The Global Forest Products Model (GFPM) simulates dynamic market equilibrium for the global forest sector. Every year, demand, supply, trade and prices are computed that clear markets for all products and in all regions (static phase). Then, the model parameters are updated to reflect exogenous and endogenous changes from one year to the next (dynamic phase). Exogenous changes include economic growth, technical change, potential timber supply and trade inertia, they are assumptions. Endogenous changes include capacity growth and availability of recycled fibres, they are determined by the model. The model then computes the quantity-price equilibrium next year as shaped by the intervening changes. It reiterates the static and dynamic phases for every year until the end of the projection.
The equilibrium for each year of the projection is obtained with an optimization model that simulates world markets. It finds the production, consumption and trade that maximize the total value of consumption minus the total cost of production for all products in all countries, in a given year. All the variables refer to that year.
Objective function:
[1]
where:
i,k = country, commodity,
P = price in US dollars,
D = final product demand,
S = raw material supply,
Y = quantity manufactured,
m = cost of manufacture.
Demand for final products:
[2]
where:
D-1 = demand in the previous year,
X = gross domestic product, in real US dollars,
= elasticities with respect to price, GDP, and past demand.
Wood supply:
[3]
where:
P0 = cost of production.
Su = potential supply.
Material balance:
[4]
where:
aikn = input of commodity k per unit of n.,
T = trade flow. Each country exports to and imports from a "world market", Tu,TL= upper and lower bounds on imports and exports.
Manufacturing capacity:
[5]
where:
K = current capacity of production.
Waste paper recovery:
[6]
where:
r = recycled paper,
SU = upper bound on recycled paper supply.
Yearly changes in the market equilibrium conditions are brought about by:
1) shifts of the demand curves, due to changes in X at the projected GDP growth rate.
2) shifts of the upper bounds on wood supply, S, at the assumed rate of growth of potential supply.
3) changes of manufacturing coefficients m to reflect technical change, especially increasing use of paper recycling.
4) changes of capacity, determined as follows:
At global level, capacity change is a function of changes in production during the past three years:
[7]
then, global capacity change is allocated to each country in proportion of its production level and the marginal value of capacity revealed by the shadow price of capacity in the static phase.
[8]
where:
= yearly change,
= shadow price of capacity (endogenous, from constraint (5)),
= parameters.
5) Changes in waste paper recovery:
[9]
wikr= maximum possible recovery rate (exogenous).
6) Trade inertia:
[10]
= upper bound on relative change in trade flow (exogenous).