L. David Roper

http://www.roperld.com/personal/RoperLDavid.htm

2 July, 2016

Silver has been used for making currency coins for many millennia. In the minds of many people it is still the basis for an international monetary standard. Since about 1980 is has been used extensively in electronics manufacturing, because it is very ductile and malleable and is a good conductor of electricity and heat

The graph below shows the silver extraction data for the world and the best Verhulst function fit to the data in order to extrapolate into the future.

Silver extraction rate for the world and a Verhulst function fit to the data.

Total extraction was set at 2250x10^{3} tonnes,which corresposnds to larger than the estimated reserves of about 520x10^{3} tonnes.

It appears that world-silver extraction will peak at ~2020.

Taking an average extraction curve of the two fits, the crossover point at year ~2007 when the amount extracted is equal to the amount left to be extracted is shown here:

Undoubtedly there is much recycling of silver, especially since many people and nations hold silver as a "currency". By the term "recycle" I refer to silver that is resold for storage as well as to be used to make items.

Assume that:

- Recycling of silver follows a hyperbolic tangent curve from 60% to 80% recycling with a break point of year 1900 and width 50 years.
- The recycling is delayed by a Gaussian curve peaking at a delay of 40 years and a width of 10 years.

The effective silver available for purchase after the first ten recycling cycles is shown in the following graph, along with the effective silver available for each cycle for the average of the two extraction cases described above:

The equation for a recycling cycle is

,

where E_{i} is the amount available from the previous cycle. Here is an example of the Excel coding:

{=(($J$2+$I$2)/2+(($J$2-$I$2)/2)*TANH((A27-$K$2)/$L$2))*SUM($I$27:I27*(EXP(-1*((A27-$A$27:A27-$N$2)/$O$2)^2/2))/$O$2/SQRT(2*PI()))} (The curly bracket surrounding the term makes it into an array; it must be entered by holding down the SHIFT & CTRL keys while pressing the ENTER key.)

Of course, the recycling could be extended to more cycles, skewing the curve further into the future. However, the peak and fall off after it will not change because further cycles are essentially zero in that time region.

Thus, under the assumptions given above, the effective amount of silver available for making items peaks before 2100 and falls off rapidly after that. Humans will have taken concentrated silver deposits and scattered them across the surface of the earth.

The Excel spreadsheet is set up to make it easy to calculate with different recycling assumptions.

Dividing the recycling curve above by the projected world population (asymptote ~10^{10}), one gets:

Although the recycling peak is at year ~2045, the per-capita peak is at year ~2035. This makes silver not a good choice for a future world representative currency.