Dust flux, Vostok ice core

Dust flux, Vostok ice core
Two dimensional phase space reconstruction of dust flux from the Vostok core over the period 186-4 ka using the time derivative method. Dust flux on the x-axis, rate of change is on the y-axis. From Gipp (2001).

Friday, January 10, 2014

Isoquants of gold

Today's plot shows a six-year scatterplot of the gold price (in USD) vs the USDX index.

The blue curves are hyperbolae of a constant level of gold x USDX. I have placed these for two reasons. Firstly, if gold and the USDX are inversely related, then the time-evolution of the scatterplot will follow one of these curves. Secondly, for companies operating gold mines outside of the US, the product of the gold price and the USDX indicates the real price they are getting for their product.

These equal-product curves, or isoquants, appear to be of some importance in constraining the evolution of the gold price over the past six years. Generally speaking, the price tends to migrate along an isoquant for an extended period of time, before jumping up (or down) to another one, typically in only a few weeks.

For much of 2008 the plot is constrained between the 600 and 700 isoquants, but the system shifted to the 800 isoquant in early 2009. The gold price advanced along the 800 isoquant until about October 2009, before shifting up to the 900 isoquant. The system then evolved along the 900 isoquant for a few months, with the gold price falling and USDX rising, until shifting to the 1000 isoquant near mid-2010. The gold price rose along the 1000 isoquant for nearly a year, whereupon it shifted to the 1100 isoquant, and after battling at that level for two months or so, advanced rapidly, ascending above the 1400 isoquant in September 2011.

A major battle was fought between the 1300 and 1400 isoquants until March of 2013, whereupon the system plummeted to the 1000 isoquant--a level at which it has remained since. The yellow circle near the middle of the plot shows the last month where we dipped below the 1000 isoquant; however today we crossed above it again.

For the time being it looks as though the 1000 isoquant will be the line in the sand for the gold-USDX system. For the gold price to go to $1000, the USDX would have to go to 100. Not impossible, but the world would have to be in pretty dire shape for us to see that, methinks. If the USG is successful in debasing the dollar to win the trade war, we might see a little advance in gold, but I'd expect it to follow the 1000 isoquant for the next six months at least. 


  1. "Definition of 'Isoquant Curve'

    A graph of all possible combinations of inputs that result in the production of a given level of output. Used in the study of microeconomics to measure the influence of inputs on the level of production or output that can be achieved."

    Forgive my ignorance, but I am quite mathematically sophisticated and I would greatly appreciate a more thorough explanation of the chart, the methodology and the brief analysis above. Despite certain unfortunate comments on ZH, I believe there is valuable analytical information here; I would greatly appreciate a better understanding. I would be pleased to provide my email address (in confidence) if you wish.
    Thanks in advance,
    Robert Davies

  2. Apologies for the second post. I found the last paragraph and the concluding sentence strongly phased and dispositive. I have been investing/studying in the PM complex for two years, and there are substantive geopolitical and geo-macroeconomic variables determining the "price" and price discovery of gold, methinks. Thanks again.

  3. My main thinking here is that for a company operating a gold mine outside of the US, the value of their product is really the gold price x the US dollar. They mine gold, sell it for US dollars, then use many of those dollars to pay for expenses in the local country. Much of the time, when the gold price x US dollar drifts along an isoquant, the varying price of gold doesn't change the company's economics. When the product shifts to a higher isoquant, the mine becomes more profitable, and when it falls to a lower one, the mine becomes less profitable.

    And I am accustomed to unfortunate comments on ZH.

    1. Understood and thank you. I need to mull the "real world" implications and causality, ref my second post above. I am thinking of dynamical systems theory models of relevant isoquant migration; any advice would be appreciated.

    2. I am planning to do a phase space reconstruction for the isoquants, but haven't got around to doing it yet. A methodology is here. http://worldcomplex.blogspot.ca/2010/08/how-life-imitates-stock-market-part-4.html

    3. Superb link and thank you. Precisely the direction of my much less articulate comment.I found substantive, in this context: "Several generalizations of mutual information to more than two random variables have been proposed, such as total correlation and interaction information. If Shannon entropy is viewed as a signed measure in the context of information diagrams, as explained in the article Information theory and measure theory, then the only definition of multivariate mutual information that makes sense[citation needed] is as follows:" [equations omitted].
      Thanks again; I shall read the precedent articles in the series. I encourage your work re phase space reconstruction for PM isoquants.

  4. What is the meaning; "the USG is successful in debasing the dollar to win the trade war," or where can I learn more about that? What is USG? Thanks!