CHAPTER • The Cost of Production 241 alumina is then converted to aluminum through a smelting process in which an electric current is used to separate the oxygen atoms from the aluminum oxide molecules It is this smelting process—which is the most costly step in producing aluminum—that we focus on here All of the major aluminum producers, including UC RUSAL, Alcoa, Alcan, Chalco, and Hydro Aluminum, operate smelting plants A typical smelting plant will have two production lines, each of which produces approximately 300 to 400 tons of aluminum per day We will examine the short-run cost of production Thus we consider the cost of operating an existing plant because there is insufficient time in the short run to build additional plants (It takes about four years to plan, build, and fully equip an aluminum smelting plant.) Although the cost of a smelting plant is substantial (over $1 billion), we will assume that the plant cannot be sold; the expenditure is therefore sunk and can be ignored Furthermore, because fixed costs, which are largely for administrative expenses, are relatively small, we will ignore them also Thus we can focus entirely on short-run variable costs Table 7.2 shows the average (per-ton) production costs for a typical aluminum smelter.5 The cost numbers apply to a plant that runs two shifts per day to produce 600 tons of aluminum per day If prices were sufficiently high, the firm could choose to operate the plant on a three-shifts-per-day basis by asking workers to work overtime However, wage and maintenance costs would likely increase about 50 percent for this third shift because of the need to pay higher overtime wages We have divided the cost components in Table 7.2 into two groups The first group includes those costs that would remain the same at any output level; the second includes costs that would increase if output exceeded 600 tons per day TABLE 7.2 PRODUCTION COSTS FOR ALUMINUM SMELTING ($/TON) (BASED ON AN OUTPUT OF 600 TONS/DAY) OUTPUT " 600 TONS/DAY OUTPUT + 600 TONS/DAY Electricity $316 $316 Alumina 369 369 Other raw materials 125 125 Plant power and fuel 10 10 $820 $820 $150 $225 120 180 PER-TON COSTS THAT ARE CONSTANT FOR ALL OUTPUT LEVELS Subtotal PER-TON COSTS THAT INCREASE WHEN OUTPUT EXCEEDS 600 TONS/DAY Labor Maintenance Freight Subtotal Total per-ton production costs 50 75 $320 $480 $1140 $1300 This example is based on Kenneth S Corts, “The Aluminum Industry in 1994,” Harvard Business School Case N9-799-129, April 1999