So let us now internalize the externality by setting a per unit tax

that exactly mimics the externality.

So we set equal to $15 per unit.

What we're doing is we're shifting up the supply curve

as it's perceived in the market.

So, our shifted up supply curve is 10 + 2Q + 15,

that's set at equal to the demand curve, and we can solve for a quantity of $15.

So, the amount that's exchanged in the market,

instead of the original quantity of $20, is now a quantity of $15.

When we want to go ahead and calculate surpluses,

we have to think about the price.

If you plug this quantity 15 into the demand curve,

you'll get that what the consumers are paying is $55 per unit.

And if you plug this quantity into the supply curve,

you'll see that what the producers are receiving Is equal to $40.

And of course the difference between the two is exactly that $15 of the tax.

Let's go ahead and calculate total surplus.

First of all, we have the consumers, consumer surplus is the area

underneath the demand curve and above the price that the consumers are paying.

So this is 15 times 15 divided by 2 which is a 112.5.

We can calculate producer surplus, it's the area underneath the price that they

are receiving and above the original supply curve, so it's this triangle here.

And it's 30 times 15 divided by 2, which is 225.

But of course, there's the cost of pollution, let's not forget that.

We're polluting less than before because we're only producing 15 units.

So the cost of pollution is 15 units times 15 per unit.

So it's this rectangle here 15 times 15 is equal to 225,

and just by chance in this case it's equal to the producer surplus.

But here we have the cost of pollution, but we're not quite done yet

because remember now we have a tax and the government is collecting the tax revenue.

And the tax revenues exactly equal to the marginal external costs,

because that's how we set the tax.

We set it equal to the marginal external cost, so

tax revenue is 15 times 15, so it's exactly the same rectangle.

225 so these two cancel each other out and

we get a total surplus that equals 337 and a half.