This appendix displays the most crucial model equations for the minerals model discussed in Chapter 29. (Note: ppp$ = constant purchasing power parity corrected dollars; J = Joules.)
Dr = WRX GDPrXP = (GDppcR + %xGDPpcR3) XFX GDPpcRXPOPRXp (29A.1)
where DR = metal demand per region (kg); IUR = intensity of use (kg/ppp$); GDPR = real regional gross domestic product (ppp$); x1, x2 and x3 are empirically determined constants (in scenarios x1 is varied); GDPpc = real regional GDP per capita (ppp$/capita); and POPR = regional population (per capita). F (= 1 by default) can be used to scale down demand from historic trends in projections (see text). P describes the effect of price on demand
P = - elas X [ln(price) - ln(pricet_1)] + 1 (29A.2)
where elas = price elasticity and price = price of metal ($/kg) at time t.
Y = learning factor; Q = cumulative production (kg); n = learning constant; and p indicates the different types of production (primary/secondary).
The following three equations (29A.4 to 29A.6) are relevant for p = 1 only.
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