Recycled toilet paper

Earlier this week I watched a presentation on positive behavior control.  In one example, one set of people were told that they use two large trees worth of toilet paper in their lives and another set were told the same thing but also asked to visualize cutting down two large virgin forest trees.  The second set of people were much more likely to use recycled toilet paper after the session.

That's great, compelling stuff.  But I don't buy it (by default).  The unspoken assumption is that if you use recycled toilet paper, you'll save two trees.

Since only one third of paper made in the US is from recycled paper, that means that all recycled paper is used (otherwise we wouldn't be cutting down trees to fulfill the need).  So, if you use two trees worth of recycled paper, you're taking two trees worth of pulp out of the pool of paper-pulp, which must be filled by cutting down two trees.  That is, you're not saving trees.  But that's just my estimate; let's do the math!

Let's start with the facts:
1. Paper can be recycled about 6 times.
2. 1/3 of paper comes from recycled sources
3. Used toilet paper is not recycled :)

Let's make some assumptions:
1. People recycle virgin paper at the same rate as recycled paper (given a piece of paper, you don't decide to recycle it based on where it came from).
2. All recycled paper is used (recycling facilities don't throw out recycled paper because there is too much).

So, let's calculate the percentage of paper that is recycled.  It should be close to 33%.  Let's call this "m"

The pool of paper pulp has equal parts paper, wood chips, and recycled paper.  Given 1/2 a tree, 1/2 a tree's worth of chips, there is 1/2 a tree's worth of recycled paper.  That is, one trees worth of wood creates 1.5 trees worth of pulp if recycled 6 times; or one trees worth of wood creates:
    m trees worth of 1st generation recycled paper
    m^2 trees worth of 2nd gen paper

    m^3 trees worth of 3nd gen paper

    m^4 trees worth of 4nd gen paper

    m^5 trees worth of 5nd gen paper

    m^6 trees worth of 6nd gen paper

There is no 7th gen recycled paper.

That means that m + m^2 + m^3 + m^4 + m^5  + m^6 = 1/2 a tree.  Solving this gives m = 0.333640134.

Reality check:  0.333650134 is close to the 33% that we'd expect.

What happens if we use 1st gen recycled paper for toilet paper?  How many trees have to be cut down to make one unit of recycled paper?  K trees create K*m trees worth of recycled paper, so K*m = 1 or K = 1 /  m = 2.997.
So, 2.997 trees creates 2.997 + 1 = 3.997 units of paper instead of the maximum potential of 2.997 * 1.5 = 4.495.  So, 4.495 - 3.997 = 0.4986 potential trees are wasted.
The total number of trees cut down is to make your toilet paper is
    N = 2 / (efficiency of using 1st gen / efficiency of using virgin wood)
    N = 2 / ( (1 + 0.4986)^(-1) / 1.5^(-1) )
    N = 2 * ( 1 + 0.4986 ) / 1.5
    N = 1.99616
You could write this as 2/m - 4/3*(1/m) = 1.99616 (which I derived by gathering the terms in the above paragraph and simplifying; we'll double-check this a little later).

If you use 2nd gen, you cut down 2/m^2 - 4/3*(1/m^2 + 1/m) = 1.992 trees
If you use 3rd gen, you cut down 2/m^3 - 4/3*(1/m^3 + 1/m^2 + 1/m) = 1.976 trees
For 4th gen, you cut down 1.926
For 5th gen, you cut down 1.778
For 6th gen, you cut down 1.333

Reality check:  If you use 6th gen paper, you waste nothing because it can't be recycled again - it'll be thrown out anyway.  In this best case, 2 trees create 3 trees worth of paper (using the 1.5 factor), so it would take 3/2 = 1.333 trees to create the two trees you needed to wipe your butt.  This is what we calculated above so the math works out :)

Now, our last step.  If you use recycled paper, you get mostly 1st gen paper, less 2nd gen, etc.  And we have the percentages above: m/0.5 1st gen, m^2/0.5 2nd gen, etc.
So, on average, you'd cut down 1/0.5 * (m*1.992 + m^2*1.976 + ... + m^6*1.333) = 1.990 trees.

1.99 trees is really close to 2 trees.  That is, you cut down the same number of trees if you use recycled paper as non-recycled paper.

So, does this mean you shouldn't use recycled toilet paper?  Not necessarily. There is some talk that toilet paper comes from virgin forest rather than tree farms.  I can't tell how true this is.  If tree farms are going unused in favor of toilet paper companies using virgin forest trees, then using recycled paper saves virgin forests.  According to this article, 9% of paper comes from virgin wood, and it would certainly be good to decrease that.  9% is pretty small though - it's conceivable that the no virgin trees are cut down for paper and the 9% comes from the wood chips left over from cutting down virgin trees for other purposes.

There is also a macro economic argument that if people buy more recycled toilet paper, the price of recycled paper will go up and business and government will persuade the people to recycle more (such as how certain states will buy back aluminum cans and beer bottles).  I expect that one person has little effect on this.

The real lesson, however, is how important it is to recycle.  The more people recycle (above 33%), the more paper each tree can produce.  If we recycle 100% of paper, then each tree can produce 7 trees worth of paper.  This is, of course, assuming that it is better for the environment to recycle paper than to cut down trees from tree farms.  An International Institute for Environment and Development study states that:
“Most of the studies support the view that recycling and incineration are environmentally preferable to landfill. There is less agreement on whether recycling is preferable to incineration. Critical factors are the nature of the pulp and paper making process, the level of technology at all stages of the life cycle and the energy structure of the countries under study. Interpretation also plays a role in weighing up of increases in some emissions against reductions in others.”

Overall, the best plan is to simply use less paper.  Everyone, wipe with your hands :)