Table 2 Estimated values of the potentials for selected commodities, assuming \(\alpha =10^{3}\), and based on the work84 of Calvo et al.

From: Macroeconomic dynamics in a finite world based on thermodynamic potential

Mineral

\(\mu _H\)

\(\mu _L\)

Aluminium (gibbsite)

0.96

0.88

Cadmium

0.72

\(1.1\cdot 10^{-4}\)

Cobalt (linnaeite)

\(2.7\cdot 10^{-3}\)

\(5.1\cdot 10^{-6}\)

Copper

0.99

0.76

Gallium (in bauxite)

0.99

0.02

Germanium (in zinc)

0.44

\(1.4\cdot 10^{-3}\)

Gold

0.52

\(1.3\cdot 10^{-6}\)

Iron ore

0.87

0.75

Lithium

0.44

0.37

Manganese (pyrolusite)

0.1

0.05

Nickel (sulfides) pentlandite

0.94

0.06

Palladium

0.46

\(3.9\cdot 10^{-7}\)

Phosphate (rock) apatite

0.99

0.38

Platinum

0.46

\(3.9\cdot 10^{-7}\)

Potassium

\(6.7\cdot 10^{-3}\)

\(2\cdot 10^{-3}\)

Silver (argentite)

0.99

\(1.2\cdot 10^{-5}\)

Sodium (halite)

0.99

0.53

Uranium

0.44

\(1.5\cdot 10^{-3}\)

  1. The high (resp. low) potential is estimated as \(\mu _{H}:=\tanh (x_c/x_m)\) (resp. \(\mu _{L}:=\tanh (x_c)\), with \(x_m:=r/m\) average density of reserves with respect to world mines (in g/g), and \(x_c:=r/c\), the crustal concentration of reserves (in g/g). This amounts to \(X_H/X_T=m/c\) and \(X_W/X_T=r/c\), with \(X_S=0\), for simplicity.