# How does social cost and social benefit work?

I am really lost right now. I have a test tomorrow and I am stressing out. Whatever I look at for externalities, which could be my textbook, a website, notes from class, they all contradict each other.

If Social benefit = private benefit + external benefit, then it is impossible for it to exceed private benefit. Yet on the supply and demand graph, it is shown that private benefit can exceed social benefit, as there are "negative benefits" of consumption.

In other words, in these graphs they only include consumption for benefits (demand curve) and production for costs (supply curve) Yet, in all my notes and our textbook, it says that benefits include positive externalities from consumption and production, and costs include negative externalities from consumption and production.

However, at the same time, everyone says you can have "negative benefits" and "positive costs". Therefore, what is the point of separating costs and benefits if they're constantly combined? How do you determine them?

I am so confused and I am sorry if this post was a train wreck but nothing makes sense and I am stressed.

Much help is needed,

Thank you.

The payoff of an individual or a group is given by $$\text{thier benefits}-\text{their costs}.$$

Let's work with an example of car ownership. It yields two benefits for me: I can use it to go to work (which is worth $$w$$) and I can use it to go shopping (which is worth $$s$$ to me). Owning the car is also costly: fuel and maintainence cost $$c$$.

Thus, the net payoff of car ownership for me is

$$[\text{benefits}]-(\text{costs})=[w+s]-(c)=w+s-c.$$

Now suppose I take the "benefit" of travelling to work and I insist that we relabel it as a negative cost. That is, I say "No, no, it's not that I get a benefit of $$w$$ from travelling to work. Rather, I save a cost of $$w$$ by being able to drive to work instead of having to find another way to get there."

Okay, so we need to rewrite our payoff equation with the new benefits and costs. We now have a benefit of $$s$$ from the shopping, a cost of $$c$$ from maintenance and fuel, and a cost of $$-w$$ from not having to worry about how I get to work. My payoff is

$$[\text{benefits}]-(\text{costs})=[s]-(c-w)=w+s-c.$$

This is exactly the same as before!

There is a much more general principle here: it is exactly equivalent to call something a positive benefit or a negative cost. Likewise, it is equivalent to call something a positive cost, or a negative benefit. That means we can always take a benefit, put a minus sign in front, and call it a cost or vice-versa. Whether we end up calling it a benefit or a cost is completely arbitrary. If we wanted to be extreme about it, we could insist there are no costs, only positive benefits and negative benefits; after all, what is a cost if not a negative benefit?

• if something is good then it is a positive benefit or a negative cost
• of something is bad then it is a positive cost or a negative benefit
• each thing should only be counted once (i.e., it should not be included as both a benefit and a cost at the same time).

A common convention is to only allow positive benefits and positive costs. Thus, if something is good we call it a benefit, and if something is bad we call it a cost. But that's not the only way.

This applies equally to private benefits/costs and social benefits/costs.

What this means for you is that you don't need to get tangled up in knots about what is a cost and what is a benefit, because you can always switch between the two.

You only need to (1) be consistent, and (2) be clear what factors you are including as benefits and which as costs. If you are confused by your books and notes it is because the author did a bad job of being clear about this.