Increasing Paper and Cardboard Recycling: Impacts on the Forest Sector and Carbon Emissions

Abstract

Recycling is emerging as both a viable alternative to extraction in many industries and a cornerstone of the circular economy. In this paper, we assess the role of paper and cardboard recycling on the forest sector, from both an economic and carbon perspective. For this purpose, we add the recycling industry to an existing forest-sector model in an attempt to capture its effects on other wood products and the overall forest resource. As the forest sector has an important potential for climate change mitigation, this model allows us to assess the effects of increased paper and cardboard recycling on the availability of the natural resource and the carbon balance of the forest sector. We show that these results are strongly linked to the hypotheses of substitutability and/or complementarity of recycled pulp and virgin pulpwood. Although we find increased emissions at the pulp sector level, the effects on emissions in other wood products are small. When pulp products are considered substitutes, we find the impact on total net sequestration to be positive. In the case where pulp products are considered complements, we find the impact on total net sequestration to be negative.

Appendix

• A. The Samuelson problem in the FFSM model

Starting with the GFPM (The Global Forest Products Model) model by Buongiorno et al. [32], forest market models generally use net social surplus maximization to solve prices and quantities equilibria (see Rivière et al. [31] and Latta et al. [51] for a general description and review of these models).

Samuelson [43] formalizes the optimal transport problem with regions having supply and demand functions for a certain product. A certain amount of the product is traded between regions depending on the price difference between regions and including transportation costs. He obtains equilibrium conditions through the maximization of a net social payoff that consists in the sum of the consumers and the suppliers’ surpluses minus the cost of transport from one region to the other.

The FFSM model can be seen as an extension of the Samuelson framework, with the introduction of the transformation industries (see Caurla et al. [35]). With this new framework, Caurla [36] demonstrates that an equilibrium also exists. Mathematically, the maximization problem relies on the following sum of surpluses:

$$\begin{aligned}& \sum_{p,i}\left({\int }_{0}^{{D}_{p,i}}{P}_{p,i}\left(D\right)dD-{P}_{p,i}{D}_{p,i}\right)+\sum_{w,i}\left({P}_{w,i}{S}_{w,i}-{\int }_{0}^{{S}_{w,i}}{P}_{w,i}\left(S\right)dS\right) \\ & \quad +\sum_{p,i}{P}_{p,i}{S}_{p,i}-\sum_{p,i}{c}_{p}{S}_{p,i}-\sum_{w,i}{P}_{w,i}{D}_{w,i} +\sum_{p,i,j\ne i}\left({P}_{p,j}-{P}_{p,i}-{C}_{p,i,j}\right){e}_{p,i,j} \\ & \quad +\sum_{w,i,j\ne i}\left({P}_{w,j}-{P}_{w,i}-{C}_{w,i,j}\right){e}_{w,i,j}\qquad,\end{aligned}$$

(5)

with $i,j$ referring to regions, $w, p$ referring to primary and transformed products respectively; prices $P$, demand $D$, supply $S$, exchanged amounts $e$ as endogenous decision variables; and transformation costs $c$ (including ${c}_{recy}$ for recycling industries) transportation costs $C$ as exogenous variables. Prices $P$ come from inverse demand and supply functions $P(D)$ and $P(S)$, by inverting Eqs. (1) and (2) for the specific case of waste and recycled pulp products (and similarly, with their specific subscripts for other products). The first two terms of Eq. (5) represent the consumers and suppliers’ surpluses; terms three to five represent the surplus of the transformation industry; and the last two terms represent the surpluses of trade agents. The maximization of the global surplus gives us the market equilibrium (under assumptions of perfect markets). Detailed setup and resolution can be found in Caurla et al. [35] and Caurla [36].