution. If nobody knows who holds the right, nobody knows who should pay.

2. Low transaction costs. Finding the other party, negotiating, writing a contract, and enforcing it must cost little compared with the gains from the deal.

3. Few, identifiable parties. In practice this is what keeps transaction costs low. Two neighbors can talk; a whole city cannot.

When these hold, any inefficient outcome leaves money on the table. One side values the change more than the other side values the status quo, so a payment exists that makes both better off, and rational parties will find it. That is why the efficient outcome appears without a Pigouvian tax or a regulator.

Coase also stressed that harm is reciprocal. A factory's smoke harms a laundry, but stopping the smoke harms the factory. The efficient answer is whichever choice costs society less in total, not automatically "make the polluter stop."

Worked example: a factory, a laundry, and four shifts

A factory sits next to a laundry. The factory can run 0 to 4 shifts per day. Each shift earns extra profit for the factory, and each shift's smoke dirties clothes at the laundry, causing $150 of damage per shift.

### Finding the efficient outcome

The efficient number of shifts maximizes joint surplus, which is total profit minus total damage. Run a shift only when its marginal profit exceeds its marginal damage. That gives 3 shifts.

Check by comparing totals:

• 2 shifts: profit 400 + 300 = 700, damage 2 × 150 = 300, joint surplus 700 - 300 = 400.
• 3 shifts: profit 700 + 200 = 900, damage 3 × 150 = 450, joint surplus 900 - 450 = 450.
• 4 shifts: profit 900 + 100 = 1,000, damage 4 × 150 = 600, joint surplus 1,000 - 600 = 400.

Three shifts is the best total. Now see what bargaining produces under each assignment of rights.

### Case A: the laundry has the right to clean air

Without permission the factory runs zero shifts. But the factory can buy permission. For each shift, the laundry accepts any payment of at least $150 (its damage), and the factory is willing to pay up to that shift's marginal profit.

• Shift 1: factory will pay up to $400, laundry needs $150. Deal.
• Shift 2: up to $300 vs $150. Deal.
• Shift 3: up to $200 vs $150. Deal.
• Shift 4: up to $100 vs $150. No deal, since the factory will not pay more than the shift earns.

Result: 3 shifts. Suppose they settle at $180 per shift. The factory nets 900 - (3 × 180) = 900 - 540 = $360. The laundry receives 540 and suffers 450 of damage, netting 540 - 450 = $90. Joint surplus: 360 + 90 = $450.

### Case B: the factory has the right to pollute

Without a deal the factory runs all 4 shifts, earning 1,000 while the laundry loses 600. Now the laundry is the buyer: it can pay the factory to cut shifts. For each shift, the laundry will pay up to $150 (the damage it avoids), and the factory accepts anything at least equal to that shift's marginal profit.

• Shift 4: laundry will pay up to $150, factory needs $100. Deal, so shift 4 is dropped.
• Shift 3: laundry will pay up to $150, factory needs $200. No deal, so shift 3 stays.

Result: 3 shifts again. Suppose they settle at $125 to drop shift 4. The factory nets 900 + 125 = $1,025. The laundry suffers 450 of damage and pays 125, a net loss of 450 + 125 = $575. Joint surplus: 1,025 - 575 = $450.

### Comparing the two cases

The quantity is identical and the joint surplus is identical. Only the distribution changes: whoever holds the right gets paid. That is the Coase theorem in one table. The specific prices ($180 and $125) are just one possible split; any price inside each bargaining range gives the same 3 shifts and the same $450 total.

Why transaction costs break it

Now add one realistic friction. Suppose arranging any deal (meeting, hiring a lawyer, writing and enforcing a contract) costs $60.

• In Case B, dropping shift 4 creates a gain of only 150 - 100 = $50. That is less than the $60 cost of negotiating, so nobody bothers. The factory runs 4 shifts.
• In Case A, buying permission for 3 shifts creates a gain of 450 compared with zero shifts, which is far more than $60. The factory negotiates and runs 3 shifts.

Same factory, same laundry, same damage, but the number of shifts now depends on who holds the right: 3 in Case A, 4 in Case B. Counting the $60 as a real cost, Case B's 4 shifts gives $400 of joint surplus (1,000 - 600) against $390 in Case A (450 - 60), so skipping a deal that would cost $60 to gain $50 is the sensible choice here. Once transaction costs are large compared with the gains from trade, the initial assignment of rights changes the outcome, not just who pays whom. When those costs block a deal worth a lot, as with many affected parties, the result can be well short of efficient. That is why Coase argued the law should assign rights where bargaining is least needed.

Why many parties break it

The example has two parties. Real pollution rarely does. A power plant's emissions might affect hundreds of thousands of people, which creates three problems:

• Free riders. If residents must pay the plant to cut emissions, each resident hopes the others will pay, since everyone breathes the cleaner air either way. This is the free-rider problem from public goods.
• Holdouts. If the plant must buy permission from every resident, any single resident can refuse in order to extract a bigger share, and the deal stalls.
• Measuring and splitting damages. Each resident is harmed by a different amount and from many sources at once, so working out who owes what is costly in itself.

All three are transaction costs, and they grow with the number of people. Shared resources with no clear owner, like ocean fisheries, add the missing first condition as well, which is how the tragedy of the commons arises.

When governments use taxes or permits instead

When bargaining cannot work, the government steps in with one of three main tools:

The tax route is covered in depth in Pigouvian tax explained. Permits are a partly Coasean idea: the government creates a clear, tradable property right to pollute, then lets the market do the bargaining among firms, which is how cap and trade works. For a direct side-by-side, see the Coase theorem vs Pigouvian tax comparison, and for the full set of market failures, the market failure module.

A note for college students: income effects

The strong version of the theorem, that the outcome is identical under either assignment, also assumes no income or wealth effects. If holding the right makes one party much richer, that party may value the activity differently, and the efficient quantity can shift slightly. Experiments also suggest people value something they already own more than something they would have to buy, which can widen the gap between what they will accept and what they will pay. Intro courses usually set these aside; intermediate courses often raise them.

Common mistakes

• Saying the outcome is the same, so the assignment does not matter. The quantity is the same, but who pays whom changes completely. Assignment decides distribution.
• Forgetting the conditions. The theorem only holds with clear property rights and low transaction costs. State both on any exam answer.
• Assuming the efficient outcome is zero pollution. Efficiency means producing until marginal benefit equals marginal damage. In the example, 3 polluting shifts is efficient.
• Applying it to large-scale pollution. With many affected parties, free riding and holdouts make bargaining fail, which is why taxes and permits exist.
• Thinking the polluter always pays. Under the Coase theorem the victim may pay the polluter, as in Case B.

To see what the overproduction looks like on a graph, try the externality sandbox.

See it move

Make it move

A negative externality: the market produces more than the socially optimal quantity. Tap it to drag the curves, open the full version, or put it on your own site free, or turn it into a five-minute class activity.