# What does the price-quantity diagram of a good with both negative production and consumption externalities look like?

The good in this case is coal, which I assume has both production and consumption externalities?

I haven't been able to find a price-quantity diagram on google so far depicting such a case, with welfare loss and especially negative externality per unit clearly depicted.

• What type of graph do you mean, what are on the axes? Feb 6 at 6:30
• @Giskard What I mean is how the graph looks, with the welfare loss and the negative externality arrows etc. Feb 6 at 7:18
• "what are on the axes"? Feb 6 at 7:19
• See a stylized version of our conversation: > A: What does "X" look like? B: What do you mean by "X"? A: I just want to know what it looks like! < Hopefully you see that B cannot hope to describe "X" without knowing what it is. Feb 6 at 7:20
• @Giskard I think I misunderstood you, sorry. The axis would be quantity on the x-axis, and price on the y-axis, somewhat similar to this: (courses.byui.edu/econ_150/econ_150_old_site/images/…). I would like to know what the shape of the welfare loss will be, as $MSB < MPB$ and $MSC > MPC$. Feb 6 at 7:50

I'm answering this from first principles as I also haven't been able to find a source illustrating the case of negative externalities in both production and consumption.

The price-quantity diagram needs 4 curves, marginal private cost (= supply) intersecting marginal private benefit (= demand) at the market equilibrium with quantity $$Q_e$$, and marginal social cost intersecting marginal social benefit at the social optimum with quantity $$Q_{opt}$$:

To identify the welfare loss we need to consider the status of the various labelled areas.

• Areas A,B,C,D,E,F are between the MPB and MPC curves, so form the private surplus, that is, the combined consumer surplus and producer surplus.
• Areas C,E,F,G are between the MPC and MSC curves, so represent the social loss due to the negative production externality.
• Areas A,D,F,H are between the MSB and MPB curves, so represent the social loss due to the negative consumption externality.

Note that area F represents a double social loss.

The net social surplus at the market equilibrium is therefore (A + B + C + D + E + F) - (C + E + F + G) - (A + D + F + H) = B - F - G - H. But at the social optimum, the net social surplus is B, the area between the MSB and MSC curves.

Therefore the welfare loss due to the externalities is the net social surplus at the welfare optimum less the net social surplus at the market equilibrium which is B - (B - F - G - H) = F + G + H, the shaded area.

The diagram also shows the total negative externality per unit, on the assumption that, as shown, the private and social curves are parallel on both the cost and benefit sides (if they are not parallel, then total negative externality per unit will be different at different quantities).

• This is by far the clearest answer I've received, thank you. Feb 14 at 0:18

Negative consumption externality shifts demand to the right (compared to counterfactual with no externality) because it means that people do not pay full cost of the consumption.

Negative production externality shifts supply to the right (compared to counterfactual with no externality) because it means producers do not need to pay for all extra costs they create for society.

Hence both happening at the same time will look something like the picture below:

• "Negative consumption externality shifts demand to the right" demand does not really shift, the curve showing marginal social benefits is a shifted version of the demand curve. Same with supply. Feb 6 at 15:50
• @Giskard I meant comparing to hypothetical counterfactual reality where externality does not exist. If you could turn on/off externality like flicking switch it would shift demand because negative consumption externality for example makes people consume more at any price compared to the case where somehow that externality is priced by market (like hypothetical where there are private rights to air). Btw that’s identical to comparing it to marginal social benefit because if there is no externality MSB=MPB and same for supply
– 1muflon1
Feb 6 at 16:01
• "If you could turn on/off externality like flicking switch it would shift demand", this is not generally true. In fact, it is usually not true. Feb 6 at 16:36
• "So, there are two scenarios: A - no externality. B - externality, no property rights or taxes, externality is not priced in. Is supply (or demand) shifted by the externality?" yes supply would shift moving from scenario A and B
– 1muflon1
Feb 6 at 17:42
• @Giskard I am sorry I am just really confused by your comments thats it
– 1muflon1
Feb 6 at 17:43