The classical Cobweb Theorem and real commodity market behavior: Modeling delayed adjustment of supply in industrial metals’ markets

In this paper we analyze how System Dynamics can help to better understand the dynamics of raw material markets and commodity price fluctuations caused by delayed adjustment of supply. We drew on the classical Cobweb Theorem and showed how this theorem can be successfully implemented into the System Dynamics approach. Regarding industrial metal markets, we systematically develop a simple model which helps to achieve a better understanding of dynamic market behavior and may be used as a flexible forecasting tool. On the example of the global copper market, we demonstrate how this simple market model can be merged with a physical material flow model capturing both market dynamics and technical aspects of raw material processing, recycling and substitution. This provides an explanation why linking physical material flows to a market model can add a substantial benefit for the systemic understanding. In a comparison of econometric forecasting methods we found System Dynamics models to be more intuitive and better suited to catch the structural market fundamentals. The classical Cobweb Theorem and delays in adjusting supply on industrial metals’ markets The 33rd International Conference of the System Dynamics Society Cambridge, Massachusetts USA July 2015 2 Introduction: problem statement High volatility in raw material prices imposes a planning problem for many manufacturing companies as material costs accounts on average for 43% of gross production value (Angerer et al. 2009). Especially over the last decade, prices for industrial metals were unstable: after a sharp increase before 2008 the prices dropped dramatically, partly due to the financial crisis in 2009. Since the last peak in 2011, prices for most industrial metals are momentarily continuously decreasing. Due to longer-term delivery contracts in manufacturing this volatility either results in direct profit losses if the company does not hedge or in an increased risk premium for futures or other commodity derivatives. A major reason for mid to long term commodity market fluctuations in the field of industrial metals can be found in the delayed adjustment of supply (Humphreys 2012, RosenauTornow et al. 2009): new mining projects have long lead times in planning phases and construction periods (5-10 years). This makes an instantaneous reaction on unexpectedly increasing demand impossible, leading to rapidly increasing prices in times of undersupply. On the other side, continuous production processes such as ore milling and concentration have got limited possibilities in adjusting their output volume. Therefore, production volumes are maintained in times of decreasing prices as long as the variable costs (cash costs) are covered by current market prices. The fact that production capacities need to be planned many years in advance based on future market expectations poses severe challenges to mining corporations. In times of high prices, expectations of future market prospects are higher, and so are the investments in new production capacities, while in times of low metal pricing investments tend to be declined, leading to an increasing risk of undersupply in future. Hence, we claim that due to adaptive expectations of market participants they cannot account correctly for time lags in the system that arises e.g. from production lead times. From a neoclassical point of view this problem simply should not exist: rational expectations include not making any systematic error in forecasting and eventual ignorance of the exact future equilibrium prices is normally distributed over all market participants. Furthermore, the prices for options should correctly account for these deviations and reflect market fundamentals, according to the efficient market theory (Fama 1970). Finally, the static general equilibrium theory does simply not account for delayed adjustments (Morishima 1996) despite the fact that a time lag between supply or demand reactions may constitute an important factor in determining market equilibrium states (Leontieff 1966 p.142 ff). Models of overlapping generations, which could account for this fact, may have pareto suboptimal equilibria or even an empty core (Geanakoplos, 2008). We will try to show in this article, whether or not it is possible to match historical data on raw material prices with a simple model accounting for the delivery delays deemed to establish the structural reason for the convergence failures in the cobweb model. As methodology we chose System Dynamics, since the combination of time delays and feedback effects in a stock and flow model enables an advanced analysis of dynamic market behavior (Sterman 2000 p. 182). Previous studies of commodity markets using a System Dynamics approach (Auping et al. 2012, van Vuuren et al. 1999, Sverdrup et al. 2014, Kwakkel et al. 2012) have proven the advantages of SD for dynamic market modeling. However, the focus of those studies did not lie in the dynamics of capacity building delays of raw material producers, something that has been proposed as a main cause for cyclical price behavior (see for example Humphreys 2012, Rosenau-Tornow 2009). This phenomenon is commonly labeled as the Cobweb The classical Cobweb Theorem and delays in adjusting supply on industrial metals’ markets The 33rd International Conference of the System Dynamics Society Cambridge, Massachusetts USA July 2015 3 Theorem (Waugh 1964) and constitutes one focus of this paper. Early System Dynamics studies on the Cobweb Theorem were developed by Meadows (1969) and have been applied to livestock markets which formed the origin of this theorem in the early 20 century (Benner 1876, Hanau 1928, Kaldor 1934, Ezekiel 1938). After discussing the basic principles of the classic Cobweb Theorem, we systematically develop a simple System Dynamics model aiming at being capable to reproduce real market behavior of industrial metals in the following sections. An enhanced model of the global copper market is provided by linking a model of physical material flows with the dynamics and feedbacks of a commodity market model, forming the structural reasons for the price behavior of the system. This enables a more detailed analysis of the copper market including recycling and substitution effects. Modeling the classical Cobweb Theorem within a System Dynamics environment First approaches of describing market fluctuations and price volatility due to delayed supply adjustment go back to the analysis of agricultural markets in the late 19 century (Benner 1876). The apparent inconsistency between these observed cycles and the claimed convergence towards an equilibrium posited by Walrasian economic theory were further analyzed in the early 20 century, particularly on agricultural markets, and were named after the commodities being analyzed, e.g. the “hog cycle” or the “corn cycle” (Hanau 1928, Ezekiel 1938). Arthur Hanau (1928) analyzed pork prices in Berlin in the late 1920s and used the observed periodically recurring price peaks to forecast future price developments. He described the “hog cycle” as shown in Figure 1. Figure 1 Classical hog cycle as described by Hanau (1928). Hanau analyzed the pork market in Berlin in the early 20 th century and identified periodical cycles of 3-4 years length. The theoretical explanation to these observed cycles in micro economic market theory has become known as the “Cobweb Theorem” (Harlow 1960, Larson 1964, Holt und Craig 2006). This term is based on the appearance of the supply and demand combinations showing the shape of a cobweb (cf. Figure 2). Ezekiel (1938) provides an overview of different cases of High pork price Increasing demand for piglets Farrowing, piglets born Increasing supply with pigs for slaughter Low pork price Less farrowing, less piglets born Decreasing supply with pigs for slaughter Weaning, pig fattening decreasing demand for piglets Less pigs for pig fattening Hog cycle: 3-4 years 60 70 80 90 100 110 120 130 P o rk P ri ce i n R M /1 0 0 kg 0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4 1896 1898 190