External costs, MPC and MSC, why the free market over-produces goods that pollute, and the welfare loss triangle. Through Lough Neagh.
In the summer of 2023, huge blooms of blue-green algae covered Lough Neagh, the UK’s largest lake, which supplies around 40% of Northern Ireland’s drinking water. Dogs were warned off the shore and fishing and boat businesses suffered. Scientists pointed to nutrients running off farmland and from sewage, made worse by a warm summer and invasive zebra mussels.
The farmers and water treatment that release nutrients do not pay for the damage. Who does, and what does that do to how much is produced?
Sources: Northern Ireland Environment Agency; NI Water (2023).
An externality is a cost or benefit to a third party, someone outside the transaction, that is not reflected in the price. A negative externality is an external cost.
Social cost = private cost + external cost
Marginal private cost (MPC) is the cost to the producer of one more unit: the supply curve. Marginal social cost (MSC) adds the external cost. Marginal private benefit (MPB) is the benefit to the buyer: the demand curve.
Assumptions: firms and consumers act in their own interest and ignore third parties; there are no external benefits here, so MPB = MSB; the external cost per unit is constant.
A factory dumps waste into a river.
It costs the factory nothing, but fishing businesses and towns downstream pay to clean the water.
Compared with what is best for society, the factory produces:
The factory decides output using only its own (private) costs. The cost it imposes on others is left out, so it produces more than society would choose. That gap is a market failure.
The free market. Buyers look at their private benefit, demand. Sellers look at their private cost, supply. The market settles where MPC = MPB, at Q1 and P1.
Each unit also imposes a cost on third parties: polluted water, algae, lost fishing. Add it to MPC and you get marginal social cost, MSC, above MPC. The vertical gap is the external cost of each unit.
Check: Why does the MSC curve lie above the MPC curve?
MSC = MPC + external cost. The vertical gap is the external cost per unit.
Society is best off where marginal social cost equals marginal social benefit: MSC = MSB, at Q*. This is the social optimum, the allocatively efficient output.
The free market over-produces, Q1 instead of Q*, and the price, P1, is too low because it leaves out the external cost.
Check: For the units between Q* and Q1, which is true?
Beyond Q*, the MSC curve is above MSB: each extra unit costs society more than it is worth.
For every unit between Q* and Q1, the cost to society, MSC, is greater than the benefit, MSB. Add up those losses and you get the welfare loss triangle: between MSC and MSB, from Q* to Q1. It points towards the social optimum.
Now think about a cost that comes from consuming a good.
Check: Passive smoking harms people near a smoker. How does marginal social benefit (MSB) compare with marginal private benefit (MPB)?
The smoker counts only their own benefit. The benefit to society is that minus the harm to others, so MSB is below MPB.
Negative externalities can come from consumption too: smoking harms others through passive smoking, and driving causes congestion. Then the marginal social benefit is below the private benefit, and the market again over-consumes.
They shaded between MSB and MPC, pointing at the free market. The welfare loss is between MSC and MSB, from Q* to Q1, pointing at the social optimum: those units cost society more than they are worth.
Using a diagram, explain why a negative production externality leads to a misallocation of resources.
A negative externality is a cost imposed on a third party that is not reflected in the market price, such as pollution from farming running into a lake.
[Diagram: D = MPB = MSB, S = MPC and MSC above MPC. Free market at Q1, P1 where MPC = MPB; social optimum at Q*, P* where MSC = MSB. Welfare loss shaded between MSC and MSB from Q* to Q1.]
Producers consider only their own marginal private costs, so the market settles where MPC = MPB, at Q1 and P1. But each unit also imposes an external cost, so the marginal social cost, MSC, is above MPC. The socially optimal output is where MSC = MSB, at Q*.
Because Q1 is greater than Q*, the market over-produces the good, at a price that is too low. For every unit between Q* and Q1, the cost to society is greater than the benefit, so resources are misallocated and there is a welfare loss, the triangle between MSC and MSB from Q* to Q1.
Lough Neagh: Northern Ireland Environment Agency and NI Water statements, 2023. Diagrams drawn with Rough.js and perfect-freehand, both MIT licensed. Your answers are saved only on this device.