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To explain fluctuations of base metals prices we propose a model of short-run pricing based on trade in international exchanges. We introduce the critical tradeoff of choosing the share of material input from risky mining extraction versus risk-free recycling. We show that if more producers participate in the international exchange, or producers are less risk averse, the prices of base metals fluctuate more. If there are more traders, or producers are less risk averse, the prices of base metals fluctuate less. These observations may shed light on price movement during the recent financial crisis and possible future liquidity crises.

Aluminum, copper, lead, nickel, tin, and zinc (industrial non-ferrous metals) are commonly known as base metals. Their extensive use in the economy leads to the hypothesis that base metals consumption and futures can predict economic trends. Famed trader Dennis Gartman uses copper―among other base metals―as a leading economic indicator. According to him a recent rise in base metals prices signals a comeback of long-waited economic growth. He also states that prior to 2007-2009 financial crisis, “many base metals prices moved downwards long before the data signaled weakness in the global economy”.^{1} Thus fluctuations of base metals prices are of a significant economic importance.

In this paper we study short-run price determinants of base metals in the global market where producers and

traders are selling and buying in well-organized commodity exchanges.^{2} We answer the question: what drives fluctuations in base metals prices? We link price fluctuations to agents’ risk preferences in exchanges and to trading activity. Prior to trade, producers have to decide on the structure of supply for smelters. Recycling constitutes a less risky supply for producers than mining. Producers have to choose the share of risky―but potentially more profitable-mining. We introduce the critical share above which the market “correctly” responds to an increase in risk aversion. We provide an explanation of higher volatility in the prices of base metals during the crisis of 2007-2009. There are two effects which contribute to this increase in volatility. Firstly, during a crisis the traders are more risk averse. Secondly, there are more producers who want to get rid of stocks during a crisis. Both effects contribute positively to the increase in price volatility.

There is an empirical literature on the volatility of metals prices. [

Studies of crude oil and precious metals pricing are closely related to base metals pricing. [

Newbery in [

Finally, [

Base metals are produced from the smelting of ore extracted from mines and/or from recycled materials. Firms in the manufacturing sector (producers) choose a share i of extracted ore; the rest ^{3} Suppose that the drilling exploration, sampling, and sample analysis reveal that

Globally, the major centers for trading base metals are the Commodity Exchange of New York (COMEX), the London Metal Exchange (LME), and the Shanghai Futures Exchange (SHFE). Commodity futures are standardized contracts for the purchase and sale of physical commodities for future delivery on a regulated commodity futures exchange. The commodity futures contract price is determined by the equilibrium between supply and demand among competing buy and sell orders.

Suppose that in the international exchange there are I identical producers and J identical traders. The quantities of futures that producers and traders are selling are

futures then

Remark: In recent years huge investments in mining have taken place in Latin America, Africa, and parts of Asia. These are likely to escalate in the next ten years [

On the other hand, recycling constitutes a more certain type of supply of materials for smelters. According to the International Copper Study Group (ICSG), recycled content in copper production has remained steadily in the 33.7% - 36.8% range over the last decade. The International Zinc Association states that 60% of zinc produc-

tion comes from mined ores and the rest from secondary materials. The Yale University Center of Ecology reports that the recycling input rate of nickel production is 33%. The International Lead Association says that the recycled content of lead production is 52.6%. In general those figures have remained stable over the last ten years.^{4}

Producers choose the share of extracted ore i before realization of the random variable

Consider price elasticity ^{5}

Therefore the price

The variance of the price is

Importantly, the volatility in prices depends on the optimal share. This is the instrument which will affect the prices. We obtain the following.

Proposition 1: The price of base metals varies with the scales of production

Proof: Follows directly from (4).

We define a coefficient

Definition 1: The generalized risk aversion coefficient of the futures market is

Notice that

If producers sell

A representative trader earns

With a normal distribution of income and

Lemma 1: Under the equilibrium in the international exchange, the optimal choices of producer and trader on

Proof : See Appendix A1.

Equilibrium of the futures market in international exchanges requires that the total selling and buying quantity of futures equals zero

From this we obtain the condition for the optimal value of i (see Appendix A3)

Denote

Note that up to this point calculations are similar to the [

Thus

Definition 2: The critical level of uncertain production scale is

We suppose that the share in risky production is larger than the critical level of investment:^{6} ^{7} and^{8} Thus

price elasticity of base metals is between 0.2 and 0.8 (aluminum 0.7 to 0.8; copper 0.4; lead 0.2; tin and zinc 0.2 to 0.4). By introducing the critical level of investments

From Proposition 1 and Inequalities (5), (13) we have

and

We obtain the following :

Proposition 2: Suppose that

Also we have

and

This leads to

Proposition 3: Suppose that

In the theoretical literature on base metals, the price is defined only by the mining industry (see for example [

The authors thank Zhiqi Chen, Jean-Francois Tremblay, Gamal Atallah for careful reading of the manuscript and many helpful comments. Our sincere thanks go to Margaret Slade, Nguyen Van Quyen for useful suggestions and David Stambrook for extensive discussions. We also thank participants of CEA Annual Conference at Ryerson 2015 and the discussant Martin Stuermer for helpful comments and suggestions. The paper was a part of a bigger project: “Trends and Fluctuations in Base Metals Prices”, which was awarded the prize for the best paper at Vietnam Economist Annual Meeting 2015 in Thai Nguyen City, Vietnam. The authors thank SSHRC for financial supports.

Nguyen BaoAnh,AggeySemenov, (2015) Fluctuations in Base Metals Prices. Theoretical Economics Letters,05,545-554. doi: 10.4236/tel.2015.54064

Proof. The metal producer maximizes his expected utility

Similarly the maximization problem of the trader is

From (6) the variance of producer’s income

Substituting (20) and (6) into (18) the problem of a metal producer is

The first order condition with respect to i is

The first order condition with respect to

From (7) the variance of a trader’s income is

Substituting (7) and (23) into (19), the problem of a trader is

The first order condition with respect to

By definition, the

Using the first order Taylor approximation expanded around R we have

By the definition of covariance

Substituting

Thus we have

The equilibrium condition is

Rearranging this yields

Substituting (29) into (9) for

Using the definition of the coefficient

Substituting (30) into (8) gives

As per the definition the term

The variance of price is

The expected value of revenue by mined extraction

The variance of revenue by mined extraction is

Substituting (28), (33), (34), (35) into (31) yields