A competitive market maximizes total surplus (Total Surplus and Deadweight Loss) when everyone affected is a buyer or a seller. When a cost falls on someone outside the deal, that is no longer true.
Key idea
A negative externality is a cost imposed on bystanders, such as pollution from a factory or noise from a highway. The marginal social cost is $MSC = MPC + MEC$: the private cost (supply) plus the marginal external cost. The market produces where demand meets private supply, more than the efficient quantity, where demand (marginal social benefit) meets MSC. The deadweight loss is the triangle between MSC and demand from the efficient quantity out to the market quantity.
Why it works
Sellers decide how much to make by comparing price with their own costs. The harm to neighbors doesn't show up in their costs, so they act as if it were zero. For units past the efficient quantity, the true cost to society (private cost plus the harm) is higher than what buyers would pay; producing them destroys surplus. That's the deadweight loss, and it sits beyond the efficient quantity, because the problem is too much, not too little.
Worked example: Too much of a polluting good
Demand for a chemical is $P = 20 - Q$. The private marginal cost is $MPC = 2 + Q$, and each unit causes \$4 of harm downstream. Find the market quantity, the efficient quantity and the deadweight loss.
- Market: $20 - Q = 2 + Q$, so $Q_m = 9$.
- Social cost: $MSC = 2 + Q + 4 = 6 + Q$. Efficient: $20 - Q = 6 + Q$, so $Q_e = 7$.
- At $Q_m = 9$ the gap between MSC and demand is $(6 + 9) - (20 - 9) = 4$.
- $DWL = \tfrac{1}{2} \times 4 \times (9 - 7) = \$4$.
Answer: Market 9, efficient 7, DWL \$4.
Worked example: Who bears the cost?
In the example, what are the total external costs at the market quantity?
- Each unit causes \$4 of harm, and 9 units are made.
- External cost: $9 \times \$4 = \$36$, borne by people downstream who are not part of the trade.
Answer: \$36.
Common mistake
Putting the deadweight loss on the wrong side of the efficient quantity, or thinking the market makes too little of a good that pollutes. Ignoring a cost makes production look cheaper than it is, so the market makes too much. Check: the market quantity is where the lower, private curve crosses demand, which is to the right of where the higher, social curve does.