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  7.4 Market Models and Forecasts A mineral-market model describes the relationship between the attributes of a particular market (such as production, consumption, prices, or inventories) and the determinants of these attributes (such as resource endowments, market structure, government  policies, technologies of production and use, income, and many others). Factors that are determinants in some models are described by other models; for example, price is a determinant in many production models and yet is itself modeled in models of price formation. Some models only partially describe the market under study (such as a model of copper production in the United States), whereas others more completely describe a market (such as a model of the world copper industry). Some models are formal in the sense that they explicitly and quantitatively describe the important relationships in a particular market, whereas other models are largely informal, intuitive, or judgmental. This chapter focuses largely on formal models. Models are used by a variety of people and organizations for a variety of purposes. Private companies active in mineral development, for example, use models as one of several tools for making decisions concerning mineral production, marketing,  pricing, exploration, and investments in new mines and processing facilities; often these models are used to forecast or predict various factors that influence the economic attractiveness of a project, including prices, capital and operating costs, world production, and consumption. Government organizations active in mineral development use models for these same purposes. Government organizations - whether or not active in mineral development - also use models for other purposes, such as assessing the potential impact of different fiscal or concessionary regimes on investment, and evaluating the likely impact of a supply disruption in an important producing country on the availability of a particular mineral in the home country. More generally, mineral-market models have at least three important purposes: (1) analysis, to understand the relationships between the attributes of a market (for example, the price of a mineral) and the important determinants of these attributes (for example, factors of supply and demand, including raw material costs, technology, income, government policies, and consumer tastes and preferences), (2) simu.lation, to assess the potential market impact of a change in one of the underlying determinants, and (3) forecasting, to predict future values of, for example, prices, production, or consumption.  Given this mwtiplicity of purposes for mineral-market models, it is not surprising that many different types of models exist. The next section reviews several of the important types. 7.4.1 Types of Mineral-Market Models Most mineral-market models belong to one of two families of model types (adapted from Labys eta!' 1985). Some models incorporate characteristics of both model types. The first family of mineral-market models is econometric models. This type of model describes the relationships among supply, demand, prices, and inventories, as well as the determinants of these market attributes (cf. Fig. 7.5). Prices adjust to changes in supply, demand, and inventories, which in turn respond to the change in  prices. A typical econometric model consists of equations for supply, demand, inventories, and prices, as shown in the illustrative example below: Mineral Markets Set) = s[P,G,GP,MS] D(t) = d[P,PSC,Y] let) = i[l(t-l) + Set) - D(t)]  pet) = p[l(t)/D(t)]. 181 Four important attributes of a market are explained in terms of a number of explanatory variables. The quantity of mineral supplied in any year t, Set), is a function of four explanatory variables: the mineral's price (P), geologic factors (G), government  policies affecting mineral production (GP), and market structure (MS). The rationale for including price in the model is that an increase (decrease) in price provides an incentive for a producer to increase (decrease) production, other factors remaining the same. Geologic factors importantly influence the availability of a mineral resource for mining, and production is likely to rise or fall with changes in the geologic favorability for mining. Government policies influence the level of mineral  production by encouraging or discouraging mining. Market structure also influences the level of production; monopolistic markets tend to supply smaller quantities at higher prices than competitive markets, whereas oligopolistic markets tend to have quantities and prices intermediate between those of monopoly and competition (see Sect. 7.1). The quantity demanded by consumers depends, in this example, on three explanatory variables: the mineral's own price (P), the prices of substitute and complement  materials (Psq, and income or industrial activity (Y). The quantity demanded is expected to be inversely related to a mineral's price; the higher the price, the less consumers will demand, other factors remaining the same. The relative price of a substitute material reflects the attractiveness of substituting one material or minerai for another in a particular use (such as aluminum for copper in electric-power transmission). As the price of a substitute falls relative to the mineral in question, consumers will demand smaller quantities. A complement is a good or service that is used along with the mineral in question (for example, copper and zinc in brass). As the price of a complement rises (falls), it is expected that consumers will consume less (more) of the mineral in question (again, other factors remaining the same). Income, sometimes measured as industrial activity, is also expected to importantly influence the quantities demanded by consumers: as income or industrial activity rise and fall, so, too, is the demand for minerals used in this industrial activity likely to rise or fall. Inventories in any year are simply the inventories from the previous year, I(t-l), plus current supply minus current demand. Finally, the system is closed by relating prices to inventories and demand. The relative importance of each explanatory variable in each equation, or in other words the sensitivity of the attribute being modeled to changes in particular explanatory variables, is determined by regression analysis using historical data. All four equations then are solved simultaneously to determine market-equilibrium values for each attribute. As noted earlier, this example is merely illustrative. Not all models include exactly the same equations or variables, and some models are much more complicated, while others are simpler. The wide variety of mineral-market econometric models should not be surprising. First of all, mineral markets differ in a number of important respects, including the extent of competition among producers, the nature of government policies influencing costs of production, the relative importance of the various sources of supply (main product, by-product and co-product, and scrap), and the nature of end uses. Second, there are different models for different purposes; for instance, a model designed for policy analysis will not necessarily be appropriate for a more purely academic study striving to understand the past. There are many examples of econometric models of mineral markets, illustrating the differences among models (although it is beyond the scope of this study to compare and contrast models). There are numerous models for the copper market, for instance.  Fisher etal. (1972) is the seminal work in copper. Their model, estimated for the period 1948-1968, divides the world into two separate, but linked, markets. The first market is the United States, where administered or producer prices dominated during the period under study. The second market is the rest of the world, governed  by free-market prices based largely on the prices of the London Metal Exchange. Seven equations describe copper supply: five equations for primary production (in four important producing countries, and the rest of the world) and two equations for secondary - or scrap - production (the United States and the rest of the world). Four equations describe copper demand in the United States, Europe, Japan, and the rest of the world. Although an important purpose of the model was to assess the impact of potential increases in Chilean output on copper prices and Chilean revenues, the model has perhaps been more influential as a standard against which to compare subsequent models of the copper industry. Charles River Associates (1978), in one subsequent model, incorporate exploration and discovery of new reserves into a copper model. Lasaga (1981) examines the role of the copper industry in the Chilean economy. Takeuchi etal. (1987) use an econometric model to forecast future consumption, mine capacity and production, production costs, and prices. For additional copper models, as well as models for other mineral markets, see Labys etal. (1985), Mikesell (1979), and the references cited therein. The second important family of mineral-market models is engineering models. This class of model includes a wider variety of models than the econometric family and thus can only be defined loosely. What distinguishes engineering models is their mathematical description of the production process largely in technical, rather than in more purely economic or behavioral, terms. Engineering models vary significantly in the extent to which they incorporate the economic determinants of the attributes of a market. The general form of this type of model is illustrated in Figure 7.6. National economic activity determines the demand for final products, which in turn determines the derived demands for inputs of raw materials (including minerals), energy, and labor. An important strength of an engineering model is its technical description of how inputs are transformed into outputs of final products. The description typically is dis aggregated into several transformations intermediate between the initial use of raw materials and the production of final goods. Most engineering models are designed either to determine the optimal combination

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