The demand for raw materials can be described as a function of per capita income levels (Groenenberg, 2002; Neelis and Patel, 2006; Roberts, 1996; Tilton, 1996; van Vuuren et al., 1999). Empirically, it has been observed that the general form for resource intensity often follows an inverted U-shaped curve. The inverted U shape can be explained in terms of superposition of three different trends: transition, substitution and technological development (van Vuuren et al., 1999). There are a number of possible formal descriptions that can be chosen that are able to describe an inverted U-shape. Based on discussion in Roorda (2006) and Neelis and Patel (2006) we here use:
In which- which IU = Intensity of Use (kg/$)- , GDPpc = Gross Domestic Product per capita (2005 PPP$)- ,α = Maximum total consumption per capita (PCC) and- β and β = GDP per capita level with the maximum IUIU
To account for changes in the maximum per capita consumption due to increased material efficiency, an additional factor was introducedadditional constant θ was introduced, which can be interpreted as the annual material efficiency improvement factor.
The total consumption per capita (PCC), is then:
where the constant θ can be interpreted as the annual material efficiency improvement factor. If material efficiency improved by 1% per year, the value of θ would be 0.99.
We used regression analysis to parameterize the PCC function to historic data, deriving values for α, β and θ in the formulas above (see Neelis and Patel, 2006; Roorda, 2006). Cement is based on a single global regression --that is in a second step adjusted for each region. For steel demand, instead, we used regression analyses for major individual regions, to reflect different consumption patterns in these regions (Neelis and Patel, 2006). We use a Gompertz curve to smooth out deviations between historic data and the PCC curve: